arXiv subjects

Till Freihaut

Publications and source records attributed to Till Freihaut.

5 recordsLinked to original sources

arXiv2026

Multi-agent imitation learning with function approximation: Linear Markov games and beyond

In this work, we present the first theoretical analysis of multi-agent imitation learning (MAIL) in linear Markov games where both the transition dynamics and each agent's reward function are linear in some given features. We demonstrate that by leveraging this structure, it is possible to replace the state-action level "all policy deviation concentrability coefficient" (Freihaut et al., arXiv:2510.09325) with a concentrability coefficient defined at the feature level which can be much smaller than the state-action analog when the features are informative about states' similarity. Furthermore, to circumvent the need for any concentrability coefficient, we turn to the interactive setting. We provide the first, computationally efficient, interactive MAIL algorithm for linear Markov games and show that its sample complexity depends only on the dimension of the feature map $d$. Building on these theoretical findings, we propose a deep MAIL interactive algorithm which clearly outperforms BC on games such as Tic-Tac-Toe and Connect4.

cs.LG↗

arXiv2025

Rate optimal learning of equilibria from data

We close open theoretical gaps in Multi-Agent Imitation Learning (MAIL) by characterizing the limits of non-interactive MAIL and presenting the first interactive algorithm with near-optimal sample complexity. In the non-interactive setting, we prove a statistical lower bound that identifies the all-policy deviation concentrability coefficient as the fundamental complexity measure, and we show that Behavior Cloning (BC) is rate-optimal. For the interactive setting, we introduce a framework that combines reward-free reinforcement learning with interactive MAIL and instantiate it with an algorithm, MAIL-WARM. It improves the best previously known sample complexity from $\mathcal{O}(\varepsilon^{-8})$ to $\mathcal{O}(\varepsilon^{-2}),$ matching the dependence on $\varepsilon$ implied by our lower bound. Finally, we provide numerical results that support our theory and illustrate, in environments such as grid worlds, where Behavior Cloning fails to learn.

cs.LG↗

arXiv2025

Learning Equilibria from Data: Provably Efficient Multi-Agent Imitation Learning

This paper provides the first expert sample complexity characterization for learning a Nash equilibrium from expert data in Markov Games. We show that a new quantity named the single policy deviation concentrability coefficient is unavoidable in the non-interactive imitation learning setting, and we provide an upper bound for behavioral cloning (BC) featuring such coefficient. BC exhibits substantial regret in games with high concentrability coefficient, leading us to utilize expert queries to develop and introduce two novel solution algorithms: MAIL-BRO and MURMAIL. The former employs a best response oracle and learns an $\varepsilon$-Nash equilibrium with $\mathcal{O}(\varepsilon^{-4})$ expert and oracle queries. The latter bypasses completely the best response oracle at the cost of a worse expert query complexity of order $\mathcal{O}(\varepsilon^{-8})$. Finally, we provide numerical evidence, confirming our theoretical findings.

cs.LG↗

arXiv2025

Clustered KL-barycenter design for policy evaluation

In the context of stochastic bandit models, this article examines how to design sample-efficient behavior policies for the importance sampling evaluation of multiple target policies. From importance sampling theory, it is well established that sample efficiency is highly sensitive to the KL divergence between the target and importance sampling distributions. We first analyze a single behavior policy defined as the KL-barycenter of the target policies. Then, we refine this approach by clustering the target policies into groups with small KL divergences and assigning each cluster its own KL-barycenter as a behavior policy. This clustered KL-based policy evaluation (CKL-PE) algorithm provides a novel perspective on optimal policy selection. We prove upper bounds on the sample complexity of our method and demonstrate its effectiveness with numerical validation.

cs.LG↗

arXiv2024

On Feasible Rewards in Multi-Agent Inverse Reinforcement Learning

Multi-agent Inverse Reinforcement Learning (MAIRL) aims to recover agent reward functions from expert demonstrations. We characterize the feasible reward set in Markov games, identifying all reward functions that rationalize a given equilibrium. However, equilibrium-based observations are often ambiguous: a single Nash equilibrium can correspond to many reward structures, potentially changing the game's nature in multi-agent systems. We address this by introducing entropy-regularized Markov games, which yield a unique equilibrium while preserving strategic incentives. For this setting, we provide a sample complexity analysis detailing how errors affect learned policy performance. Our work establishes theoretical foundations and practical insights for MAIRL.

cs.LG↗