text:
\section{Introduction}

\texttt{SGD} (stochastic gradient descent) can be efficient at training large machine learning models if one  carefully tunes a step size scheduler.
However, tuning step sizes is tedious and costly, especially with large-scale deep learning models. For this reason, a fruitful line of research has focused on
developing \emph{adaptive} methods, that require little to no tuning of the step sizes. A popular family of methods are those that use coordinate-wise (i.e., feature-wise) scaling, such as \texttt{Adagrad}~\cite{ADAGRAD}, \texttt{ADAM}~\cite{ADAM} and \texttt{AMSgrad}~\cite{AMSgrad}. More recently, a new family of methods called \texttt{SPS} (SGD with Polyak Stepsizes) has been proposed \cite{ALI-G,SPS}.
These methods make use of both the loss values and gradient norms at the sampled points, to automatically adjust the step size.
This allows to use a step size that changes from iteration to another depending on the current progress, and also adapts to the particular scaling of
the loss function at hand.

Variants of \texttt{SPS} have been shown to work very well on models that interpolate the data, and even have competitive convergence guarantees in convex~\cite{SPS} and some non-convex settings~\cite{SGDstruct}. The  effectiveness of \texttt{SPS} in the interpolated setting is not surprising, given that
\texttt{SPS} directly  solves the interpolation equations~\cite{ALI-G,TASPS}. However, when the model is far from interpolation, \texttt{SPS} and its variants can fail to converge, unless additional safe guards are put in place. As a consequence \texttt{SPS} methods tend to be less efficient when using regularization (weight decay), data augmentation (such as image rotations), and generally only work well on models with many more parameters than data.

In this paper, we develop new \emph{slack} variants of \texttt{SPS} that are less sensitive to interpolation.
Specifically,
we make the following contributions:

\paragraph{Extending (PA) Passive-Aggressive Methods.} We first show that \texttt{SPS} can be seen as a natural extension of the  \emph{Passive-Aggressive} (PA) methods~\cite{Crammer06} to nonlinear models.

\paragraph{Variational Viewpoint of Stochastic Polyak Methods.} Building upon this viewpoint, we then show that  \texttt{SPS}$_{\max}$~\cite{SPS} and \texttt{ALI-G}~\cite{ALI-G}, two recent variants of the \texttt{SPS} method, can be interpreted as \emph{slack} variants of the PA methods. That is, they allow for a margin of \emph{slack} in the interpolation equations. This in turn
provides a
\emph{variational formulation} of \texttt{SPS}$_{\max}$ and \texttt{ALI-G}. This viewpoint also gives  meaning to the tunable parameter $\lambda$ of \texttt{SPS}$_{\max}$ and \texttt{ALI-G}, namely, it can be interpreted as controlling the strength of a {slack variable}. The higher $\lambda$, the less slack we allow in the interpolation equations.

\paragraph{Max loss Viewpoint.} We also show that all slack variants of the PA methods, including  \texttt{SPS}$_{\max}$ and \texttt{ALI-G}, are in fact solving an auxiliary problem, whereby the objective is to have the \textbf{smallest maximum loss} over the data.

\paragraph{New Slack Polyak Methods.} The variational formulation then leads to the insight of further \emph{regularizing} the slack variable. This enables the slack variable to track the loss function across iterations and set a stable step size. We call our proposed variants \emph{\texttt{SPSL1}} and \emph{\texttt{SPSL2}}.

\paragraph{Convergence Theory.}  We study the \emph{convergence} of our methods, and prove convergence at ${\cal O}(1/t +\mbox{\small constant})$ rate for both \texttt{SPSL1} and \texttt{SPSL2}, where constant is zero under interpolation.

\paragraph{Experimental Validation.}  We conclude with extensive experimental results, where we test the sensitivity of each of the slack methods  \texttt{SPS}$_{\max}$, \texttt{ALI-G}, \texttt{SPSL1} and \texttt{SPSL2} to how far the underlying problem is to interpolation. We also show that the new methods  \texttt{SPSL1} and \texttt{SPSL2} are \emph{competitive} on the benchmark vision classification problems, despite \emph{not using any additional safe guards} as required to make \texttt{SPS}$_{\max}$ and \texttt{ALI-G} stable and competitive.

\section{Related work}
\label{sec:related_work}

\paragraph{ Setup and Notation.}
Let $(x_i,y_i)$ denote the  $i$\textsuperscript{th} data point, where $x_i$ is an input and $y_i$ is an output.
We use $\ell_i(w) \coloneqq \ell(w ; (x_i,y_i))$ to denote the loss evaluated at parameters $w \in \R^d$ over the $i$\textsuperscript{th} data point.
Our objective is to minimize the \emph{average loss} $\ell(w) \coloneqq \frac{1}{n} \sum_{i=1}^n \ell_i(w)$ over a given data set with $n$ data examples. We note that our results also hold for a true expectation where $\ell(w) = \EE{(x,y) \sim {\cal D}}{\ell(w ; (x,y)}$, also known as the test error. Furthermore, our results hold verbatim for an \emph{online regret} given by $\frac{1}{T}\sum_{t=1}^T \ell_{t}(w),$ where $\ell_t$ is an online loss that could be chosen adversarially, which is the original setting of \texttt{PA} methods. For  simplicity, we use the average loss.

\paragraph{ Passive-Aggressive for linear models.}
The Passive-Aggressive (\texttt{PA}) methods \cite{Crammer06} are online learning algorithms that update a model only when the loss on a new example is greater than zero. They do this by introducing the minimal perturbation into the parameters so that this new example is correctly labelled. This is the \emph{aggressive} step. On the other hand, if the example is correctly labelled already, then the methods are \emph{passive} and do nothing.
A similar online algorithm, but using Kullback-Leibler projections instead of Euclidean ones, was proposed in \cite{Herbster01}.
\texttt{PA} methods have been especially successful in natural language processing \cite{mcdonald_2005,blitzer_2006,chechik_2010}.

To formally introduce the \texttt{PA} methods, suppose  that the loss is non-negative and that $\ell_i(w) =0$ if our model correctly labels the $i$\textsuperscript{th} example. Let $w^t \in \R^d$ be the current parameters of our model at some time $t$.
At iteration $t+1$, \texttt{PA} methods update the parameters to $w^{t+1}$ such that the $i$\textsuperscript{th} example, usually randomly sampled, is correctly classified, that is $\ell_i(w^{t+1})=0$.
They do this by making the smallest possible perturbation to the current parameter vector $w^t$ by solving the projection
\begin{equation}
    w^{t+1} = \mbox{argmin}_{w\in\R^d} \norm{w-w^t}^2
    \mbox{subject to} ~ \ell_i(w) = 0 \enspace. \label{eq:PAproj}
\end{equation}
For simple loss functions, the update~\eqref{eq:PAproj} often enjoys a closed-form solution.
For instance, let us consider binary classification problems where data points $(x_i,y_i)$ are such that $y_i\in \{-1,  1\}$. If one minimizes the hinge-loss $\ell_i(w) = (1- y_i\dotprod{w,x_i})_+$ over a linear model, where $a_+ \coloneqq \max\{0, a\}$ denotes the non-negative part, then the closed-form solution to~\eqref{eq:PAproj} is given by
\begin{equation} \label{eq:PA}
    w^{t+1} = w^t +\frac{\ell_i(w^t)}{\norm{x_i}^2} y_i \, x_i \enspace.
\end{equation}
See Appendix A in~\cite{Crammer06} for the proof.
The \texttt{PA} method~\eqref{eq:PAproj} is appealing because it does not require learning rates and the update~\eqref{eq:PA} adapts to the \emph{scale} of $x_i$. Unfortunately for most nonlinear models and loss functions there is no closed form solution to the projection in~\eqref{eq:PAproj}, greatly restricting the applications of \texttt{PA} methods.

\paragraph{ Passive-Aggressive extensions.}
The \texttt{PA} methods \cite{Crammer06} were initially applied to regression, classification and structured prediction problems, but always with an underlying linear model. \texttt{PA} methods have subsequently been adapted to solving the non-negative matrix factorization (NMF) problem ~\cite{BlondelKU14}. NMF can be cast as solving a nonlinear matrix equation, which is bilinear in the two unknown matrices. In \cite{BlondelKU14} the authors proposed to solve this bilinear problem by alternating between freezing one of the two unknown matrices and applying a \texttt{PA} step. This approach cannot be extended to general nonlinear models and problems since it relies on the bilinear nature of NMF.

The \texttt{PA} framework has also been very recently used in conjunction with a class of quadratic models given by a difference-of-squares (DoS)~\cite{Saul2021}. Although there is no closed-form update for~\eqref{eq:PAproj} for these DoS models, the authors propose a simple bounded one-dimensional search based on the S-procedure to find an approximate solution.

\paragraph{ \texttt{SGD} with Polyak stepsize (\texttt{SPS}).} \texttt{SPS} methods use both the gradient norm and the loss value of the sampled points. The vanilla \texttt{SPS} update is
\begin{align}
    w^{t+1} = w^t -\frac{\ell_i(w^t)}{\norm{\nabla \ell_i(w^t)}^2} \nabla \ell_i(w^t) \enspace. \label{eq:SPS}
\end{align}
\texttt{SPS} methods have drawn much attention recently as an effective method for training deep neural networks, even though to work effectively in practice, the update above needs some additional alterations and safe-guards; otherwise the method can diverge when $\norm{\nabla \ell_i(w^t)}$ in the denominator is near zero.

A practical update to avoid this issue is that of \texttt{ALI-G} \cite{ALI-G}:
\begin{equation}
     w^{t+1} = w^t - \min\left\{\frac{\ell_i(w^t)}{\norm{\nabla \ell_i(w^t)}^2+\varepsilon}, \; \eta \right\} \nabla \ell_i(w^t) \enspace,
\label{eq:exact_ALIG}
\end{equation}
where $\varepsilon \geq 0$ and $\eta > 0$ are tunable parameters.
If $\varepsilon$ is set to $0$ and $\ell_i (w^t) - \ell_i^*$, with nonzero $\ell_i^*$, is used in the numerator of the Polyak step size of~\eqref{eq:exact_ALIG}, then one recovers \texttt{SPS}$_{\max}$ later introduced in~\cite{SPS}.

