Multi-Agent Imitation Learning: Value is Easy, Regret is Hard (2406.04219v2)

Abstract: We study a multi-agent imitation learning (MAIL) problem where we take the perspective of a learner attempting to coordinate a group of agents based on demonstrations of an expert doing so. Most prior work in MAIL essentially reduces the problem to matching the behavior of the expert within the support of the demonstrations. While doing so is sufficient to drive the value gap between the learner and the expert to zero under the assumption that agents are non-strategic, it does not guarantee robustness to deviations by strategic agents. Intuitively, this is because strategic deviations can depend on a counterfactual quantity: the coordinator's recommendations outside of the state distribution their recommendations induce. In response, we initiate the study of an alternative objective for MAIL in Markov Games we term the regret gap that explicitly accounts for potential deviations by agents in the group. We first perform an in-depth exploration of the relationship between the value and regret gaps. First, we show that while the value gap can be efficiently minimized via a direct extension of single-agent IL algorithms, even value equivalence can lead to an arbitrarily large regret gap. This implies that achieving regret equivalence is harder than achieving value equivalence in MAIL. We then provide a pair of efficient reductions to no-regret online convex optimization that are capable of minimizing the regret gap (a) under a coverage assumption on the expert (MALICE) or (b) with access to a queryable expert (BLADES).

• The paper introduces the regret gap objective, measuring the incentive differences that prompt strategic agent deviations from expert behavior.
• The authors prove that minimizing the regret gap is inherently harder than the value gap, showing single-agent IL approaches fall short in multi-agent contexts.
• They develop MALICE and BLADES algorithms under specific assumptions to efficiently minimize the regret gap, ensuring robust coordination in uncertain environments.

Multi-Agent Imitation Learning: Value is Easy, Regret is Hard

The paper of Multi-Agent Imitation Learning (MAIL) has received considerable attention, particularly in contexts where a group of agents must be coordinated based on expert demonstrations. The paper by Tang, Swamy, Fang, and Wu from Carnegie Mellon University addresses a fundamental gap in our understanding of MAIL problems: What should be the optimal learning objective when attempting to imitate expert behavior in environments involving strategic agents?

The authors explore the limitations of the traditional value gap objective and advocate for an alternative objective, namely the regret gap, which explicitly accounts for potential deviations by strategic agents. The distinction between value gap and regret gap objectives is not only theoretical but has significant practical implications, especially in scenarios where the agents involved are strategic and not merely non-strategic followers of the coordinator’s recommendations.

Key Contributions:

1. Introduction of the Regret Gap Objective: The regret gap measures the difference in the maximum incentive that any agent has to deviate from the coordinator’s recommendations when comparing the learner to the expert. This counterfactual consideration is critical when dealing with strategic agents who may not blindly follow the recommendations.
2. Difference Between Value and Regret Gaps: The authors prove that while the value gap can be minimized using single-agent IL algorithms extended to multi-agent settings, these algorithms do not provide guarantees on minimizing the regret gap. The paper establishes that regret equivalence is inherently more challenging - or "harder" - than value equivalence in MAIL.
3. Efficient Algorithms Under Certain Assumptions:

   The paper presents two efficient algorithms (MALICE and BLADES) to minimize the regret gap under specific assumptions:

   • MALICE operates under a coverage assumption on the expert.
   • BLADES requires access to a queryable expert. These algorithms are shown to minimize the regret gap efficiently, achieving upper bounds of $O(\epsilon u H)$, where $H$ is the horizon length and $\epsilon$ is the respective algorithm’s error term.

Implications and Future Developments:

• Practical Implications:

  The shift from value to regret gap as a learning objective is crucial when dealing with strategic agents. The necessity of considering potential deviations makes the regret gap a more robust measure, ensuring that learned policies perform well even when agents do not follow recommendations perfectly. This has direct applications in routing systems, autonomous driving fleets, and other coordination tasks in uncertain environments.

• Theoretical Contributions:

  The paper highlights a fundamental distinction between single-agent and multi-agent imitation learning, emphasizing the importance of counterfactual reasoning. This insight may inspire further theoretical work on robust multi-agent learning frameworks and stimulate the development of new models that incorporate strategic deviations.

• Future Directions:

  Though the current methods efficiently minimize the regret gap under certain assumptions, future research could focus on relaxing these assumptions or finding novel equivalence guarantees under more general conditions. Additionally, practical implementations and empirical evaluations of MALICE and BLADES in real-world scenarios would validate the theoretical findings.

In conclusion, the exploration of regret in multi-agent imitation learning by Tang et al. provides significant insights and advances the field by challenging traditional objectives and proposing robust alternatives. The distinction between value and regret gaps underscores the necessity for more comprehensive learning paradigms in strategic environments and sets a solid foundation for future evolution in this domain. This work is poised to influence both theoretical research and practical implementations in multi-agent systems.