Learning Gaussian Policies from Smoothed Action Value Functions
State-action value functions (i.e., Q-values) are ubiquitous in reinforcement learning (RL), giving rise to popular algorithms such as SARSA and Q-learning. We propose a new notion of action value defined by a Gaussian smoothed version of the expected Q-value used in SARSA. We show that such smoothed Q-values still satisfy a Bellman equation, making them naturally learnable from experience sampled from an environment. Moreover, the gradients of expected reward with respect to the mean and covariance of a parameterized Gaussian policy can be recovered from the gradient and Hessian of the smoothed Q-value function. Based on these relationships we develop new algorithms for training a Gaussian policy directly from a learned Q-value approximator. The approach is also amenable to proximal optimization techniques by augmenting the objective with a penalty on KL-divergence from a previous policy. We find that the ability to learn both a mean and covariance during training allows this approach to achieve strong results on standard continuous control benchmarks.
 The paper introduces smoothed Q-values, defined as the value of drawing an action from a Gaussian distribution and following a given policy thereafter. It demonstrates that this formulation can still be optimized with policy gradients, and in fact is able to dampen instability in this optimization using the KL-divergence from a previous policy, unlike preceding techniques. Experiments are performed on an simple domain which nicely demonstrates its properties, as well as on continuous control problems, where the technique outperforms or is competitive with DDPG. The paper is very clearly written and easy to read, and its contributions are easy to extract. The appendix is quite necessary for the understanding of this paper, as all proofs do not fit in the main paper. The inclusion of proof summaries in the main text would strengthen this aspect of the paper. On the negative side, the paper fails to make a strong case for significant impact of this work; the solution to this, of course, is not overselling benefits, but instead having more to say about the approach or finding how to produce much better experimental results than the comparative techniques. In other words, the slightly more stable optimization and slightly smaller hyperparameter search for this approach is unlikely to result in a large impact. Overall, however, I found the paper interesting, readable, and the technique worth thinking about, so I recommend its acceptance.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Learning Gaussian Policies from Smoothed Action Value Functions
State-action value functions (i.e., Q-values) are ubiquitous in reinforcement learning (RL), giving rise to popular algorithms such as SARSA and Q-learning. We propose a new notion of action value defined by a Gaussian smoothed version of the expected Q-value used in SARSA. We show that such smoothed Q-values still satisfy a Bellman equation, making them naturally learnable from experience sampled from an environment. Moreover, the gradients of expected reward with respect to the mean and covariance of a parameterized Gaussian policy can be recovered from the gradient and Hessian of the smoothed Q-value function. Based on these relationships we develop new algorithms for training a Gaussian policy directly from a learned Q-value approximator. The approach is also amenable to proximal optimization techniques by augmenting the objective with a penalty on KL-divergence from a previous policy. We find that the ability to learn both a mean and covariance during training allows this approach to achieve strong results on standard continuous control benchmarks.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 The paper introduces smoothed Q-values, defined as the value of drawing an action from a Gaussian distribution and following a given policy thereafter. It demonstrates that this formulation can still be optimized with policy gradients, and in fact is able to dampen instability in this optimization using the KL-divergence from a previous policy, unlike preceding techniques. Experiments are performed on an simple domain which nicely demonstrates its properties, as well as on continuous control problems, where the technique outperforms or is competitive with DDPG. The paper is very clearly written and easy to read, and its contributions are easy to extract. The appendix is quite necessary for the understanding of this paper, as all proofs do not fit in the main paper. The inclusion of proof summaries in the main text would strengthen this aspect of the paper. On the negative side, the paper fails to make a strong case for significant impact of this work; the solution to this, of course, is not overselling benefits, but instead having more to say about the approach or finding how to produce much better experimental results than the comparative techniques. In other words, the slightly more stable optimization and slightly smaller hyperparameter search for this approach is unlikely to result in a large impact. Overall, however, I found the paper interesting, readable, and the technique worth thinking about, so I recommend its acceptance.
assistant
 The paper introduces smoothed Q-values, defined as the value of drawing an action from a Gaussian distribution and following a given policy thereafter. It demonstrates that this formulation can still be optimized with policy gradients, and in fact is able to dampen instability in this optimization using the KL-divergence from a previous policy, unlike preceding techniques. Experiments are performed on an simple domain which nicely demonstrates its properties, as well as on continuous control problems, where the technique outperforms or is competitive with DDPG. The paper is very clearly written and easy to read, and its contributions are easy to extract. The appendix is quite necessary for the understanding of this paper, as all proofs do not fit in the main paper. The inclusion of proof summaries in the main text would strengthen this aspect of the paper. On the negative side, the paper fails to make a strong case for significant impact of this work; the solution to this, of course, is not overselling benefits, but instead having more to say about the approach or finding how to produce much better experimental results than the comparative techniques. In other words, the slightly more stable optimization and slightly smaller hyperparameter search for this approach is unlikely to result in a large impact. Overall, however, I found the paper interesting, readable, and the technique worth thinking about, so I recommend its acceptance.