In~\cite{TASPS}, the authors showed that \texttt{SPS} is formally a subsampled Newton-Raphson method~\cite{SNR}  for solving the nonlinear equations
\begin{equation}\label{eq:interpolate}
    \ell_i(w) = 0 \; , \quad \mbox{for }i=1,\ldots, n \enspace.

\end{equation}
There only exists a solution to~\eqref{eq:interpolate} if we are in the \emph{interpolation regime}, that is to say, that our model has sufficient degrees of freedom that it can \emph{perfectly fit} all of the given examples.
This assumption is typically met with over-parametrized deep neural networks~\cite{ZhangBHRV17,MaBB18} or in non-parametric regression models~\cite{belkin2019does,liang2020just}.
In~\cite{TASPS} the authors develop a weaker type of interpolation assumption that rests on knowing the total optimal loss $\ell(w^\star)= \frac{1}{n}\sum_{i=1}^n\ell_i(w^\star)$ and using this as a \emph{target} value.

\paragraph{ Adaptive methods.}
The ultimate goal of adaptive methods is to have a method that works well with little to no parameter tuning.
One such adaptive method is \texttt{ADAM}~\cite{ADAM}, which works remarkably well on a wide range of DNNs with default parameter settings.
The practical success of \texttt{ADAM} has inspired a large number of papers that attempts to improve upon \texttt{ADAM}~\cite{AMSgrad}, understand \texttt{ADAM}~\cite{balles2018dissecting,AMSgrad}, or extend it~\cite{Zaheer2018}.
Due to the vast number of variants of \texttt{ADAM} that now exist in the literature, we cannot do the literature justice, since it would require a dedicated survey paper.
Here, we restrict ourselves to the admittedly limited scope of developing a foundation for adaptive methods based on Polyak step sizes.
\texttt{SPS} has an intuitive and mathematically grounded motivation, one that we further develop here.
Though our methods share the same overarching objective as adaptive methods such as \texttt{ADAM} and its variants, our methods represent a distinct approach, and enjoy a formal derivation.

Model-based methods \cite{asi2019importance, Chada-accel-model-2021}  also make use of linearizations in combination with proximal operators to derive new stochastic gradient methods. In fact, the \texttt{SPS} and \texttt{ALI-G} methods can be understood as a model based method~\cite{TASPS}.
For an excellent introduction to  online learning, with connections to model based and  PA methods we recommend the monograph~\cite{Orabona:2019} and its related blog.
Finally, another approach that is being actively researched recently is the use of \texttt{SGD} in combination with a line search~\cite{vaswani2019painless}.

\section{Variational perspective of SPS}
\label{sec:slack}
We now present our novel insights into viewing SPS and its variants as
an extension of the PA (Passive-Aggressive) methods. In doing so, we also give new variational perspectives on SPS methods, show that the new variants of the SPS methods can be interpreted as methods that solve a weaker form of interpolation, and as consequence, also as methods that solve a certain \emph{max} loss problem.

\subsection{Passive-Aggressive for general nonlinear models}

Although Passive-Aggressive methods have been developed for some nonlinear models
(cf.\ Section \ref{sec:related_work}), we are not aware of an efficient approach
that works for general nonlinear models.
Indeed, for most nonlinear models, such as Deep Neural Networks (DNNs), there is no closed-form solution to the projection~\eqref{eq:PAproj}. To retain much of the appeal of \texttt{PA} methods and make use of nonlinear models, we propose to linearize the loss around $w^t$ and project
\begin{align}
    w^{t+1} =  & \mbox{argmin}_{w\in\R^d} \norm{w-w^t}^2 \label{eq:PAprojlin} \;\;  \mbox{ s.t. }\ell_i(w^t)+ \dotprod{\nabla \ell_i(w^t), w-w^t}=0 \enspace.
\end{align}
The linearization in~\eqref{eq:PAprojlin} is a reasonable approximation to $\ell_i(w)$ when $w$ is close to $w^t$, and because of the projection, we choose $w$ to be as close as possible to $w^t$. It turns out that the closed-form solution of \eqref{eq:PAprojlin} is exactly given by the SPS update in \eqref{eq:SPS}.

Using this connection between the \texttt{SPS} and \texttt{PA} methods, we first formalize typical
safe-guarded variants of \texttt{SPS} as \texttt{PA} methods that make use of a \emph{slack} variable. We
 use these  insights to develop new and efficient slack \texttt{SPS} variants.

\subsection{Adding slack}

In most settings, the \texttt{PA} methods are in fact too aggressive. In particular,
outside of the interpolation regime, where there exists no solution to~\eqref{eq:interpolate}, setting all losses to zero is not possible, and thus eventually forcing a particular $\ell_i(w) =0$ will deviate other losses from zero. To better control the trade-off between losses over different examples, in \cite{Crammer06} a slack variable $s \in \R$ was introduced and finding $w \in \R^d$ such that
\begin{equation}\label{eq:slackconstraint}
    \ell_i(w) \leq s, \quad \mbox{for }i=1,\ldots, n \enspace,
\end{equation}
while simultaneously forcing $s$ to be as small as possible. To make $s$ small, we can either
minimize what we call the \emph{L1 slack formulation} given by
\begin{align}
    &\min_{w\in\R^d, \, s \geq 0} s  \label{eq:slackobjmax} \quad\mbox{s.t.} \quad \ell_i(w)  \leq s, \quad \mbox{for }i=1,\ldots, n \enspace,
\end{align}
or the \emph{L2 slack formulation} given by
\begin{align}
    \label{eq:slackobjL2}
    &\min_{w \in \R^d, \, s \in \R} s^2 \quad \mbox{s.t.} \quad \ell_i(w)  \leq s, \quad \mbox{for }i=1,\ldots, n \enspace.
\end{align}
The slack variable allows us to control the global trade-off between different losses.

When $\ell_i(w)$ is a relatively simple function, such as the hinge loss over a linear model, then after sampling the $i$\textsuperscript{th} constraint in either~\eqref{eq:slackobjmax} or~\eqref{eq:slackobjL2}, there is a closed-form solution to the resulting variational problem as shown in~\cite{Crammer06}.
For most nonlinear losses and models, however, there is no solution, and thus we resort to linearization once again.
But first, we present an alternative interpretation of~\eqref{eq:slackobjmax} and~\eqref{eq:slackobjL2}.

\subsection{Max loss Viewpoint}
\label{sec:maxloss}
The slack formulations can also be seen through the lens of robust learning.
Indeed, we can substitute out the slack variable in~\eqref{eq:slackobjmax} by
observing that the smallest possible $s$ that is greater than every $\ell_i(w)$
is necessarily $\displaystyle s = \max_{i=1,\ldots, n} \ell_i(w).$
Thus~\eqref{eq:slackobjmax}  and~\eqref{eq:slackobjL2} are equivalent to
\begin{equation}
    \min_{w \in \R^d} \max_{i=1,\ldots, n} \ell_i(w) \enspace. \label{eq:minmax}
\end{equation}
We refer to~\eqref{eq:minmax}
as the max loss.
 The max loss~\eqref{eq:minmax}
can be seen as robust learning tasks, where the aim is to find $w$ such that no single example is badly classified. Contrast this with the Empirical Risk Minimization (ERM) task where the goal is to minimize the average of the losses. In particular~\eqref{eq:minmax} is a conservative upper bound on the ERM since
\begin{equation} \label{eq:maxbound}
    \ell(w) = \frac{1}{n} \sum_{i=1}^n \ell_i(w) \leq \max_{i=1,\ldots, n} \ell_i(w) \enspace.
\end{equation}
If interpolation holds, then the above is a tight over-approximation, in that the ERM and the robust objective have the same solution set. Next, we propose methods for approximately solving~\eqref{eq:slackobjmax} and~\eqref{eq:slackobjL2}.

\subsection{A Variational form of \texttt{SPS}$_{\max}$}

Let  $\lambda>0$ be a  \emph{slack} parameter.
Our first method for solving~\eqref{eq:slackobjmax} proceeds by
by sampling the $i$\textsuperscript{th} constraint, linearizing and projecting as follows
\begin{align}
    w^{t+1}, s^{t+1} =& \mbox{argmin}_{w\in\R^d, s \geq 0} \tfrac{1}{2}\norm{w - w^t}^2 +\lambda s, \nonumber \\
    &\; \; \mbox{s.t. } \ell_i(w^t) + \dotprod{\nabla \ell_i(w^t), w - w^t} \leq s \enspace. \label{eq:SPSmaxproj}
\end{align}
Fortunately this method has a simply closed form solution.
\begin{lemma}\label{lem:SPSmax}
The closed-form solution to~\eqref{eq:SPSmaxproj} is
\begin{align}
    w^{t+1} &= w^t - \min\left\{\frac{\ell_i(w^t)}{\norm{\nabla \ell_i(w^t)}^2}, \; \lambda \right\} \nabla \ell_i(w^t) \enspace, \quad  \label{eq:SPSmax}\\
s^{t+1} &= \max\{\ell_i(w^t)- \lambda \norm{\nabla \ell_i(w^t)}^2 , \; 0 \} \enspace.
\end{align}
\end{lemma}
\begin{proof}
    The proof follows by applying Lemma~\ref{lem:slackL1ineqconst}
\end{proof}

Update~\eqref{eq:SPSmax} was recently introduced in an adhoc manner in~\cite{SPS} as a practical variant of the SPS method that caps the step size and named the \texttt{SPS}$_{\max}$ method.
Lemma~\ref{lem:SPSmax} thus gives a novel formalization of \texttt{SPS}$_{\max}$ as a projection method, and as an extension of the \texttt{PA-I} method
proposed in~\cite{Crammer06} to nonlinear models.
Analogously, the ALI-G method~\cite{ALI-G} can also be seen as an extension of the \texttt{PA-II} method proposed in~\cite{Crammer06}, as we show next.

