Proximal Learning With Opponent-Learning Awareness

TL;DR

This paper introduces proximal LOLA (POLA), a new multi-agent reinforcement learning algorithm that improves upon LOLA by being parameterization invariant, leading to more reliable reciprocity-based cooperation in complex environments.

Contribution

The paper reinterprets LOLA as a proximal operator and develops POLA, a parameterization-invariant algorithm that enhances cooperation in multi-agent settings.

Findings

POLA achieves more reliable reciprocity-based cooperation than LOLA.

POLA's updates are parameterization invariant, ensuring behaviorally equivalent policies lead to similar updates.

Empirical results show POLA outperforms LOLA in complex partially competitive environments.

Abstract

Learning With Opponent-Learning Awareness (LOLA) (Foerster et al. [2018a]) is a multi-agent reinforcement learning algorithm that typically learns reciprocity-based cooperation in partially competitive environments. However, LOLA often fails to learn such behaviour on more complex policy spaces parameterized by neural networks, partly because the update rule is sensitive to the policy parameterization. This problem is especially pronounced in the opponent modeling setting, where the opponent's policy is unknown and must be inferred from observations; in such settings, LOLA is ill-specified because behaviorally equivalent opponent policies can result in non-equivalent updates. To address this shortcoming, we reinterpret LOLA as approximating a proximal operator, and then derive a new algorithm, proximal LOLA (POLA), which uses the proximal formulation directly. Unlike LOLA, the POLA updates are parameterization invariant, in the sense that when the proximal objective has a unique optimum, behaviorally equivalent policies result in behaviorally equivalent updates. We then present practical approximations to the ideal POLA update, which we evaluate in several partially competitive environments with function approximation and opponent modeling. This empirically demonstrates that POLA achieves reciprocity-based cooperation more reliably than LOLA.