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### P3O: Policy-on Policy-off Policy Optimization

On-policy reinforcement learning (RL) algorithms have high sample complexity while off-policy algorithms are difficult to tune. Merging the two holds the promise to develop efficient algorithms that generalize across diverse environments. It is however challenging in practice to find suitable hyper-parameters that govern this trade off. This paper develops a simple algorithm named P3O that interleaves off-policy updates with on-policy updates. P3O uses the effective sample size between the behavior policy and the target policy to control how far they can be from each other and does not introduce any additional hyper-parameters. Extensive experiments on the Atari-2600 and MuJoCo benchmark suites show that this simple technique is highly effective in reducing the sample complexity of state-of-the-art algorithms.

### Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor

Model-free deep reinforcement learning (RL) algorithms have been demonstrated on a range of challenging decision making and control tasks. However, these methods typically suffer from two major challenges: very high sample complexity and brittle convergence properties, which necessitate meticulous hyperparameter tuning. Both of these challenges severely limit the applicability of such methods to complex, real-world domains. In this paper, we propose soft actor-critic, an off-policy actor-critic deep RL algorithm based on the maximum entropy reinforcement learning framework. In this framework, the actor aims to maximize expected reward while also maximizing entropy - that is, succeed at the task while acting as randomly as possible. Prior deep RL methods based on this framework have been formulated as Q-learning methods. By combining off-policy updates with a stable stochastic actor-critic formulation, our method achieves state-of-the-art performance on a range of continuous control benchmark tasks, outperforming prior on-policy and off-policy methods. Furthermore, we demonstrate that, in contrast to other off-policy algorithms, our approach is very stable, achieving very similar performance across different random seeds.

### Doubly Robust Off-Policy Actor-Critic Algorithms for Reinforcement Learning

We study the problem of off-policy critic evaluation in several variants of value-based off-policy actor-critic algorithms. Off-policy actor-critic algorithms require an off-policy critic evaluation step, to estimate the value of the new policy after every policy gradient update. Despite enormous success of off-policy policy gradients on control tasks, existing general methods suffer from high variance and instability, partly because the policy improvement depends on gradient of the estimated value function. In this work, we present a new way of off-policy policy evaluation in actor-critic, based on the doubly robust estimators. We extend the doubly robust estimator from off-policy policy evaluation (OPE) to actor-critic algorithms that consist of a reward estimator performance model. We find that doubly robust estimation of the critic can significantly improve performance in continuous control tasks. Furthermore, in cases where the reward function is stochastic that can lead to high variance, doubly robust critic estimation can improve performance under corrupted, stochastic reward signals, indicating its usefulness for robust and safe reinforcement learning.

### Relative Importance Sampling For Off-Policy Actor-Critic in Deep Reinforcement Learning

Off-policy learning is more unstable compared to on-policy learning in reinforcement learning (RL). One reason for the instability of off-policy learning is a discrepancy between the target ($\pi$) and behavior (b) policy distributions. The discrepancy between $\pi$ and b distributions can be alleviated by employing a smooth variant of the importance sampling (IS), such as the relative importance sampling (RIS). RIS has parameter $\beta\in[0, 1]$ which controls smoothness. To cope with instability, we present the first relative importance sampling-off-policy actor-critic (RIS-Off-PAC) model-free algorithms in RL. In our method, the network yields a target policy (the actor), a value function (the critic) assessing the current policy ($\pi$), and behavior policy. We use action value generated from the behavior policy to train our algorithm rather than from the target policy. We also use deep neural networks to train both actor and critic. We evaluated our algorithm on a number of Open AI Gym benchmark problems and demonstrate better or comparable performance to several state-of-the-art RL baselines.

### Off-Policy Policy Gradient Algorithms by Constraining the State Distribution Shift

Off-policy deep reinforcement learning (RL) algorithms are incapable of learning solely from batch offline data without online interactions with the environment, due to the phenomenon known as \textit{extrapolation error}. This is often due to past data available in the replay buffer that may be quite different from the data distribution under the current policy. We argue that most off-policy learning methods fundamentally suffer from a \textit{state distribution shift} due to the mismatch between the state visitation distribution of the data collected by the behavior and target policies. This data distribution shift between current and past samples can significantly impact the performance of most modern off-policy based policy optimization algorithms. In this work, we first do a systematic analysis of state distribution mismatch in off-policy learning, and then develop a novel off-policy policy optimization method to constraint the state distribution shift. To do this, we first estimate the state distribution based on features of the state, using a density estimator and then develop a novel constrained off-policy gradient objective that minimizes the state distribution shift. Our experimental results on continuous control tasks show that minimizing this distribution mismatch can significantly improve performance in most popular practical off-policy policy gradient algorithms.