\section{A Variational form of \emph{Almost} \texttt{ALI-G}}
\label{sec:ALI-G-almost}
Analogously to the previous section, we derive an iterative method for solving~\eqref{eq:slackobjL2} by sampling a single constraint, linearizing and projecting.
\begin{align}
    w^{t+1}, s^{t+1} =& \mbox{argmin}_{w\in\R^d} \tfrac{1}{2}\norm{w - w^t}^2 +\lambda s^2 \nonumber  \\
    &\; \; \mbox{s.t. } \ell_i(w^t) + \dotprod{\nabla \ell_i(w^t), w - w^t} \leq s \enspace.
    \label{eq:ALIGproj}
\end{align}

The key difference with \eqref{eq:SPSmaxproj} is that $s$ is squared. The closed-form solution is given as follows.
\begin{lemma}
Let $\lambda  \geq 0$.
The solution to~\eqref{eq:ALIGproj} is
\begin{align} \nonumber
    w^{t+1} & =  w^t -  \frac{\ell_i(w^t)}{ \lambda^{-1} + \norm{\nabla \ell_i(w^t)}^2} \nabla \ell_i(w^t) \enspace, \\
    s^{t+1} & =   \frac{ \ell_i(w^t)}{ 1 +\lambda \norm{\nabla \ell_i(w^t)}^2} \enspace. \label{eq:SPSdam}
\end{align}
We refer to this method as \texttt{SPS}$_{dam}$.
\end{lemma}
\begin{proof}
The solution follows by Lemma~\ref{lem:slackL2ineqconst}.
\end{proof}
We call~\eqref{eq:SPSdam} the \texttt{SPS}$_{dam}$ method because it is equivalent to \texttt{SPS} but with an additional dampening term $\lambda^{-1}$.
\texttt{SPS}$_{dam}$  is an extension of the \texttt{PA-II} method given in~\cite{Crammer06} to nonlinear models. It is also very similar to the \texttt{ALI-G} update in \eqref{eq:exact_ALIG} with $\varepsilon = \lambda^{-1}$.
The only difference being that \texttt{ALI-G}  caps the step size at a prescribed maximum $\eta$.

From the perspective of \texttt{SPS} methods, both slack variants help stabilize the \texttt{SPS} method~\eqref{eq:SPS}, and avoid a large step size by capping it as in~\eqref{eq:SPSmax}, or by dampening it in~\eqref{eq:SPSdam}.
But both methods still need to carefully choose
$\lambda$ to work well in practice.
Indeed, $\lambda$ here plays much the same role as a step size. If $\lambda$ is small, or converges to zero, both \texttt{SPS}$_{\max}$~\eqref{eq:SPSmax} and \texttt{SPS}$_{dam}$~\eqref{eq:SPSdam} halt.
On the other extreme, if $\lambda$ is large, both methods can diverge.
In \cite{SPS} the authors propose a rule of thumb that chooses a different $\lambda$ at each iteration for~\eqref{eq:SPSmax}. As for~\eqref{eq:SPSdam}, in \cite{ALI-G} the authors cap the step size, which requires another tunable parameter.

In the next section, we propose new \texttt{SPS} variants that iteratively update the slack variable and then use it to adjust the step size.

\section{Regularizing the Slack}

Both variational forms~\eqref{eq:SPSmaxproj} and~\eqref{eq:ALIGproj} rely on linearizing around $w^t$ and $s^t$ the constraints~\eqref{eq:slackconstraint} that depend on both $w$ and $s$. These linearizations are only accurate when both $w$ and $s$ are close to $w^t$ and $s^t$. Yet, the objective in both~\eqref{eq:SPSmaxproj} and~\eqref{eq:ALIGproj}
only incentivises $w$ to be close to $w^t$, but allows $s$ to be far from $s^t.$ We find this to be a cause of instability in these methods.
Furthermore, because of this,  both in \eqref{eq:SPSmax} and \eqref{eq:SPSdam}, the slack variable $s^{t+1}$ plays no direct role in updating $w^{t+1}$. This is a missed opportunity, because the slack variable can be used to track the progress towards the solution and ultimately help halt the method.

\subsection{L1-Regularized Slack}

Suppose we have a current estimate of the slack variable $s^t$.
We can use our current estimate of the slack to add some regularization to the variational form of \texttt{SPS}$_{\max}$ in~\eqref{eq:SPSmaxproj} as follows
\begin{align}
    w^{t+1},  s^{t+1}& = \underset{w\in\R^d, s\geq 0}{\mbox{argmin}} \tfrac{1}{2}\norm{w - w^t}^2  + \tfrac{1}{2} (s-s^t)^2+ \lambda s \nonumber \\ \,  &\quad  \mbox{s.t. } \;\ell_i(w^t) + \dotprod{\nabla \ell_i(w^t), w - w^t} \leq s \enspace.     \label{eq:SPSL1proj}
\end{align}
With this small change, the resulting method now makes use of the slack variable to set the step size, as can be seen in the following closed-form solution to~\eqref{eq:SPSL1proj}.
\begin{lemma} \label{lem:ProjL1pludL2}
The closed-form solution to~\eqref{eq:SPSL1proj} is given by~\eqref{eq:SPSL1} . We call this the \texttt{SPSL1} method.
\begin{align}
    \gamma_t^{L1} &= \frac{(\ell_i(w^t)-s^t+\lambda)_+}{1+ \norm{\nabla \ell_i(w^t)}^2} \nonumber  \\
    \gamma_t &= \min\left\{ \gamma_t^{L1}, \; \frac{ \ell_i(w^t)}{\norm{\nabla \ell_i(w^t)}^2} \right\}\nonumber \\
    w^{t+1} &= w^t - \gamma_t \nabla \ell_i(w^t) \\
    s^{t+1} &= \left(s^t - \lambda + \gamma_t^{L1}\right)_+ +\label{eq:SPSL1}
\end{align}

\end{lemma}
Missing proofs can  be found in the appendix.

What sets the \texttt{SPSL1} update~\eqref{eq:SPSL1} apart from the previous two slack methods in Section~\ref{sec:slack} is that the slack variable is now being updated iteratively and is used to update the step size adaptively.
For instance,  starting from $s^0 = 0$ and if $\lambda$ is small enough\footnote{Specifically if $\lambda \leq \tfrac{\ell_i(w^t)}{\norm{\nabla \ell_i(w^t)}^2}$, which in the convex and $L_{\max}$--smooth setting occurs if $\lambda \leq \frac{1}{2L_{\max}}.$ This is exactly the restriction we apply to $\lambda$ in the forthcoming Theorem~\ref{theo:SPSL1smooth}. }, the  \texttt{SPSL1} takes the more aggressive \texttt{SPS} updates in $w^t$~\eqref{eq:SPS} since then $\gamma_t = \ell_i(w^t)/\norm{\nabla \ell_i(w^t)}^2$.
As $s^t$ starts to increase, the more conservative smaller step sizes $\gamma_t = \gamma_t^{L1}$ will be used. Finally if $s^t$ is too large, then $\gamma_t = \gamma_t^{L1} =0$ and the method will not update $w^t$, but will instead decrease $s^t$ since in this case $s^{t+1} = (s^t -\lambda)_+$
We can observe this behavior experimentally  in Figure~{\bf a)}.

\begin{minipage}[l]{0.5\textwidth}
Regularizing the slack variable can also smooth the trajectory of $s^t$, as we see
in Figure~{\bf a)} where we show how $s^t$ for both \texttt{SPSL1} and \texttt{SPS}$_{\max}$ converge to the same value, but the slack variable of \texttt{SPSL1} takes a smoother route.
Finally, we can also see that  \texttt{SPS}$_{\max}$ is more sensitive to the tuning of $\lambda$ as compared to \texttt{SPSL1} by comparing the two update formulas~\eqref{eq:SPSmax} and~\eqref{eq:SPSL1}.
When $\lambda$ is small for \texttt{SPS}$_{\max}$ the method necessarily slows down, and in the extreme when $\lambda \rightarrow 0$ the \texttt{SPS}$_{\max}$ stops.
In contrast, for $\lambda$ small, we have that $\gamma_t = \gamma_t^{L1}$ and \texttt{SPSL1} switches to a more conservative update but does not stop.
\end{minipage}
\begin{minipage}[r]{0.5\textwidth}
    \centering
     \includegraphics[width=3.0cm]{colon-cancer-l-01-slack-reg-1.00e-01} \hspace{0.2cm}

     \includegraphics[width=3.0cm]{mushrooms-l-01-slack-reg-1.00e-01}\\

    { {\bf Figure a).} Slack variable $s^t$ for \texttt{SPS}$_{\max}$, \texttt{SPS}$_{dam}$, \texttt{SPSL2} and \texttt{SPSL1} all with $\lambda =0.01$ on logistic regression. Left: \texttt{colon-cancer} dataset. Right:  \texttt{mushrooms} dataset.}

\end{minipage}

\subsection{L2-Regularized Slack}

We can also regularize the slack variable in the variational form of \texttt{SPS}$_{dam}$ in~\eqref{eq:ALIGproj} as follows
\begin{align}

    \underset{w \in \R^d, s \in \R}{\min}&  \;\norm{w - w^t}^2 +(s-s^t)^2 + \lambda s^2,\, \mbox{  s.t.  } \ell_i(w^t) + \dotprod{\nabla \ell_i(w^t), w - w^t} \leq s \enspace,    \label{eq:SPSL2proj}
\end{align}
where again $\lambda >0$ is a regularization parameter.
\begin{lemma}\label{lem:SPSdam}
The closed-form update of~\eqref{eq:SPSL2proj} is given by
\begin{align}

    w^{t+1} &= w^t - \frac{(\ell_i(w^t) - \hat{\lambda} s^t)_+}{\norm{\nabla \ell_i(w^t)}^2 +\hat{\lambda}} \nabla \ell_i(w^t)\\
    s^{t+1} &= \hat{\lambda}\left(s^t + \frac{(\ell_i(w^t) - \hat{\lambda}s^t)_+}{\norm{\nabla \ell_i(w^t)}^2 +\hat{\lambda}}\right). \label{eq:SPSL2}
\end{align}
where  $\hat{\lambda} \coloneqq 1/(1 + \lambda)$.
We refer to~\eqref{eq:SPSL2}  as \texttt{SPSL2}.

