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Exploiting Structure in Offline Multi-Agent RL: The Benefits of Low Interaction Rank

Wenhao Zhan, Scott Fujimoto, Zheqing Zhu, Jason D. Lee, Daniel R. Jiang, Yonathan Efroni

TL;DR

The paper tackles the challenge of learning approximate equilibria in offline multi-agent RL by introducing interaction rank (IR) as a structural assumption on reward decompositions. It proves that low-IR functions are markedly more robust to distribution shift, enabling decentralized, regularized, no-regret learning for contextual games and Markov games with decoupled transitions. The proposed Decentralized χ^2-Regularized Policy Gradient (CG) and Decentralized Regularized Actor-Critic (DR-AC) frameworks achieve polynomial sample complexity in the number of agents when the IR is small and single-agent concentrability holds. The work contrasts with prior offline MARL methods by offering oracle-efficient, decentralized algorithms with provable guarantees and demonstrates empirically that low-IR critics outperform more expressive joint-action or single-agent critics in offline settings, underscoring the practical value of exploiting IR structure.

Abstract

We study the problem of learning an approximate equilibrium in the offline multi-agent reinforcement learning (MARL) setting. We introduce a structural assumption -- the interaction rank -- and establish that functions with low interaction rank are significantly more robust to distribution shift compared to general ones. Leveraging this observation, we demonstrate that utilizing function classes with low interaction rank, when combined with regularization and no-regret learning, admits decentralized, computationally and statistically efficient learning in offline MARL. Our theoretical results are complemented by experiments that showcase the potential of critic architectures with low interaction rank in offline MARL, contrasting with commonly used single-agent value decomposition architectures.

Exploiting Structure in Offline Multi-Agent RL: The Benefits of Low Interaction Rank

TL;DR

The paper tackles the challenge of learning approximate equilibria in offline multi-agent RL by introducing interaction rank (IR) as a structural assumption on reward decompositions. It proves that low-IR functions are markedly more robust to distribution shift, enabling decentralized, regularized, no-regret learning for contextual games and Markov games with decoupled transitions. The proposed Decentralized χ^2-Regularized Policy Gradient (CG) and Decentralized Regularized Actor-Critic (DR-AC) frameworks achieve polynomial sample complexity in the number of agents when the IR is small and single-agent concentrability holds. The work contrasts with prior offline MARL methods by offering oracle-efficient, decentralized algorithms with provable guarantees and demonstrates empirically that low-IR critics outperform more expressive joint-action or single-agent critics in offline settings, underscoring the practical value of exploiting IR structure.

Abstract

We study the problem of learning an approximate equilibrium in the offline multi-agent reinforcement learning (MARL) setting. We introduce a structural assumption -- the interaction rank -- and establish that functions with low interaction rank are significantly more robust to distribution shift compared to general ones. Leveraging this observation, we demonstrate that utilizing function classes with low interaction rank, when combined with regularization and no-regret learning, admits decentralized, computationally and statistically efficient learning in offline MARL. Our theoretical results are complemented by experiments that showcase the potential of critic architectures with low interaction rank in offline MARL, contrasting with commonly used single-agent value decomposition architectures.
Paper Structure (50 sections, 18 theorems, 125 equations, 4 figures, 2 tables, 2 algorithms)

This paper contains 50 sections, 18 theorems, 125 equations, 4 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. General-sum contextual MG.
  4. Policy and value functions.
  5. Offline equilibrium learning.
  6. Interaction Rank Implies Robustness to Distribution Shift
  7. Relation to Taylor series.
  8. Bounded interaction rank implies distribution shift robustness.
  9. Warm Up: Contextual Games
  10. Offline CG.
  11. Algorithm: Decentralized $\chi^2$-Regularized Policy Gradient.
  12. Theoretical analysis.
  13. Optimal bias-variance tradeoff.
  14. Polynomial sample complexity with single-agent concentrability.
  15. Proof highlights.
  16. ...and 35 more sections

Key Result

Theorem 1

If $f^{\star}$ and $\widehat{f}$ are $K$-IR, we have

Figures (4)

  • Figure 1: Network diagrams for the $i$th agent.
  • Figure 2: Comparison of TD3+BC instantiated with different critic architectures, i) 1-IR critic, ii) 2-IR critic, and iii) joint-action critic. The underlying true reward is a 2-IR. This figure showcases the advantage of using 2-IR critic architecture compared to 1-IR or the general joint-action critics when the underlying model is 2-IR. The shaded area represents the standard error across trials.
  • Figure 3: Comparison of TD3+BC instantiated with different critic architectures, i) 1-IR critic, ii) 2-IR critic, and iii) joint-action critic. The underlying true reward is a 2-IR. The shaded area represents the standard error computed across trials.
  • Figure 4: Comparison of TD3+BC instantiated with different critic architectures, i) 1-IR critic, ii) 2-IR critic, and iii) joint-action critic. The underlying true reward is a 1-IR. The shaded area represents the standard error computed across trials.

Theorems & Definitions (26)

  • Definition 1: Coarse Correlated Equilibrium
  • Definition 2: Interaction Rank
  • Theorem 1
  • Remark 1
  • Theorem 2: Informal
  • Lemma 1: Sub-function Alignment for $K=2$, informal
  • Remark 2
  • Theorem 3
  • Remark 3
  • Lemma 2: Q-function estimation error
  • ...and 16 more