Anchor-Changing Regularized Natural Policy Gradient for Multi-Objective Reinforcement Learning

Abstract

We study policy optimization for Markov decision processes (MDPs) with multiple reward value functions, which are to be jointly optimized according to given criteria such as proportional fairness (smooth concave scalarization), hard constraints (constrained MDP), and max-min trade-off. We propose an Anchor-changing Regularized Natural Policy Gradient (ARNPG) framework, which can systematically incorporate ideas from well-performing first-order methods into the design of policy optimization algorithms for multi-objective MDP problems. Theoretically, the designed algorithms based on the ARNPG framework achieve Õ(1/T ) global convergence with exact gradients. Empirically, the ARNPG-guided algorithms also demonstrate superior performance compared to some existing policy gradient-based approaches in both exact gradients and sample-based scenarios.We study policy gradient-based approaches that optimize over parameterized policies Π = {π θ : θ ∈ Θ} through policy gradient. In general, the optimization problems above may not be convex in terms of θ, not even for single-objective MDPs with direct parameterization by θ s,a = π θ (a|s) [2]. Due to the nonconvexity, O(1/T ) global convergence of policy gradient-based methods was only established very recently for single-objective MDPs with exact gradients [2,21]. These breakthrough results have motivated the study of policy optimization for multi-objective MDPs, e.g., smooth concave scalarization [5], constrained MDPs (CMDPs) [11,31].However, under the exact gradients scenario, the previous approaches for multi-objective MDPs, either suffer from slow provable O(1/ √ T ) global convergence [11], or require extra assumptions [37,33,18]. The compactness of Θ is assumed in [37], but this assumption forbids a very common softmax parameterization, where Θ = R |S||A| . The NPG-based methods have been analyzed in [33,18] under an ergodicity assumption, but such an assumption is not required for NPG in single-objective MDPs [2], and therefore appears artificial.