  We propose and investigate a class of new algorithms for sequential decision
making that interacts with \textit{a batch of users} simultaneously instead of
\textit{a user} at each decision epoch. This type of batch models is motivated
by interactive marketing and clinical trial, where a group of people are
treated simultaneously and the outcomes of the whole group are collected before
the next stage of decision. In such a scenario, our goal is to allocate a batch
of treatments to maximize treatment efficacy based on observed high-dimensional
user covariates. We deliver a solution, named \textit{Teamwork LASSO Bandit
algorithm}, that resolves a batch version of explore-exploit dilemma via
switching between teamwork stage and selfish stage during the whole decision
process. This is made possible based on statistical properties of LASSO
estimate of treatment efficacy that adapts to a sequence of batch observations.
In general, a rate of optimal allocation condition is proposed to delineate the
exploration and exploitation trade-off on the data collection scheme, which is
sufficient for LASSO to identify the optimal treatment for observed user
covariates. An upper bound on expected cumulative regret of the proposed
algorithm is provided.

Machine Learning;Machine Learning