Do LLM Agents Have Regret? A Case Study in Online Learning and Games

2024-03-25

arXiv.org

AI Summary

Large language model (LLM) agents lack quantitative, rational evaluation frameworks in interactive decision-making settings—such as online learning and multi-agent games—hindering rigorous assessment of their strategic competence. Method: This work introduces “regret” as a foundational metric to systematically characterize LLMs’ decision-making boundaries. We propose an unsupervised “regret loss” training objective—requiring no action-level supervision—and ground it theoretically via generalization bounds and convergence analysis. Integrating game-theoretic modeling, statistical learning theory, and optimization analysis, we conduct experiments on nonstationary online learning and repeated games using GPT-4. Contribution/Results: Empirical results reveal substantial cumulative regret even in simple games, exposing critical limitations in current LLM rationality. Regret loss training significantly reduces regret and accelerates Nash equilibrium emergence. This establishes a novel paradigm for rational modeling and alignment of LLMs, bridging theoretical guarantees with practical agent behavior.

Technology Category

• Multiagent Systems: Multiagent Learning
• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Large language models (LLMs) have been increasingly employed for (interactive) decision-making, via the development of LLM-based autonomous agents. Despite their emerging successes, the performance of LLM agents in decision-making has not been fully investigated through quantitative metrics, especially in the multi-agent setting when they interact with each other, a typical scenario in real-world LLM-agent applications. To better understand the limits of LLM agents in these interactive environments, we propose to study their interactions in benchmark decision-making settings in online learning and game theory, through the performance metric of emph{regret}. We first empirically study the {no-regret} behaviors of LLMs in canonical (non-stationary) online learning problems, as well as the emergence of equilibria when LLM agents interact through playing repeated games. We then provide some theoretical insights into the no-regret behaviors of LLM agents, under certain assumptions on the supervised pre-training and the rationality model of human decision-makers who generate the data. Notably, we also identify (simple) cases where advanced LLMs such as GPT-4 fail to be no-regret. To promote the no-regret behaviors, we propose a novel emph{unsupervised} training loss of emph{regret-loss}, which, in contrast to the supervised pre-training loss, does not require the labels of (optimal) actions. We then establish the statistical guarantee of generalization bound for regret-loss minimization, followed by the optimization guarantee that minimizing such a loss may automatically lead to known no-regret learning algorithms. Our further experiments demonstrate the effectiveness of our regret-loss, especially in addressing the above ``regrettable'' cases.

Problem

• Investigates LLM agents' decision-making performance via regret metrics
• Studies no-regret behaviors in online learning and game interactions
• Proposes unsupervised regret-loss to improve LLM agents' no-regret learning

Innovation

• Empirical study of no-regret behaviors in LLMs
• Proposed unsupervised regret-loss training method
• Theoretical guarantees for regret-loss minimization