Consistent Opponent Modeling in Imperfect-Information Games

TL;DR

This paper introduces a new opponent modeling algorithm for imperfect-information games that guarantees convergence to the true opponent strategy using a convex optimization approach, outperforming existing methods.

Contribution

The paper proposes a novel, efficient opponent modeling algorithm that guarantees convergence to the true opponent strategy in imperfect-information games, unlike prior approaches.

Findings

The new algorithm guarantees convergence to the true opponent strategy.

It efficiently solves a convex minimization problem using projected gradient descent.

The approach outperforms existing opponent modeling methods in imperfect-information settings.

Abstract

The goal of agents in multi-agent environments is to maximize total reward against the opposing agents that are encountered. Following a game-theoretic solution concept, such as Nash equilibrium, may obtain a strong performance in some settings; however, such approaches fail to capitalize on historical and observed data from repeated interactions against our opponents. Opponent modeling algorithms integrate machine learning techniques to exploit suboptimal opponents utilizing available data; however, the effectiveness of such approaches in imperfect-information games to date is quite limited. We show that existing opponent modeling approaches fail to satisfy a simple desirable property even against static opponents drawn from a known prior distribution; namely, they do not guarantee that the model approaches the opponent's true strategy even in the limit as the number of game iterations approaches infinity. We develop a new algorithm that is able to achieve this property and runs efficiently by solving a convex minimization problem based on the sequence-form game representation using projected gradient descent. The algorithm is guaranteed to efficiently converge to the opponent's true strategy under standard Bayesian identifiability and visitation assumptions, given observations from gameplay and possibly additional historical data if it is available.