Distributed Forward-Backward algorithms for stochastic generalized Nash equilibrium seeking

2020

Preprint

Self Cite

We consider the stochastic generalized Nash equilibrium problem (SGNEP) with joint feasibility constraints and expected-value cost functions. We propose a distributed stochastic preconditioned projected reflected gradient algorithm and show its almost sure convergence when the pseudogradient mapping is cocoercive. The algorithm is based on monotone operator splitting methods for SGNEPs when the expected-value pseudogradient mapping is approximated at each iteration via an increasing number of samples of the random variable, an approach known as sample average approximation. Finally, we show that a non-preconditioned variant of our proposed algorithm has less restrictive convergence guarantees than stateof-the-art (preconditioned) forward-backward algorithms.

“…(iv) Φ −1 D is maximally monotone. Proof: it follows from [8] and [15]. To guarantee that the weak sharpness property holds, we assume to have a strong solution.…”

Section: Convergence Under Uniqueness Of Solutionmentioning

confidence: 99%

Section: A Illustrative Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Distributed projected-reflected-gradient algorithms for stochastic generalized Nash equilibrium problems

Franci¹,

2020

Preprint

Self Cite

“…We propose two theoretical comparison between the most used algorithms for GANs [8]. In both the examples, we simulate our SRFB algorithm, the SpFB algorithm [15], the EG algorithm [13], the EG algorithm with extrapolation from the past (PastEG) [8] and Adam, a typical algorithm for GANs [20].…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…The iterates of the FB algorithm involve an evaluation of the pseudogradient and a projection step. These iterates are known to converge if the pseudogradient mapping is cocoercive or strongly monotone [14], [15]. However, such technical assumptions are quite strong if we consider that in GANs the mapping is rarely monotone.…”

Section: Introductionmentioning

confidence: 99%

A game-theoretic approach for Generative Adversarial Networks

Franci¹,

2020

Preprint

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Generative adversarial networks (GANs) are a class of generative models, known for producing accurate samples. The key feature of GANs is that there are two antagonistic neural networks: the generator and the discriminator. The main bottleneck for their implementation is that the neural networks are very hard to train. One way to improve their performance is to design reliable algorithms for the adversarial process. Since the training can be cast as a stochastic Nash equilibrium problem, we rewrite it as a variational inequality and introduce an algorithm to compute an approximate solution. Specifically, we propose a stochastic relaxed forward-backward algorithm for GANs. We prove that when the pseudogradient mapping of the game is monotone, we have convergence to an exact solution or in a neighbourhood of it.

Stochastic generalized Nash equilibrium seeking in merely monotone games

Franci¹,

2020

Preprint

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We solve the stochastic generalized Nash equilibrium (SGNE) problem in merely monotone games with expected value cost functions. Specifically, we present the first distributed SGNE seeking algorithm for monotone games that only requires one proximal computation (e.g., one projection step) and only one pseudogradient evaluation per iteration.Our main contribution is to build upon the relaxed forward-backward operator splitting by Malitsky (Mathematical programming, 2019) and in turn to show almost sure convergence to a SGNE when the expected value of the pseudogradient is approximated by the average over a number of random samples.