Learning generalized Nash equilibria from pairwise preferences

TL;DR

This paper introduces a novel active-learning approach to learn generalized Nash equilibria solely from pairwise preference queries, enabling equilibrium approximation without explicit knowledge of agents' objective functions.

Contribution

The paper proposes a new method for learning GNEPs from preference data using active learning, bypassing the need for explicit objective functions or best response queries.

Findings

Effective in approximating GNEs from preference data

Demonstrated success on linear quadratic regulation problems

Applicable to various GNEP examples in literature

Abstract

Generalized Nash Equilibrium Problems (GNEPs) arise in many applications, including non-cooperative multi-agent control problems. Although many methods exist for finding generalized Nash equilibria, most of them rely on assuming knowledge of the objective functions or being able to query the best responses of the agents. We present a method for learning solutions of GNEPs only based on querying agents for their preference between two alternative decisions. We use the collected preference data to learn a GNEP whose equilibrium approximates a GNE of the underlying (unknown) problem. Preference queries are selected using an active-learning strategy that balances exploration of the decision space and exploitation of the learned GNEP. We present numerical results on game-theoretic linear quadratic regulation problems, as well as on other literature GNEP examples, showing the effectiveness of the proposed method.