Linear Generalized Nash Equilibrium Problems

In der vorliegenden Arbeit werden verallgemeinerte Nash Spiele (LGNEPs) unter Linearitätsannahmen eingeführt und untersucht. Durch Ausnutzung der speziellen Struktur lassen sich theoretische und algorithmische Resultate erzielen, die weit über die Ergebnisse für allgemeine LGNEPs hinausgehen

Stochastic mirror descent dynamics and their convergence in monotone variational inequalities

We examine a class of stochastic mirror descent dynamics in the context of monotone variational inequalities (including Nash equilibrium and saddle-point problems). The dynamics under study are formulated as a stochastic differential equation driven by a (single-valued) monotone operator and perturbed by a Brownian motion. The system's controllable parameters are two variable weight sequences that respectively pre- and post-multiply the driver of the process. By carefully tuning these parameters, we obtain global convergence in the ergodic sense, and we estimate the average rate of convergence of the process. We also establish a large deviations principle showing that individual trajectories exhibit exponential concentration around this average.Comment: 23 pages; updated proofs in Section 3 and Section

Online Convex Optimization for Sequential Decision Processes and Extensive-Form Games

Regret minimization is a powerful tool for solving large-scale extensive-form games. State-of-the-art methods rely on minimizing regret locally at each decision point. In this work we derive a new framework for regret minimization on sequential decision problems and extensive-form games with general compact convex sets at each decision point and general convex losses, as opposed to prior work which has been for simplex decision points and linear losses. We call our framework laminar regret decomposition. It generalizes the CFR algorithm to this more general setting. Furthermore, our framework enables a new proof of CFR even in the known setting, which is derived from a perspective of decomposing polytope regret, thereby leading to an arguably simpler interpretation of the algorithm. Our generalization to convex compact sets and convex losses allows us to develop new algorithms for several problems: regularized sequential decision making, regularized Nash equilibria in extensive-form games, and computing approximate extensive-form perfect equilibria. Our generalization also leads to the first regret-minimization algorithm for computing reduced-normal-form quantal response equilibria based on minimizing local regrets. Experiments show that our framework leads to algorithms that scale at a rate comparable to the fastest variants of counterfactual regret minimization for computing Nash equilibrium, and therefore our approach leads to the first algorithm for computing quantal response equilibria in extremely large games. Finally we show that our framework enables a new kind of scalable opponent exploitation approach