\end{lemma}

This new \texttt{SPSL2} method now uses the slack variables $s^t$ to adjust the step size, which helps integrate information across iterations.
As we start from $s^0 = 0$, the \texttt{SPSL2} update in $w$ is similar to the \texttt{ALI-G} method~\eqref{eq:exact_ALIG} (with $\eta$ very large).
As the slack variable increases,  the resulting step size  decreases, which in turn makes $s^t$ decrease, thus making an effective feedback between slack and step size. See Figure~{\bf a)} for a sample trajectory of the slack, and this ``increase then decrease'' phenomenon.

Furthermore, as $\lambda$ increases,  \texttt{SPSL2}  is closer  to the \texttt{SPS} update~\eqref{eq:SPS}.
In the extreme where $\lambda \rightarrow \infty$ (thus $\hat{\lambda} \rightarrow 0$) we have that  \texttt{SPSL2} is equivalent to \texttt{SPS}.

\section{Convergence of \texttt{SPSL1}}
\label{sec:sonv_spspl1_main}

To prove convergence of \texttt{SPSL1}, we consider a small simplifying change to the method: we remove the explicit non-negativity constraint on the slack variable and add relaxation. That is, by dropping $s \geq 0$ in~\eqref{eq:SPSL1proj} we have
\begin{align}
    w^{t+\tfrac{1}{2}}, s^{t+\tfrac{1}{2}} &= \! \underset{w\in\R^d, s \in \R}{ \mbox{argmin}}  \tfrac{1}{2}\norm{w - w^t}^2 + \tfrac{1}{2}(s-s^t)^2 +\lambda s, \;
    \mbox{s.t. }  \ell_i(w^t) + \dotprod{\nabla \ell_i(w^t), w - w^t} \leq s \enspace.  \nonumber \\
    [ w^{t+1},s^{t+1} ] &= (1-\gamma)[ w^{t}, s^t] + \gamma [w^{t+\tfrac{1}{2}}, s^{t+\tfrac{1}{2}}]

    \label{eq:SPSL1noposproj-main}
\end{align}
where the second step is the relaxation and $\gamma \in (0,  1)$ is the relaxation parameter.
The closed-form solution of~\eqref{eq:SPSL1noposproj-main} can be found in detail in Section~\ref{sec:SPSL1nopos}.
This version of \texttt{SPSL1} in~\eqref{eq:SPSL1noposproj-main} is equivalent to~\eqref{eq:SPSL1proj} for non-negative losses that are convex and smooth, since  these assumptions guarantee the non-negativity of the slack variables $s^t$.
We use this property to establish the next theorem.
\begin{theorem} \label{theo:SPSL1smooth}
Fix $(w^\star,s^{\star}) \in \R^{d+1}$ and consider the $(w^t,s^t)$ iterates given by~\eqref{eq:SPSL1noposproj-main}.
Let $\bar{w}^T = \frac{1}{T} \sum_{t=0}^{T-1} w^t$, let $\ell_i$ be non-negative and let $s^0 \geq 0.$
If $\ell_i$ is convex, $L_{\max}$--smooth,  and $\lambda \leq 1/2L_{\max}$, then $s^t \geq 0 $  and
\begin{align}
  \E{ \ell (\bar{w}^T)}
   & \leq \frac{1}{2 \gamma \lambda T}\frac{\norm{w^{0} -w^\star}^2  + (s^{0} -s^{\star})^2}{(1-\gamma )(1- \lambda L_{\max})}  +  \frac{1}{n} \sum_{i=1}^n\frac{(\ell_i(w^\star)+\lambda)^2 - \lambda^2  }{2\gamma \lambda (1-\gamma) (1- \lambda L_{\max}) } \enspace. \label{eq:SPSL1convsmooth}
\end{align}
Furthermore, if there exists a solution $w^\star$ to the interpolation equations~\eqref{eq:interpolate} and $\lambda = 1/2L_{\max}$ we have that
\begin{align} \label{eq:SPSL1convsmoothLmax}
 \E{ \ell (\bar{w}^T)}
   & \leq \frac{2L_{\max}}{T}\frac{\norm{w^{0} -w^\star}^2  + (s^{0} -s^{\star})^2}{\gamma(1-\gamma )} \enspace. \quad
\end{align}
\end{theorem}
This convergence in~\eqref{eq:SPSL1convsmooth} gives a rate of ${\cal O}(\frac{1}{T} + \mbox{constant})$, where this constant depends on $w^\star$ and the parameters. Under these same assumptions this is also the convergence rate of  \texttt{SPS}$_{\max}$ (Theorem 3.4~\cite{SPS}) and \texttt{SGD} (Theorem 4.1~\cite{SPS} and Corollary 4.4~\cite{KSLGR2020unifiedsgm}).
 What is different is this constant  term on the right hand side of~\eqref{eq:SPSL1convsmooth}. Though this term is different, under interpolation we have that this constant term is zero giving~\eqref{eq:SPSL1convsmoothLmax}, which excluding the factor of $\frac{1}{\gamma(1-\gamma)}$,  is identical to the convergence of both \texttt{SPS}$_{\max}$ (Theorem 3.4~\cite{SPS}) and \texttt{SGD} (Theorem 4.1~\cite{SPS} and Corollary 4.4~\cite{KSLGR2020unifiedsgm}).

Next we prove  convergence for nonsmooth functions.

\begin{theorem}\label{theo:SPSL1lip}
Let $w^* \in \mbox{argmin}_{w \in \R^d} \max_{i=1,\ldots, n} \ell_i(w)$ and $s^* = \ell_i(w^*) +  \lambda$.
Consider the $(w^t,s^t)$ iterates given by~\eqref{eq:SPSL1noposproj-main}.
Let $\bar{w}^T = \frac{1}{T} \sum_{t=0}^{T-1} w^t$ and let $\ell_i$ be non-negative.

      If  $\ell_i$ is $\sigma$--Lipschitz, convex  and $s^0 \geq -\lambda \sigma^2$, then
\begin{align}
    &\E{\frac{1 }{n} \sum_{i=1}^n \ell_i(\bar{w}^T) }
    \leq \frac{\norm{w^{0} -w^*}^2 +(s^0-s^*)^2 }{2\gamma (1-\gamma) \lambda T} + \frac{\lambda}{2} \frac{1  + \sigma^2 (1 + \gamma)}{ 1-\gamma }
    + \frac{\max_{i=1,\ldots, n} \ell_i(w^\star) }{1-\gamma} \; . \label{eq:SPSL1convLip}
\end{align}
\end{theorem}
In Theorem~\ref{theo:SPSL1lip} we can see that $\lambda$ trades off speed of convergence and the \emph{radius of convergence}.
In some ways, it plays the same role as constant step size for \texttt{SGD}.
On the one hand, when $\lambda$ goes to infinity \texttt{SPSL1} escapes faster from the initial conditions as the convergence rate is ruled by ${\cal O} (1/\lambda T)$.
On the other hand, when $\lambda$ goes to zero, the first term of~\eqref{eq:SPSL1convLip} goes to infinity, whereas the second term, the constant error one, goes to zero.
Furthermore, the radius of convergence also depends on the remaining term $\max_{i=1,\ldots, n} \ell_i(w^\star)$, which vanishes in the interpolated setting as it is close to zero or can be controlled for $\gamma$ small.

\section{Convergence of \texttt{SPSL2}}
\label{sec:sonv_spspl2_main}

To prove convergence of \texttt{SPSL2} we also introduce a relaxation parameter $\gamma \in [0, 1]$ and a relaxation step analogously to the relaxation we introduced in~\eqref{eq:SPSL1noposproj-main}. The details of this change can be found in Section~\ref{sec:spsl2_convergence_theory} and specifically formula~\eqref{eq:SPSL2SGD}.
With this one additional change, we can  prove the convergence of \texttt{SPSL2} in terms of the average of the square of the losses, as we show in the next theorem.

\begin{theorem}
\label{theo:SPSDAMfmax_main}
Fix $(w^\star,s^{\star}) \in \R^{d+1}$ and consider the $(w^t,s^t)$ iterates given by~\eqref{eq:SPSL2} with a relaxation parameter $\gamma \in (0,  1)$.
Let $\bar{w}^T = \tfrac{1}{T} \sum_{t=0}^{T-1} w^t$ and let $\ell_i$ be non-negative.

If $\ell_i$ is  $\sigma$--Lipschitz for every $i\in \{1,\ldots, n\}$ then
\begin{align*}
    \tfrac{1}{n} \sum_{i=1}^n\E{\ell_i(\bar{w}^T)^2}
    & \leq \frac{1}{C (\hat{\lambda})}\frac{\norm{w^{0} -w^\star}^2+(s^0 -s^{\star})^2}{\gamma(1-\gamma)  T} +  \frac{1}{C (\hat{\lambda})} \frac{1-\hat{\lambda}}{\hat{\lambda}^2 (1-\gamma)} \max_{i=1,\ldots, n} \ell_i(w^\star)^2 \enspace.

