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

Ruida Zhou, Tao Liu, Dileep Kalathil, Panganamala Kumar, Chao Tian

Keywords: Multi-Objective Markov Decision Process, Constrained Markov Decision Process, Policy Optimization

TL;DR: We propose an anchor-changing natural policy gradient framework to incorporate ideas from first-order methods into policy optimization with fundamental theoretical guarantees as well as superior empirical performances for multi-objective MDP.

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 $\tilde{O}(1/T)$ 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.