Learning generalized Nash equilibria from pairwise preferences

Researchers Pablo Krupa and Alberto Bemporad have introduced a novel method for solving Generalized Nash Equilibrium Problems (GNEPs), a class of problems central to non-cooperative multi-agent systems in areas like control theory and economics. Traditional methods require full knowledge of each agent's objective function or the ability to query their optimal responses—assumptions often unrealistic in real-world scenarios. This new approach bypasses those requirements by learning equilibria using only pairwise preference queries. Essentially, instead of asking an agent, "What's your best move?" the system asks, "Do you prefer option A or option B?"

The team employs an active-learning strategy that intelligently selects which preference queries to make, balancing the exploration of the decision space with exploitation of the currently learned model. This allows the system to efficiently approximate a Generalized Nash Equilibrium (GNE) of the underlying, unknown problem. In their paper, the researchers demonstrated the method's effectiveness on benchmark GNEP examples and, notably, on game-theoretic linear quadratic regulation problems—a common framework in control systems. The results show the technique can successfully learn stable, optimal strategies for multiple interacting agents using this minimalistic feedback mechanism, opening doors for applications where agent models are opaque or too complex to define explicitly.