\end{align*}
\begin{equation}
    \label{eq:Capp_main}
    \mbox{where     }  \bar{w}^T = \sum_{t=0}^{T-1} w^k/T, \; \hat{\lambda} = 1/(1+\lambda)\mbox{   and   }
    C (\hat{\lambda}) \coloneqq \frac{1 - \hat{\lambda}}{\hat{\lambda}^2 + (1 - \hat{\lambda}) \left(\hat{\lambda} + L_{\max}^2 \right)} \enspace.
\end{equation}
\end{theorem}

This last result in Theorem~\eqref{theo:SPSDAMfmax_main} shows that \texttt{SPSL2} converges to a minimizer of $\tfrac{1}{n} \sum_{i=0}^n \ell_i(w)^2$ up to an additive constant error proportional to $\max_{i=1,\ldots, n} \ell_i(w^\star)^2.$
This is perhaps not so surprising given that \texttt{SPSL2} is indeed solving the max squared loss~\eqref{eq:slackobjL2}, which in turn is an over-approximation of the average squared loss.
As in Theorems~\ref{theo:SPSL1lip} and~\ref{theo:SPSL1smooth}, the slack parameter $\lambda$ (through $\hat{\lambda}$) trades off the speed of convergence and the constant error term. Furthermore, under interpolation we have again that the constant error term is zero.

In the appendix in Theorem~\ref{theo:SPSDAMregret} we also provide an extension of the regret analysis for \texttt{PA} methods, given in Theorem 5 in~\cite{Crammer06}, from hinge loss over linear models to a more general class of nonlinear convex models.

\section{Numerical Experiments}

We perform several numerical experiments for validating the usefulness of the proposed SPS variants on logistic regression and DNNs. Specifically, we compare: \texttt{ADAM} \cite{ADAM};
 \texttt{ALI-G}, i.e., update \eqref{eq:exact_ALIG};
\texttt{SPS}$_{\max}$, i.e., update \eqref{eq:SPSmaxproj};
\texttt{SPS}$_{dam}$ (proposed), i.e., update \eqref{eq:SPSdam};
\texttt{SPSL1} (proposed), i.e., update \eqref{eq:SPSL1};
\texttt{SPSL2} (proposed), i.e., update \eqref{eq:SPSL2}.
Apart from \texttt{ADAM}, all methods are SPS variants.

\begin{figure*}
\centering\includegraphics[width=\linewidth]{figures/fig1.pdf}
\centering\includegraphics[width=0.5\linewidth]{figures/fig2.pdf}
\includegraphics[width=0.23\linewidth]{colon-cancer-compare-0.01-loss-reg-1.00e-01}
 \includegraphics[width=0.23\linewidth]{mushrooms-compare-0.01-loss-reg-1.00e-01}
\caption{Comparison of the proposed and related methods on different computer vision problems in terms of both error in a validation set and loss in the train set. With the same set of parameters, the new slack variants are competitive throughout different datasets and models. In terms of validation error, \texttt{SPSL1} achieves the best result in the MNIST and arrives at a close second on the CIFAR-10.}
\label{figure:deep_results}
\end{figure*}

We compared the aforementioned methods on 4 different deep learning vision problems and one convex logistic regression problem.
The datasets for the vision problem we used are the MNIST dataset (60,000  $28\times28$ images, 10 classes) \cite{lecun2010mnist}, the CIFAR10, and \mbox{CIFAR-100} datasets (60,000 32$\times$32 color images in 10 and 100 classes respectively) \cite{krizhevsky2009learning}  We use 3 different models that are known to work well on these datasets: a multi-layer perceptron (MLP) with one hidden layer on the MNIST dataset, a ResNet18 \cite{he2016deep} on CIFAR-10, and a ResNet34 on the CIFAR-100 dataset.
For our logistic regression problem we used the  colon-cancer (    $d =2001$ and  $n =62$)~\cite{uci} data set.

Because of the importance of momentum in speeding up \texttt{ALI-G} and \texttt{SPS}$_{\max}$ for DNNs~\cite{ALI-G-vs-SPS},  we also use momentum in our implementations of \texttt{SPSL1} and \texttt{SPSL2}.
Formally, we replace $w_{t+1} = w_t - u_t$, where $u_t$ corresponds to the method-specific update, by
$v_{t+1} = \beta v_t - u_t$ and
$w_{t+1} = w_t + v_{t+1}$.
We fix the momentum parameter to $\beta =0.5$ in the following experiments.

All methods were implemented in PyTorch. For the \texttt{SPS}$_{\max}$ method, we used the authors' implementation,\footnote{https://github.com/IssamLaradji/sps} which derives from the analyzed method in that it uses a ``step size smoothing'' technique that prevents the step size from increasing too rapidly. The Adam method uses the default PyTorch parameters (lr=0.001, betas=(0.9, 0.999)).
All methods use batch-size of 128 and relaxation parameter $\gamma = 2$. We report the validation error and train loss averaged over 3 runs.

Our results, shown in Figure \ref{figure:deep_results}, confirm that both $\texttt{SPSL1}$ and $\texttt{SPSL2}$ are highly competitive. In terms of validation error, \texttt{SPSL1} achieves the best result in the MNIST dataset (0.0159 vs 0.0165 for the second-best, \texttt{ALI-G}), arrives second on the CIFAR-10 dataset (0.075 vs 0.070 for \texttt{ALI-G}), and third on the CIFAR-100 (0.31 vs 0.27 for \texttt{SPS}$_{\max}$).

\section{Conclusion}

We studied in this paper SPS (SGD with Polyak step size), a family of stochastic algorithms with step size adaptive to the gradient norm and loss value at the sampled points.
Our first contribution was a novel connection with Passive-Aggressive methods, leading to a variational perspective of not only vanilla \texttt{SPS} but also recently-proposed variants \texttt{SPS}$_{\max}$ and \texttt{ALI-G}. Based on this viewpoint, our second contribution was two new SPS variants, \texttt{SPSL1} and \texttt{SPSL2}, that regularize the slack variable, for which we provide a convergence-rate analysis.
Experiments confirmed that \texttt{SPSL1} and \texttt{SPSL2}, are competitive, both on logistic regression and DNN tasks.

