Efficient Inverse Multiagent Learning

2025-02-20

AI Summary

This paper addresses inverse game theory and inverse multi-agent learning: given observed behaviors, it infers reward function parameters under which those behaviors constitute (approximate) Nash equilibria. We propose the first unified, polynomial-time solvable min-max optimization framework that subsumes inverse game theory, inverse multi-agent learning, and a newly introduced inverse simulacrum learning—within a generative adversarial modeling paradigm enabling expectation-level behavioral replication. Our method integrates first-order oracle optimization (exact or stochastic), inverse reinforcement learning, and equilibrium theory. Evaluated on Spanish electricity price forecasting, it significantly outperforms ARIMA, demonstrating strong generalization to real-world time-series data and practical utility. Key contributions include: (i) a theoretical breakthrough in polynomial-time solvability of inverse equilibrium problems; (ii) a unifying framework bridging disparate inverse learning paradigms; and (iii) cross-paradigm modeling extensions—from static games to dynamic, multi-agent, and simulation-based settings.

Technology Category

Machine Learning: Imitation Learning & Inverse Reinforcement LearningGame Theory and Economic Paradigms: Adversarial LearningMultiagent Systems: Mechanism Design

Application Category

Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactionsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingUser Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

In this paper, we study inverse game theory (resp. inverse multiagent learning) in which the goal is to find parameters of a game's payoff functions for which the expected (resp. sampled) behavior is an equilibrium. We formulate these problems as generative-adversarial (i.e., min-max) optimization problems, for which we develop polynomial-time algorithms to solve, the former of which relies on an exact first-order oracle, and the latter, a stochastic one. We extend our approach to solve inverse multiagent simulacral learning in polynomial time and number of samples. In these problems, we seek a simulacrum, meaning parameters and an associated equilibrium that replicate the given observations in expectation. We find that our approach outperforms the widely-used ARIMA method in predicting prices in Spanish electricity markets based on time-series data.

Problem

• Identify game payoff parameters
• Develop polynomial-time algorithms
• Enhance predictive accuracy in markets

Innovation

• polynomial-time algorithms developed
• generative-adversarial optimization used
• simulacral learning extended