Training Generative Adversarial Networks via Stochastic Nash Games

Generative adversarial networks (GANs) are a class of generative models with two antagonistic neural networks: a generator and a discriminator. These two neural networks compete against each other through an adversarial process that can be modeled as a stochastic Nash equilibrium problem. Since the associated training process is challenging,...

Optimal Selection and Tracking of Generalized Nash Equilibria in Monotone Games

A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE seeking algorithms have in fact convergence guarantees toward an arbitrary, possibly inefficient,...

Local Stackelberg equilibrium seeking in generalized aggregative games

We propose a two-layer, semi-decentralized algorithm to compute a local solution to the Stackelberg equilibrium problem in aggregative games with coupling constraints. Specifically, we focus on a single-leader, multiple follower problem, and after equivalently recasting the Stackelberg game as a mathematical program with complementarity...

Nash equilibrium seeking under partial-decision information: monotonicity, smoothness and proximal-point algorithms

We consider Nash equilibrium problems in a partial-decision information scenario, where each agent can only exchange information with some neighbors, while its cost function possibly depends on the strategies of all agents. We characterize the relation between several monotonicity and smoothness assumptions postulated in the literature....

A distributed forward-backward algorithm for stochastic generalized Nash equilibrium seeking

We consider the stochastic generalized Nash equilibrium problem (SGNEP) with expected-value cost functions. Inspired by Yi and Pavel (2019), we propose a distributed generalized Nash equilibrium seeking algorithm based on the preconditioned forward-backward operator splitting for SGNEPs, where, at each iteration, the expected value of the...

Full-EoS based thermal multiphase compositional simulation of CO₂ and steam injection processes

Several compositional reservoir simulators based on equations of state (EoS) have been designed. Yet, few of them can deal with thermal processes such as steam injection and no fully compositional thermal simulation of the steam injection process has been proposed with extra-heavy oils yet. Those simulations appear essential and will offer...