\bibliographystyle{abbrv}

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VIRUS OUTBREAK-COLLEGE SPORTSAP Source: Pac-12 sets Sept. 26 start for football scheduleUNDATED (AP) — The Pac-12 has set Sept. 26 as the start of its 10-game, conference-only football schedule, joining the Southeastern Conference in pushing back its season by nearly a month because of the coronavirus pandemic.The Pac-12 announced three weeks ago it would eliminate nonconference games to give its 12 member schools a better chance to manage complications and disruptions caused by the health crisis. The plan approved by university presidents adds an additional cross-divisional game to each team's slate and moves the conference championship game back two weeks from Dec. 4 to Dec. 18 or 19. NFL-NEWS ESPN was first to report the conversation.Concerns have been expressed about lax behavior by players on the field — such as spitting or high-fives — and off. The scrambled schedule has also heightened doubts about whether the owners' desire to play is realistic.MLB-NEWSChapman rejoins YankeesUNDATED (AP) — All-Star closer Aroldis Chapman has been cleared to return to Yankee Stadium following a bout with the coronavirus. He was expected to play catch before New York hosted the Boston Red Sox. Brown has caught 841 passes for 11,236 yards and 75 touchdowns in parts of 10 NFL seasons.In other NFL news:— Lions safety Jayron Kearse has been suspended by the league for the first three games of the 2020 regular season for violating league policy on substance abuse. Kearse is eligible to participate in all preseason practices and can return to the active roster after the team's Week 3 game at Arizona. Formerly with division rival Minnesota, Kearse signed a one-year, $2 million deal with Detroit as a free agent. — Bills starting right guard Jon Feliciano is out indefinitely after having surgery to repair a torn pectoral muscle. The team did not reveal when or how Feliciano was hurt in making the announcement on its website.— Steve Levy, Brian Griese and Louis Riddick will be the new announce team for ESPN's "Monday Night Football," according to a person familiar with the decision. The trio has familiarity working together. They called the late game in last season's Week 1 doubleheader between Denver and Oakland. Antonio Brown suspended 8 games by NFLUNDATED (AP) — The NFL has suspended wide receiver Antonio Brown for the first eight regular-season games of the 2020 season under the league's personal conduct policy.Brown currently is a free agent. He played one game last season for the Patriots before being released. Brown can be signed by any team and would be eligible to participate in all of his club's preseason activities. The suspension would take effect when teams make their final cuts on Sept. 5. Brown pleaded no contest on June 12 to charges related to a fight with a moving truck driver outside his South Florida home earlier this year. July 31, 2020 Associated Press Antetokounmpo had 36 points, 15 rebounds and seven assists to help Milwaukee get within one victory of wrapping up the No. 1 seed.In other Day 2 action of the NBA restart:— The Magic picked up their fourth straight win as Evan Fournier scored 24 points and Nikola Vucevic had 22 in a 128-118 dismantling of the Nets. Orlando led by 30 at one point and moved ahead of Brooklyn for seventh in the Eastern Conference. The Nets are missing Spencer Dinwiddie, DeAndre Jordan and Taurean Prince after they tested positive for the coronavirus.— CJ McCollum scored 33 points and teamed with Damian Lillard to provide 11 of Portland's 16 in overtime, leading the Blazers past the Grizzlies, 140-135. Lillard finished with 29 points and nine assists, while Carmelo Anthony added 21. The Blazers are within 2 1/2 games of Memphis as Portland seeks its seventh consecutive playoff appearance.— The Suns cruised to a 125-112 win over the Wizards as Devin Booker scored 27 points and Deandre Ayton added 24 with 12 rebounds. The Suns hit 30 of 32 from the line, with Booker hitting all nine of his attempts. Phoenix 52% from the field in propping up its playoff hopes. — The White Sox have promoted second baseman Nick Madrigal, adding one of their top prospects to the roster. The 23-year-old had been training at the team's auxiliary site. Madrigal was selected by Chicago with the fourth overall pick in the 2018 draft after a standout collegiate career at Oregon State. NBA-SCHEDULEBucks outlast CelticsUNDATED (AP) — The Milwaukee Bucks are on the verge of clinching the top seed in the NBA's Eastern Conference after winning their re-opening game.Giannis Antetokounmpo (YAH'-nihs an-teh-toh-KOON'-poh) converted a tiebreaking three-point play with 1:28 left before the Bucks finished off a 119-112 win over the Celtics. Antetokounmpo was then called for a charging foul, appearing to negate his basket and giving him a sixth foul. The call was changed to a blocking foul on Boston's Marcus Smart after review. Yankees manager Aaron Boone confirmed Chapman's return and said he wasn't sure when the hard-throwing left-hander would be ready for game action. Chapman had been isolating in his Manhattan apartment since registering a positive test July 11. Also, Yanks right-hander Tommy Kahnle was added to the injured list with forearm tightness. He had an MRI taken Friday.In other MLB news:— The Cubs have signed former Indians closer Cody Allen to a minor league deal and sent him to their team's training site in South Bend, Indiana. The Cubs' bullpen struggled in the first week of the season. Closer Craig Kimbrel walked four batters and allowed two runs in his season debut Monday night. Share This StoryFacebookTwitteremailPrintLinkedinRedditMLB-SCHEDULEYankees top Bosox behind Judge, MontgomeryUNDATED (AP) — The New York Yankees were winners in their first game against the rival Red Sox this season. NEW YORK (AP) — The coronavirus continues to alter the Major League Baseball schedule.Friday's game between Milwaukee and visiting St. Louis had to be postponed after two Cardinals players tested positive for COVID-19. The teams are now expected to play a doubleheader on Sunday.The Cardinals are quarantined in their Milwaukee hotel. The team says it learned of the positive tests on Thursday night.Eight teams have been affected in the first nine days of the season. The Phillies and Marlins haven't played since Sunday and are on hiatus until at least Sunday after 17 Marlins tested positive while staying in Philadelphia. Four other teams had their schedules altered due to the virus.Meanwhile, Commissioner Rob Manfred spoke to union leader Tony Clark about the importance of players following the sport's coronavirus protocols. A person familiar with the conversation told The Associated Press that the two discussed what is needed to be done to complete the season. Update on the latest sports Fowler closed with birdies on his final two holes for a 67.LPGA-DRIVE ON CHAMPIONSHIPKang leads as LPGA returnsTOLEDO, Ohio (AP) — The LPGA has made its return following a hiatus caused by the pandemic. Danielle Kang looked as though she's been playing every week.Kang was bogey-free at Inverness Club for a 6-under 66 and a one-shot lead in the LPGA Drive On Championship. With no leaderboards or fans at the course, Kang said she had no idea where she stood after closing with a birdie. NHL-HURRICANES-HAMILTONHurricanes' Dougie Hamilton out for Rangers series openerTORONTO (AP) — All-Star defenseman Dougie Hamilton won't play for the Carolina Hurricanes in Saturday's opener against the New York Rangers in the NHL's Eastern Conference's expanded playoff qualifying round.Hamilton has missed multiple practices, though the league has prohibited teams from disclosing whether a player is injured or ill amid the coronavirus pandemic. Carolina coach Rod Brind'Amour (BRIHN'-dah-mohr) says Hamilton is "getting better for sure," and the team hopes he will play in the best-of-5 series. Aaron Judge homered for the third straight night as the Yankees dumped the Red Sox, 5-1. Judge took aim at Yankee Stadium's short right field porch in the third, a half-inning after starting a double play from right. Gio Urshela (ur-SHEH'-luh) and Brett Gardner hit their first home runs of the season to back Jordan Montgomery, who was reached for just one run and five hits over 5 2/3 innings versus a hot lineup.Boston entered the day leading the majors in with a .276 batting average and the AL with a .783 OPS.Michael Chavis homered for Boston and Phillips Valdez impressed over 2 2/3 scoreless innings, but the club couldn't overcome another poor start by Ryan Weber.VIRUS OUTBREAK-BASEBALLCards-Brewers postponed after 2 St. Louis positive tests Hamilton broke his left leg in January and was sidelined until the NHL suspended the season because of the pandemic.PGA-FEDEX INVITATIONALBrendon Todd takes 2-stroke lead with 65 at WGC in MemphisMEMPHIS, Tenn. (AP) — Brendon Todd will carry a two-shot advantage into the third round of the PGA's FedEx St. Jude Invitational.Todd followed Thursday's 64 with a 5-under 65 that leaves him two ahead of Rickie Fowler. First-round leader Brooks Koepka (KEHP'-kuh) shot a 1-over 71 that drops him into a third-place tie with Chez Reavie and Byeong Hun An at minus-7. Jodi Ewart Shadoff also played bogey-free for a 67. Celine Boutier and Lee-Anne Pace also were at 5 under until both made bogey on the closing hole. TENNIS-US OPENUS Tennis Association says it's still preparing for US OpenUNDATED (AP) — As coronavirus cases spike in other parts of the country a month before the U.S. Open is supposed to start in New York, the U.S. Tennis Association said Friday it "continues its plans" to hold its marquee event and another tournament beforehand.The U.S. Open usually is the year's last Grand Slam tournament and its slated to run Aug. 31 to Sept. 13. It's now the second major championship because of the pandemic. read more
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No antivirus protection can claim to be infallible – and indeed there are products out there which definitely have weak spots, as you'll see from the results security suite testing labs such as AV Test regularly publish. So even though you've got protection up and running, there's a chance that your computer could still get infected by a virus.
So what should you do if your machine suddenly starts behaving oddly, assaulting you with multiple pop-ups or running sluggishly (or all of the above), and you suspect you're a victim of malware that your security product hasn't detected? For starters, you can make sure your suite's virus definitions are totally up to date, and also ensure you've run a full scan (which takes in everything on the PC – you'll have to wait a while for it to complete).
When tech support agents for some security vendors run into a problem their own product can't handle, they sometimes turn to Malwarebytes Anti-Malware for help with clean-up (there's a free version, and a Pro one). If the real problem is that the malware fights back against removal, try a free Rescue CD that boots into a non-Windows operating system and thereby prevents the malware from running. For example, you can grab AVG's Rescue CD here.
One of these simple and easy to use tools should hopefully help to shed light on your situation. Another option, if you're using one of the less reliable security vendors according to AV Test's regular evaluations, is to switch to a different product – see our guide to buying security software, and our piece on the best security products of 2013 for recommendations.


