Paper:
In recent years, advances in deep learning have enabled the application of reinforcement learning algorithms in complex domains. However, they lack the theoretical guarantees which are present in the tabular setting and suffer from many stability and reproducibility problems [10]. In this work, we suggest a simple approach for improving stability in off-policy actor-critic deep reinforcement learning regimes. Experiments on continuous action spaces, in the MuJoCo control suite, show that our proposed method reduces the variance of the process and improves the overall performance across most domains.

Review:
[Summary]
This paper proposes an approach called conservative policy gradients to stabilize the training of deep policy gradient methods. At fixed intervals, the current policy and a separate target policy are evaluated with a number of rollouts. The target policy is then updated to match the current policy only if the current policy is better than the target policy. Experiments show that the proposed method, when applied to TD3, reduces the variance in performance through the training.
[Decision]
I am not convinced that the proposed method is sound and indeed useful and I vote for rejecting this paper. Experiments show stable performance. However, this stability comes at the cost of extra computation and interaction with the environment (to evaluate the policies). Claims about the method's stability guarantees and overall performance are not supported by theory and experiments. The submitted paper also needs major improvements in presentation.
[Explanation]
While Proposition 1 provides insights on how the policy evolves, it is too limited to serve as a guarantee. First, performance does not improve or degrade by a constant number. Second, the time it takes for the policy to improve is not captured by the theory. In reality, this time can depend on the hyperparameters or the policy's current performance and might even be unbounded. 
I do not understand why a characterization of the performance in the limit of time in Proposition 1 is called a stability guarantee while in the rest of the paper stability refers to consistent improvements in the interim performance. Does stability in this proposition mean that the performance will reach a stationary distribution with bounded support? This property is merely a result of the assumptions that the performance evolves by a constant number at bounded times and that it does not exceed [v_min,v_max].
The theory studies the stationary distribution of the target policy's performance but the algorithm uses the online policy to interact with the environment. In Algorithm 5, line 8 (Section D in the Appendix) the target policy is only used for bootstrapping. How can a stable target policy result in more stable performance if it is not used to take actions?
The paper claims that the proposed method results in improvements in stability and overall performance. In Figure 3, the proposed method is more stable than the baseline but the overall performance is not better.
The proposed method requires more computation and interaction with the environment than the baseline. The experiments do not seem to compare these two methods with the same number of samples or with the same amount of computation. Perhaps the extra computation and samples are better spent on training TD3 for a longer time.
I find Section 2 hard to follow. This section describes Value Iteration, Policy Iteration, DQN, and DDPG in detail (with pseudocode) along with their convergence rates. The message that deep RL algorithms generally lack theoretical guarantees can be conveyed by just describing the linear and deep variants of one method. In fact, the algorithm whose stability is analyzed in the next sections, TD3, is not described in Section 2 or anywhere else in the paper.
Later in Section 3, DDPG and DQN are described as off-policy Deep RL variants of Value Iteration and Policy Iteration. DQN and DDPG are actually built on Q-learning and Deterministic Policy Gradient (DPG).
[Minor comments]
In the learning curves in Figure 1, what is the measure of performance and how is it estimated? A description of the plotted measure is necessary to show that the drops in the estimated performance are indeed due to policy degradation rather than poor estimation.
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After rebuttal: I have read the authors' response, the other reviews, and the revision. The revised version has improved presentation, but the proposed method is still introduced as a method with stability guarantees while the proposition in the paper cannot serve as a stability guarantee, and can only provide intuition on the asymptotic performance.