Relational Reasoning via Set Transformers: Provable Efficiency and Applications to MARL

TL;DR

This paper demonstrates that transformers can perform complex relational reasoning in multi-agent reinforcement learning, providing provable efficiency guarantees and addressing the curse of many agents.

Contribution

It introduces and analyzes transformer-based algorithms for MARL with theoretical guarantees, including a novel generalization error bound and the first provably efficient permutation-invariant MARL algorithm.

Findings

Transformer-based algorithms mitigate the curse of many agents.

Suboptimality gaps are independent or logarithmic in the number of agents.

The generalization bound applies broadly to transformer regression problems.

Abstract

The cooperative Multi-A gent R einforcement Learning (MARL) with permutation invariant agents framework has achieved tremendous empirical successes in real-world applications. Unfortunately, the theoretical understanding of this MARL problem is lacking due to the curse of many agents and the limited exploration of the relational reasoning in existing works. In this paper, we verify that the transformer implements complex relational reasoning, and we propose and analyze model-free and model-based offline MARL algorithms with the transformer approximators. We prove that the suboptimality gaps of the model-free and model-based algorithms are independent of and logarithmic in the number of agents respectively, which mitigates the curse of many agents. These results are consequences of a novel generalization error bound of the transformer and a novel analysis of the Maximum Likelihood Estimate (MLE) of the system dynamics with the transformer. Our model-based algorithm is the first provably efficient MARL algorithm that explicitly exploits the permutation invariance of the agents. Our improved generalization bound may be of independent interest and is applicable to other regression problems related to the transformer beyond MARL.