We then demonstrate a lower-bound performance guarantee on policies regularized by the stationary state distribution. In practice, SRPO can be an add-on module to context-based algorithms in both online and offline RL settings.

In many real-world scenarios, Reinforcement Learning (RL) algorithms are trained on data with dynamics shift, i.e., with different underlying environment dynamics. A majority of current methods address such issue by training context encoders to identify environment parameters. Data with dynamics shift are separated according to their environment parameters to train the corresponding policy.However, these methods can be sample inefficient as data are used \textit{ad hoc}, and policies trained for one dynamics cannot benefit from data collected in all other environments with different dynamics. In this paper, we find that in many environments with similar structures and different dynamics, optimal policies have similar stationary state distributions. We exploit such property and learn the stationary state distribution from data with dynamics shift for efficient data reuse. Such distribution is used to regularize the policy trained in a new environment, leading to the SRPO (\textbf{S}tate \textbf{R}egularized \textbf{P}olicy \textbf{O}ptimization) algorithm. To conduct theoretical analyses, the intuition of similar environment structures is characterized by the notion of homomorphous MDPs. We then demonstrate a lower-bound performance guarantee on policies regularized by the stationary state distribution. In practice, SRPO can be an add-on module to context-based algorithms in both online and offline RL settings.Experimental results show that SRPO can make several context-based algorithms far more data efficient and significantly improve their overall performance.

To provide an additional demonstrating example to the intuition in Sec.

In many real-world scenarios, Reinforcement Learning (RL) algorithms are trained on data with dynamics shift, i.e., with different underlying environment dynamics. A majority of current methods address such issue by training context encoders to identify environment parameters. Data with dynamics shift are separated according to their environment parameters to train the corresponding policy.However, these methods can be sample inefficient as data are used \textit{ad hoc}, and policies trained for one dynamics cannot benefit from data collected in all other environments with different dynamics. In this paper, we find that in many environments with similar structures and different dynamics, optimal policies have similar stationary state distributions. We exploit such property and learn the stationary state distribution from data with dynamics shift for efficient data reuse.

In many real-world scenarios, Reinforcement Learning (RL) algorithms are trained on data with dynamics shift, i.e., with different underlying environment dynamics. A majority of current methods address such issue by training context encoders to identify environment parameters. Data with dynamics shift are separated according to their environment parameters to train the corresponding policy. However, these methods can be sample inefficient as data are used \textit{ad hoc}, and policies trained for one dynamics cannot benefit from data collected in all other environments with different dynamics. In this paper, we find that in many environments with similar structures and different dynamics, optimal policies have similar stationary state distributions. We exploit such property and learn the stationary state distribution from data with dynamics shift for efficient data reuse. Such distribution is used to regularize the policy trained in a new environment, leading to the SRPO (\textbf{S}tate \textbf{R}egularized \textbf{P}olicy \textbf{O}ptimization) algorithm. To conduct theoretical analyses, the intuition of similar environment structures is characterized by the notion of homomorphous MDPs. We then demonstrate a lower-bound performance guarantee on policies regularized by the stationary state distribution. In practice, SRPO can be an add-on module to context-based algorithms in both online and offline RL settings. Experimental results show that SRPO can make several context-based algorithms far more data efficient and significantly improve their overall performance.

Reinforcement learning (RL) algorithms have been successfully applied to a range of challenging sequential decision making and control tasks. In this paper, we classify RL into direct and indirect methods according to how they seek optimal policy of the Markov Decision Process (MDP) problem. The former solves optimal policy by directly maximizing an objective function using gradient descent method, in which the objective function is usually the expectation of accumulative future rewards. The latter indirectly finds the optimal policy by solving the Bellman equation, which is the sufficient and necessary condition from Bellman's principle of optimality. We take vanilla policy gradient and approximate policy iteration to study their internal relationship, and reveal that both direct and indirect methods can be unified in actor-critic architecture and are equivalent if we always choose stationary state distribution of current policy as initial state distribution of MDP. Finally, we classify the current mainstream RL algorithms and compare the differences between other criteria including value-based and policy-based, model-based and model-free.

The policy gradient theorem is defined based on an objective with respect to the initial distribution over states. In the discounted case, this results in policies that are optimal for one distribution over initial states, but may not be uniformly optimal for others, no matter where the agent starts from. Furthermore, to obtain unbiased gradient estimates, the starting point of the policy gradient estimator requires sampling states from a normalized discounted weighting of states. However, the difficulty of estimating the normalized discounted weighting of states, or the stationary state distribution, is quite well-known. Additionally, the large sample complexity of policy gradient methods is often attributed to insufficient exploration, and to remedy this, it is often assumed that the restart distribution provides sufficient exploration in these algorithms. In this work, we propose exploration in policy gradient methods based on maximizing entropy of the discounted future state distribution. The key contribution of our work includes providing a practically feasible algorithm to estimate the normalized discounted weighting of states, i.e, the \textit{discounted future state distribution}. We propose that exploration can be achieved by entropy regularization with the discounted state distribution in policy gradients, where a metric for maximal coverage of the state space can be based on the entropy of the induced state distribution. The proposed approach can be considered as a three time-scale algorithm and under some mild technical conditions, we prove its convergence to a locally optimal policy. Experimentally, we demonstrate usefulness of regularization with the discounted future state distribution in terms of increased state space coverage and faster learning on a range of complex tasks.

This paper extends our earlier analysis on approximate linear programming as an approach to approximating the cost-to-go function in a discounted-cost dynamic program [6]. In this paper, we consider the average-cost criterion and a version of approximate linear programming that generates approximations to the optimal average cost and differential cost function. We demonstrate that a naive version of approximate linear programming prioritizes approximation of the optimal average cost and that this may not be well-aligned with the objective of deriving a policy with low average cost. For that, the algorithm should aim at producing a good approximation of the differential cost function. We propose a twophase variant of approximate linear programming that allows for external control of the relative accuracy of the approximation of the differential cost function over different portions of the state space via state-relevance weights. Performance bounds suggest that the new algorithm is compatible with the objective of optimizing performance and provide guidance on appropriate choices for state-relevance weights.