The computation of approximate feedback Stackelberg equilibria in multi-player nonlinear constrained dynamic games
CoRR(2024)
摘要
Solving feedback Stackelberg games with nonlinear dynamics and coupled
constraints, a common scenario in practice, presents significant challenges.
This work introduces an efficient method for computing local feedback
Stackelberg policies in multi-player general-sum dynamic games, with continuous
state and action spaces. Different from existing (approximate) dynamic
programming solutions that are primarily designed for unconstrained problems,
our approach involves reformulating a feedback Stackelberg dynamic game into a
sequence of nested optimization problems, enabling the derivation of
Karush-Kuhn-Tucker (KKT) conditions and the establishment of a second-order
sufficient condition for local feedback Stackelberg policies. We propose a
Newton-style primal-dual interior point method for solving constrained linear
quadratic (LQ) feedback Stackelberg games, offering provable convergence
guarantees. Our method is further extended to compute local feedback
Stackelberg policies for more general nonlinear games by iteratively
approximating them using LQ games, ensuring that their KKT conditions are
locally aligned with those of the original nonlinear games. We prove the
exponential convergence of our algorithm in constrained nonlinear games. In a
feedback Stackelberg game with nonlinear dynamics and (nonconvex) coupled costs
and constraints, our experimental results reveal the algorithm's ability to
handle infeasible initial conditions and achieve exponential convergence
towards an approximate local feedback Stackelberg equilibrium.
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