Learning generalized Nash equilibria from pairwise preferences
This addresses a limitation in multi-agent control and game theory by enabling equilibrium learning from limited preference data, though it is incremental as it builds on existing GNEP frameworks.
The paper tackles the problem of learning generalized Nash equilibria (GNEs) without requiring full knowledge of objective functions or best responses, by using pairwise preference queries from agents and an active-learning strategy. The method is shown to be effective in numerical experiments on game-theoretic linear quadratic regulation and other GNEP examples.
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.