Policy Gradient Method For Robust Reinforcement Learning (2205.07344v1)

Abstract: This paper develops the first policy gradient method with global optimality guarantee and complexity analysis for robust reinforcement learning under model mismatch. Robust reinforcement learning is to learn a policy robust to model mismatch between simulator and real environment. We first develop the robust policy (sub-)gradient, which is applicable for any differentiable parametric policy class. We show that the proposed robust policy gradient method converges to the global optimum asymptotically under direct policy parameterization. We further develop a smoothed robust policy gradient method and show that to achieve an $\epsilon$-global optimum, the complexity is $\mathcal O(\epsilon^{-3})$. We then extend our methodology to the general model-free setting and design the robust actor-critic method with differentiable parametric policy class and value function. We further characterize its asymptotic convergence and sample complexity under the tabular setting. Finally, we provide simulation results to demonstrate the robustness of our methods.

Overview of Policy Gradient Method for Robust Reinforcement Learning

This paper presents an investigation into developing a policy gradient method tailored for robust reinforcement learning that ensures global optimality despite model mismatch. Through this paper, the authors introduce a novel method that not only extends the capabilities of policy gradient methods but also provides a complexity analysis for robust reinforcement learning.

The primary motivation stems from the challenges posed when the simulator model deviates from real-world implementation, leading to performance degradation. The paper identifies the uncertainty within model mismatch as a critical aspect of applied reinforcement learning, especially in environments affected by adversarial perturbations or inherent non-stationarity. In response, the paper advocates the robust Markov decision process (MDP) framework, targeted at optimizing policy against the worst-case scenarios dictated by an uncertainty set of MDPs.

The paper makes substantial contributions in several key areas:

1. Robust Policy Gradient Development: The authors introduce the robust policy (sub-)gradient methodology applicable to any differentiable parametric policy class. The paper demonstrates that the gradient applies almost everywhere, a necessity given the non-differentiable landscape of robust value functions. This generalizability is a noteworthy strength of the proposed approach.
2. Global Optimality and Complexity Analysis: Building on techniques from vanilla policy gradients, the authors show that global optimality can be achieved despite obstacles posed by the non-differentiable robust value functions. Under direct parametric policy class assumptions, the robust policy gradient method is proven to satisfy the Polyak-{\L}ojasiewicz (PL) condition, enabling convergence to a global optimum.
3. Smoothed Robust Policy Gradient Method: To address the intricacies linked to non-differentiable objectives, the paper proposes a smoothed robust policy gradient approximation. The smoothed method ensures convergence within a complexity of $\mathcal{O}(\epsilon^{-3})$ to an $\epsilon$-global optimum.
4. Model-free Robust Actor-Critic Methodology: The paper extends robust policy gradient into a versatile actor-critic method effective in model-free settings. The use of differentiable parametric policy classes and value functions is a modern approach that showcases adaptability to real-world problems characterized by limited sample availability.
5. Empirical Investigations: Through simulations, the paper substantiates the robustness of its methods, offering empirical support to theoretical claims. These investigations further validate the practical implications by demonstrating superior performance under model mismatch conditions compared to conventional methods.

Implications and Future Directions

The paper ultimately opens further avenues in robust reinforcement learning by offering a framework to tackle reliability challenges ubiquitous in AI applications with skewed models. Practically, these robust methods hold promise for implementations in environments susceptible to adversarial attacks or unpredicted changes in dynamics.

Theoretically, bridging the gap between robust MDPs and practical implementable policy methods underlines the need for continuous exploration into substantial parametric and non-parametric extensions. As reinforced learning continue to evolve, exploring real-world difficulties such as data corruption or adversarial conditions remains imperative.

In conclusion, the methods laid out in the paper offer a solid foundation in policy gradient approaches for robust RL, with viability seen in both theoretical refinement and scalable practical deployment. Future work could build on these strategies by enriching the scope with robust natural policy gradients or extending to diverse uncertainty set models.