Suboptimality Loss for Inverse Learning from Imperfect Equilibria

2026-09-19

AI Summary

本文通过引入衡量玩家单方面偏离观察策略可获得总效用增益的游戏理论次优损失，解决了从不完美均衡中反向学习时对噪声和不一致均衡观测敏感的问题。

Abstract

Many modern systems involve the strategic interaction of multiple agents. In such settings, observed actions typically reflect equilibrium behavior under utilities that are only partially known. Recovering these hidden utilities from data - the central goal of inverse game theory - is key for prediction, counterfactual analysis, and mechanism design. However, existing approaches based on inverse variational inequalities are highly sensitive to noisy and inconsistent equilibrium observations, thus limiting their applicability. In this paper, we resolve this issue by introducing a game-theoretic suboptimality loss that measures the aggregate utility gain players could obtain by unilaterally deviating from an observed strategy profile. First, we show that this loss is convex and admits an efficient decomposition into player-wise best-responses. Second, we show this loss is sandwiched between the predictability loss and the inverse variational inequality loss, making it a tractable surrogate for equilibrium prediction. Third, we develop a mirror descent algorithm to minimize it and demonstrate on a heterogeneous networked Cournot competition that our approach remains accurate under noisy observations and inconsistent equilibrium data while inverse variational inequality methods produce degenerate estimates.

Problem

• inverse game theory
• equilibrium behavior
• hidden utilities
• noisy observations
• inconsistent equilibrium

Innovation

• suboptimality loss
• inverse game theory
• mirror descent algorithm
• noisy observations