text:
Attorney general appeals 15 year-old girl's flogging sentence as authorities contemplate legal reforms
Attorney General (AG) Azima Shukoor has appealed a court decision to sentence a 15 year-old girl alleged to be the victim of multiple cases of sexual abuse to 100 lashes on charges of fornication, the government confirmed today.
The Juvenile Court sentenced the girl after she confessed to authorities of having consensual sex with an unknown man during investigations into a separate case of abuse against the minor. The abuse was alleged to have been carried out by her stepfather.
President Mohamed Waheed's government has previously criticised the verdict, pledging back in January to review the use of flogging as a punishment for sexual offences – a practice it has alleged in some cases actually serves to punish victims of rape and abuse.
Sources on Feydhoo in Shaviyani Atoll, where the 15 year-old girl originates from, last week told Minivan News that concerns had been raised by islanders since 2009 that the minor had allegedly been the victim of sexual abuse not just by her stepfather, but by a number of other unidentified men on the island.
The case has brought international attention to the country's legal system, including the launch of an online Avaaz.org petition signed by 1.3 million people that threatens to boycott Maldivian tourism, as well as public criticism from British multi-billionaire Sir Richard Branson, founder of the Virgin group of companies.
In a statement posted on his website yesterday (March 26), Branson spoke of the "enormous damage" he believed the verdict was causing the country. As a result, Branson said he had written to President Waheed, who in turn claimed he had pledged to review the case through a ministerial committee.
"The attorney general has now appealed the case on behalf of the child," Branson wrote.
Speaking to Minivan News today, President's Office Spokesperson Masood Imad confirmed that the attorney general had now appealed the court's ruling, but that he was still waiting on the exact details from the AG's Office. Massod added that further details would be provided on the appeal later this week.
He was also unable to confirm if a time-line had yet been established for consultations between various state bodies to oversee any proposed reforms to the legal system.
The Maldives Constitution does not allow any law that contradicts the tenets of Islam, with the criminal charge of fornication outlined under Islamic Sharia.
However, Masood has previously noted that the Maldives had a tradition of turning away from practices such as the death sentence and corporal punishment that form part of Sharia law.
According to Masood, punishments such as removing the hand of a suspect in the case of theft had not been used since back in the 1960′s.
He maintained that there was a history of reviewing the country's relationship with Sharia law in the past and that a similar process could be had with the debate about flogging.
Masood said that all authorities involved in proposed legal reforms would have to tread "a very fine line" in order to tackle long standing "traditions" and beliefs in the country.
Avoiding prosecution
A senior legal expert with experience of working under both the present and former governments has told Minivan News that that while the Maldives Constitution requires that laws in the country do not contradict Islamic Sharia, there were ways of avoiding prosecuting suspects on charges of fornication.
"There are many Islamic legal interpretations that place several conditions to fulfill before a prosecution on fornication be brought forward. Some scholars even go further and argue that hudood offences cannot be practiced in the legal justice systems at the current time," claimed the legal source, who spoke on condition of anonymity.
"Their argument is that Islamic Sharia is a way of life and you cannot pick and choose which areas you need to implement. Basically, you cannot implement Islamic criminal justice system in its original form when Islamic commercial system or Islamic governance is not observed."
Addressing the wider issues of how minors were identified and viewed in the eyes of Maldivian law, the legal source added that the culpability of children was identified in a regulation called 'Kuda kudhin kuraa kushuge masala thah balai, thahugeegu koh, insaafu koh, adhabu dhinumugai amalu kuraane gothuge gavaidu'
The legal source said that the culpability of minors is specifically dealt with in section five of the regulations.
"According to section five, children above the age of 10 and below the age of 15 are criminally responsible for five offences, which are apostasy, treason, fornication, falsely accusing fornication and consumption of alcohol," the source said.
"Children above 15 years are criminally responsible for their actions. With children who are below 10, parents are required to make good any damage because of a criminal act. There is no criminal liability for below 10."
Minister of Islamic Affairs Sheikh Mohamed Shaheem Ali had his phone switched off at time of press.
High Court appeal of 15 year-old rape victim's sentence begins
Fifteen year-old's appeal of flogging sentence for fornication stalled in High Court
Trial against minor for "consensual sexual relations" to continue this week
Advocacy group requests government "not delay" reform of child sex abuse laws
Government schedules talks over reforming sexual abuse laws
Defence lawyer of minor sentenced to flogging appeals case in High Court
Posted on March 27, 2013 March 27, 2013 Author Neil MerrettCategories Politics, Society & CultureTags allegations, child abuse, fornication, juvenile court, maldives, maldives news, minivan news, minor, sexual abuse, Shaviyani Feydhoo, Sir Richard Branson, Virgin Group
13 thoughts on "Attorney general appeals 15 year-old girl's flogging sentence as authorities contemplate legal reforms"
Nahi says:
Mi othee ves gaumah jehnnu v Balaa veri kameh.
simple and honest says:
Well done Avaaz! We trust you more than the old CMAG who sit on their chairs and fart only. Now I am hoping that you launch a petition on the transfer of power in Maldives in 2012. Its a mutiny in pure day light and I hope you launch this petition soon.
Well now we know how international pressure - especially financial one - can do wonders. You see when rich guys see threat to their riches, they will give up their BS about religion, sovereignty and imperialism and start working sensibly.
Mohamed Naseem says:
I want lay the Golden egg to Maldives
Attorney general appealed the 15 year-old girl's flogging sentence before Avaaz even started their campaign. LOL
Avaaz was used by FOM (friends of maldives) as part of the tourism boycott campaign they started since feb 2012.
We all know this, also the message by Avaaz was so misleading. Anyway, FOM has achieved their objective to some extent as a few hundred tourists (mostly europeans) has actually cancelled their bookings to visit Maldives.
As soon as the girl case gets solved, next campaign to destroy our fragile tourism industry will be under the titles Govt. supporting and promoting Islamic Extremism and so and so.. terrorists.. bla bla bla.. a friendly source told me.
Michael Fahmy says:
Vivendra you are right. Quite right. I agree with you.
Kuribee says:
even entire world is one one side want Nasheed to be the president of Maldives, that is not going to happened unless 51% of the Maldivian elects him to be the next president.
I doubt that the world is wanting Nasheed to be the president either .
Nasheed did resigned and he did it knowing that his popularity was decreasing and he would have no chance of standing for his second term unless he does stupid thing like what he had done on Feb. 7th.
To some extend the guy had won some sympathy vote and many people were fooled by him like before in 2008.
The junta says:
Jabba the hut finally showing signs of a moral conscience. Well done jabba.
Hathim says:
Kuribee President Nasheed was elected to the post of presidency by Maldivians.
He was not ousted by an election but by a coup. So unless and until there is a free and fair election where even Nasheed is also able to participate we will not know if Maldivians wish to see his presidency or not.
Roly Poly says:
@The junta
A case of the pot calling the kettle black?
mathias says:
Raabo President nasheed can fake up awwaz.org and any other website. But this is something that was going to be discouraged by the government anyway. Good Luck Mr. president.. keep up the good work your are doing for this nation.
@Kuribee
Take my advice and get professional help for your delusions.
When someone is as obsessed as you are about someone it is a clear sign of mental illness or fear.
Nasheed resigned under duress over his stand against a dysfunctional judiciary. It is clear to me from your comments that you have a lot to lose with judicial reform in our country.
Kuribee, wake up and look around you. Te nation has woken up, the world has woken up to the reality of a country that has its leaders talk about rule of law but where there is no justice.
Nasheed had his share of errors of judgement and not all his decisions were in the interests of the people.
There is a process in our constitution for holding an President accountable if his policies and actions were counterproductive to the interests of the people and that is called impeachment. However those opposed to him as you are could not do that because you did not have enough support in parliament for that. And hence the coup.
Regardless of the CONI report most of us believe there was a coup in the Maldives.
You can believe what you like, and the administration of Dr Waheed can say what they like but it is clear from the testimonies of the senior officers of the armed forces that what happened on the 7 February 2012 was a coup.
Shimy says:
Why don't this billionaire Branson help his own fellow country men in the army by reducing the suicide rate in America rather than meddling in our affairs!??? What a lot of seyku anni nutshells here! I thought he can change the govt within a wink after the so called coup but alas he is no god! what fools!!
And let the teenagers and adults have sex, beer, drugs free and let the epidemic called aids, Stds and other evils run in this country. The tourism industry will come in handy as they will provide relief for these innocent sex offenders and drug addicts who go on to butcher innocent people!
and of course it will relieve only the west and the riches who benefit from this!what a world we live in!
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text:
Chain Lightning Chords - Bruce Springsteen
Chain Lightning Chords
by Bruce Springsteen. From 'The Ties That Bind: The River Collection".
Transcribed by burnmik.
Intro / also played during Em on verses / palm mute
e|--------------------|--------------------|
B|--------------------|--------------------|
G|--------------------|--------------------|
D|--------------------|--------------------|
A|--------------------|--------------------|
E|--0-0-3-0--0-0-3-0--|--0-0-3-0--0-0-3-0--|
Well there's a rumble in the park, there's a thunder in the dark
The night's so quiet, it's chain lightning
Beneath a street light two boys bopping in the night
They have something that I call, chain lightning
A                           G
Though you never hear a sound, there's fire underground
F#                                   B
Rambling through the town, you can't keep it from coming down
Lovers walking through the mist, Romeo he steal a kiss
Caught up in the moment at chain lightning
Now I don't know about romance, baby, the latest dance
Everybody's getting up, doing it, chain lightning
All along the strand, baby, down in jungleland
Everybody's caught up in chain lightning
A                        G
Ever hear the sound of a fire underground
F#                               B
Rumbling through the town, the big cold is coming down
Sitting at the light, I'm a rider in the night
Streaking light to light for chain lightning
Em |  |  |  |
A |  |  |  |  |  |  |  |
Baby, I ain't into style, baby, I ain't into fashion
I just got a passion for chain lightning
Sitting at light, I'm a rider in the night
Bruce Springsteen - Chain Lightning Chords :: indexed at Ultimate Guitar.
Chain Lightning tabs @ 911Tabs
People who played Bruce Springsteen - Chain Lightning Chords also played these songs by Bruce Springsteen:
The River Chords, Im On Fire Chords, If I Should Fall Behind Chords, Brilliant Disguise Chords, Tougher Than The Rest Chords, Dancing In The Dark Tab, This Little Light Of Mine Chords, Born To Run Chords
About the artist behind Chain Lightning Chords:
Bruce Frederick Joseph Springsteen (born September 23, 1949) is an American songwriter, singer and guitarist. He has recorded and toured with the E Street Band. Springsteen is widely known for his brand of heartland rock infused with pop hooks, poetic lyrics, and Americana sentiments centered around his native New Jersey. His eloquence in expressing ordinary, everyday problems has earned him numerous awards, including eighteen Grammy Awards and an Academy Award, along with a notoriously dedicated and devoted global fan base. His most famous albums, Born to Run and Born in the U.S.A., epitomize his penchant for finding grandeur in the struggles of daily life. He has sold over 65 million albums in the U.S.[1]
Springsteen's lyrics often concern men and women struggling to make ends meet. He has gradually become identified with progressive politics. Springsteen is also noted for his support of various relief and rebuilding efforts in New Jersey and elsewhere, and for his response to the September 11, 2001 attacks, on which his album The Rising reflects.
Springsteen's recordings have tended to alternate between commercially accessible rock albums and somber folk-oriented works. Much of his iconic status stems from the concerts and marathon shows in which he and the E Street Band present intense ballads, rousing anthems, and party rock and roll songs, amongst which Springsteen intersperses long, whimsical or deeply emotional stories.
Springsteen has long had the nickname "The Boss", a term which he was initially reported to hate but now seems to have come to terms with, as he sometimes jokingly refers to himself as such on stage. The nickname originated when a young Springsteen, playing club gigs with a band in the 1960s, took on the task of collecting the band's nightly pay and distributing it amongst his bandmates.[2]
Show us your talent, perform Chain Lightning Chords!
Here you can post a video of you playing the Chain Lightning Chords, so your fellow guitarists will be able to see you and rate you.


text:
Judge Orders Paul Manafort To Jail To Await Trial
By Briana Koeneman
A federal judge revoked Manafort's bail and ordered him to await trial in jail after special counsel Robert Mueller accused him of witness tampering.
Former Trump campaign chairman Paul Manafort will spend some time behind bars.
On Friday, a federal judge revoked Manafort's bail and ordered him to jail to await trial after special counsel Robert Mueller accused him of witness tampering.
CNN quotes the judge as saying: "I thought about this long and hard, Mr. Manafort. I have no appetite for this."
Manafort is facing multiple charges, including allegations of money laundering, tax evasion, conspiracy to obstruct justice and failure to register as a foreign agent.


