On the Global Optimum Convergence of Momentum-based Policy Gradient

TL;DR

This paper proves the first global convergence results for momentum-based policy gradient methods in reinforcement learning, showing improved sample complexity and providing a framework for analyzing stochastic PG algorithms.

Contribution

It establishes the first global convergence guarantees for momentum-enhanced policy gradient methods, with improved sample complexity bounds for different policy parametrizations.

Findings

Momentum improves global optimality sample complexity.

First single-loop, finite-batch PG algorithm with $ ilde{O}( ext{epsilon}^{-3})$ complexity.

Framework applicable to various PG estimators.

Abstract

Policy gradient (PG) methods are popular and efficient for large-scale reinforcement learning due to their relative stability and incremental nature. In recent years, the empirical success of PG methods has led to the development of a theoretical foundation for these methods. In this work, we generalize this line of research by studying the global convergence of stochastic PG methods with momentum terms, which have been demonstrated to be efficient recipes for improving PG methods. We study both the soft-max and the Fisher-non-degenerate policy parametrizations, and show that adding a momentum improves the global optimality sample complexity of vanilla PG methods by $\tilde{\mathcal{O}}(\epsilon^{-1.5})$ and $\tilde{\mathcal{O}}(\epsilon^{-1})$, respectively, where $\epsilon>0$ is the target tolerance. Our work is the first one that obtains global convergence results for the momentum-based PG methods. For the generic Fisher-non-degenerate policy parametrizations, our result is the first single-loop and finite-batch PG algorithm achieving $\tilde{O}(\epsilon^{-3})$ global optimality sample complexity. Finally, as a by-product, our methods also provide general framework for analyzing the global convergence rates of stochastic PG methods, which can be easily applied and extended to different PG estimators.