Revisiting Peng's Q($\lambda$) for Modern Reinforcement Learning

TL;DR

This paper provides the first theoretical convergence proof for Peng's Q(λ), a non-conservative off-policy reinforcement learning algorithm, and demonstrates its practical effectiveness in complex continuous control tasks.

Contribution

It proves Peng's Q(λ) converges to an optimal policy under certain conditions and validates its empirical performance in complex tasks.

Findings

Peng's Q(λ) converges to an optimal policy when the behavior policy tracks a greedy policy.

Peng's Q(λ) often outperforms conservative algorithms in continuous control tasks.

Theoretical analysis confirms Peng's Q(λ) is both sound and effective.

Abstract

Off-policy multi-step reinforcement learning algorithms consist of conservative and non-conservative algorithms: the former actively cut traces, whereas the latter do not. Recently, Munos et al. (2016) proved the convergence of conservative algorithms to an optimal Q-function. In contrast, non-conservative algorithms are thought to be unsafe and have a limited or no theoretical guarantee. Nonetheless, recent studies have shown that non-conservative algorithms empirically outperform conservative ones. Motivated by the empirical results and the lack of theory, we carry out theoretical analyses of Peng's Q($\lambda$), a representative example of non-conservative algorithms. We prove that it also converges to an optimal policy provided that the behavior policy slowly tracks a greedy policy in a way similar to conservative policy iteration. Such a result has been conjectured to be true but has not been proven. We also experiment with Peng's Q($\lambda$) in complex continuous control tasks, confirming that Peng's Q($\lambda$) often outperforms conservative algorithms despite its simplicity. These results indicate that Peng's Q($\lambda$), which was thought to be unsafe, is a theoretically-sound and practically effective algorithm.