Risk aware modeling improves predictions in large multi group systems
Beyond Nominal Equilibria: Risk-Averse Multi-Population Mean-Field Games
Computer Science and Game TheoryMachine Learning
Summary
When many different groups interact, it is hard to predict what will happen because each group’s behavior is uncertain. The authors study a way to model these systems by letting each group plan for the worst possible scenarios coming from other groups’ behaviors. They prove that under reasonable conditions, there exists a stable solution where everyone acts based on this cautious approach. They also show how to find such solutions by repeatedly simulating best responses while considering risk. Their experiments show that this method converges and captures risk-averse decisions in complex multi-group settings.
What this means in practice
- •For transportation planners: Model traffic flows involving different traveler groups while accounting for uncertainty in others’ behaviors.
- •For energy grid operators: Improve management of interconnected energy consumers and producers by modeling risk-averse reactions to uncertain demands.
Authors
Bhavini Jeloka, Siddhartha Ganguly, Panagiotis Tsiotras
Abstract
Recent advances in mean-field games and its multi-population variants enable large-scale heterogeneous multi-agent systems to be modeled through representative agents and their associated mean-field distributions. However, existing approaches do not explicitly account for uncertainty in the behavior of other populations. To this end, we introduce a new paradigm: risk-averse multi-population mean-field games, where each population optimizes a worst-case expected reward over dynamically feasible ambiguity sets of mean-field flows of a subset of the other populations. Employing an occupation-measure formulation along with tools from set-valued analysis, we establish, under mild assumptions, several theoretical properties of the multi-population game, including the geometric properties of the ambiguity sets and the existence of a novel risk-averse multi-population mean-field equilibrium. Further, we derive contractivity results of the fixed-point operator under entropy regularization and show that it can be utilized to learn the equilibrium. Finally, we propose a risk-averse fictitious-play scheme and show that exploitability decays to zero, despite the additional nonlinearity introduced by the worst-case objective. We report several numerical experiments to illustrate convergence and risk-averse behavior.