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text:
Time Reduced to a "Cinder": No One Knows What the Dead Think, Featuring Former Discordance Axis Members
Jon Rosenthal
Jon Rosenthal Published: July 24, 2019
It is difficult to measure grindcore in time, mostly due to the genre's significant lack of it. Looking at neo-stalwarts No One Knows What the Dead Think, it is impossible to measure their debut and sole eponymous release in standard time. At only 19 minutes in length, time is not enough.
In Chicago and Los Angeles, time is used to measure distance (mostly due to traffic), but that type of philosophy can be healthy when describing the immensity of former Discordance Axis members Jon Chang and Rob Marton's new project and final chapter.
Take, for example, "Cinder," which can be streamed exclusively below. At a paltry two minutes and 40 seconds in length, this is both a short song, but also the lengthiest on the album itself. Therein lies the duality of grindcore's time as distance and distance as time existence. How far can one go in this short duration? At walking speed? Maybe a few blocks, but at the warp speed performed by this trio? It's hard to say -- maybe it hasn't even been mapped yet.
Musically, this is a beautiful continuation of what the world missed after The Inalienable Dreamless. Marton's dizzying, staccato guitar weaving melody in with the incredible momentum set forth by the album up to this point. It is atypical, strange, and emotive music, especially when heralded by Chang's own alien screaming. Two minutes and 40 seconds seems like nothing, at first. Blink and you miss it, but travel with this trio and find yourself in the stratosphere, or even further. Don't fall.
No One Knows What the Dead Think releases September 20th via Willowtip Records. Stream another single below:
Support Invisible Oranges on Patreon and check out our merch.
Filed Under: discordance axis, grindcore, jon chang, No One Knows What The Dead Think, rob marton
Essential Albums On Essential Labels #2: Hydra Head Records
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Join Voidgazer in the Perilous, Tempting "Dance of the Undesirables" (Early EP Stream)
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Six Grindcore Releases To Soundtrack The Mania Of 2021


Some of the best wine producers are again in this region, but most of the modern production of wine started only in the 1970s; the Apostelhoeve is one of the oldest and still one of t he best !(the 2-day excursion to SE-Netherlands/Maastricht will visit this vineyard/producer).
In fact the commercial wine production is steadily increasing, and passed in 2010, a total of 1 million bottles of wine. Quantity is not all that counts, prices were won at international wine fairs (e.g. Apostelhoeve wines have received various medals at international concourses: 9 gold and 11 silver medals). Also Y. Robinson, a famous wine-taster/evaluator/writer was recently pleasantly surprised by the unexpected high quality of Dutch wines.
Large quantities of Dutch cheeses are exported around the world, but for tasting the really good cheeses, you have to be in the Netherlands.
The Wine & Cheese tasting event will take place in a historical setting, namely in the Auditorium and the adjacent ancient monastery herbal garden, the 'Pandhof' (courtyard). This garden is situated between the St. Martin's Cathedral and the University Hall in the Medieval centre of Utrecht. The Pandhof is an idyllic monastery garden, where ornamental plants and herbs bloom. It is without a doubt one of the most beautiful enclosed gardens in the Netherlands.
The oldest part of the Utrecht University Hall is the Auditorium, completed in 1462. In here the Treaty of Utrecht was signed in 1579, marking the origin of the Dutch nation. When Utrecht University was founded in 1636 it was given the Auditorium by the city.
During this Dutch Wines & Cheeses Tasting, a fine selection of different wines and cheeses will be presented and introduced by local experts.


Congratulations to Abhinav Suresh, clear and undefeated winner of the top section of the 2nd Spence Quads. His rating continues its climb to the stratosphere – he's now among the club's top rated players 1t 1764!
There was a three-way tie for first in the second section. Caravaggio Caniglia, Thomas Freed and Arnie Schulze all scored 2.0/3 to share the crown.
10 players turned up to play in the 2nd Spence Quads. Because 10 is not divisible by 4, we created a top quad section and a bottom six person swiss.
Congratulations to state co-champ Ben Fabrikant, clear and undefeated (7/7!) winner of the 4th Spence Blitz! Abhinav Suresh and Tony Dutiel tied for 2nd/3rd with 5.0/7.


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Cristhian Rivera, a suspect in the death of Mollie Tibbetts, did not provide the same name to his employer, Yarrabee Farms.
DES MOINES, Iowa – When the Lang family watched the news about Mollie Tibbetts unfold Tuesday, a familiar face flashed on the screen.
They were shocked. The face of the suspect was familiar to them as one of their employees at Yarrabee Farms, but the name that went with the picture was completely different.
"What we learned within the last 24 hours is that our employee was not who he said he was," said Dane Lang, manager of Yarrabee Farms.
Cristhian Bahena Rivera, the 24-year-old immigrant accused of abducting and killing Tibbetts, allegedly used a different name and provided false identification when he applied for employment at the farm just outside of Brooklyn, Iowa, his employer said Wednesday.
Rivera worked at Yarrabee Farms in rural Poweshiek County for four years, Lang said. Yarrabee Farms is owned by multiple generations of the Lang family, including Craig Lang, former Farm Bureau President and prominent Iowa Republican.
Rivera was charged with first-degree murder Tuesday in the July 18 disappearance of Tibbetts, whose remains were found in a cornfield in Poweshiek County. A criminal complaint released Tuesday said Rivera directed law enforcement to Tibbetts' body.
Rivera worked on day-to-day operations with the cows. He was introduced to the Lang family and gained employment there through a former girlfriend.
He also lived on the property in a mobile home, said Mitch Mortvedt, assistant director of the Iowa Division of Criminal Investigation.
"We continue to cooperate with the investigation, and we have provided information about our former employee, including his hiring records, to authorities," Craig Lang said during a press conference at the farm Wednesday. "There will be plenty of time later to discuss immigration. However, now is not that time."
Dane Lang is Craig's son. He said Rivera provided a state-issued government ID and Social Security number when applying for employment. The information is required to file a Form I-9, which verifies the identity and employment eligibility of a person in the U.S.
As a voluntary second verification step, the business put Rivera's information through the Social Security Administration's number verification service, but Dane Lang said he and others assumed it was E-Verify.gov.
E-verify.gov allows employers to check if the information on a Form I-9 matches Social Security Administration and Department of Homeland Security records.
Employment verification officials consider E-Verify a more robust backgrounding system because it includes immigration status and eligibility to work in the United States. A check of only a Social Security number verifies that the number, name and birth date an employee provided match information that exists in the federal Social Security database.
Dane Lang said Rivera provided a different name when he applied for employment, but he would not share it on Wednesday, citing the investigation.
"This employee was considered in good standing," Lang said. Rivera showed up to work on time, cooperated with the other employees and showed up every day, he said.
Over the last month, the younger Lang said he didn't notice any changes in Rivera's behavior. He said he always worked well with his colleagues.
"I wish I had seen a difference, but I didn't," Lang said.
About 10 full-time and part-time employees work on the farm, and all current employees now will go through the E-Verify background check. Dane Lang would not confirm whether there were any non-U.S. citizens employed at the farm.
He said his employees are a part of the community and some of their kids have gone on to become homecoming king or a valedictorian.
At least 100 threatening voicemail messages have been sent to Dane Lang since Tuesday, he said. People have threatened to burn down buildings and even kill his dog after learning Rivera was employed at the farm.
"This is a really scary situation," he said. "And the unfortunate thing is, people are paying attention to me and we're forgetting about the heartbroken family in Brooklyn and the heartbroken community."


Join us for our FIRST field trip, Saturday, August 27! (We say first because we have already started planning more). For a limited engagement, the South Carolina State Museum is hosting the blockbuster exhibit, RACE ARE WE SO DIFFERENT?, a project of the American Anthropological Association and funded by the Ford Foundation & National Science Foundation.
As with all Brownicity events, this field trip is family friendly. So bring your kids!—but only if you want to.
We will carpool from Charlotte to Columbia, SC (or you can meet us at the museum), tour the exhibit, engage in a reflection and discussion session led by our own Brownicity leaders, and enjoy a meal together.
$10 per person includes museum admission and admission to the exhibit.
RSVP through the field trip announcement by Friday, August 19, so we can make group reservations and coordinate carpool.
If you have any questions, contact us through the field trip announcement.


Are Mental Health Services Included In Medical Health Insurance?
Does Major Medical Insurance Cover Mental Health Services?
So many people are worried about having to pay for mental health services. They already know they get these types of services from health care professionals, or sometimes by physicians, and they also need to know if their own health plan can help cover them. The solution to the issue for just about any particular person is, obviously, this will depend.
Many group major medical policies do provide employees with comprehensive coverage. This might include mental coverage of health. Other employers may provide these types of services under another advantage program. When you get your medical benefits at the office, you have to talk to your policy or ask a persons sources department. Some companies publish free, private phone figures for workers who want to seek help.
If it's not an urgent situation, it's safer to obtain an treatment pre-approved. By doing this you will be aware just how much the audience health plan pays and just how much you spend up front.
Individuals with individual or family policies my not have access to comprehensive mental health advantages. Despite the fact that private insurers cannot cancel an insurance policy just because a covered person develops an ailment, most refuse a preliminary application due to mental illness. The brand new health reform bill helps it to be so people can't be declined an insurance policy for pre-existing conditions later on, however this part is not implemented yet.
Mental health services can be quite costly, especially if you want to purchase private treatment. Lots of people who require help have to return for repeated therapy, treatment, or prescriptions too. But there are lots of sources to help individuals get free or lower cost treatment. However , many people who require treatment might not understand how to search for help! Another issue is that lots of individuals who need assistance may fear they don't have the funds to cover costly therapists or doctors.
You will find a handful of excellent free and occasional cost clinic finders online. These types of services will help you find a variety of medical facilities, including mental health centers. Both Partnership for Prescription Assistance (PPARX.org) and also the US Department of Health insurance and Human Services provide handy zipcode searches.
One enters your zipcode, along with maximum distance you want to travel. The internet system displays any free or reduced fee clinics in your town. If you fail to find the correct service not far from home, you might want to expand your research a little.
This telephone number can keep you in touch with 24/7, free, private phone help. They may also lead you to 1 of countless crisis centers in america.
On other place to consider assistance is at neighborhood centers or non profit organizations. Some have social workers within the company or can lead you with other local sources where one can get help. The local pastor also needs to have these details, and perhaps they might draw upon sources from the congregation.
Student Plans – Why Choose Student Healthcare?