Single timescale regularized stochastic approximation schemes for monotone nash games under uncertainty

Jayash Koshal, Angelia Nedich, Uday V. Shanbhag

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (Scopus)

Abstract

In this paper, we consider the distributed computation of equilibria arising in monotone stochastic Nash games over continuous strategy sets. Such games arise in settings when the gradient map of the player objectives is a monotone mapping over the cartesian product of strategy sets, leading to a monotone stochastic variational inequality. We consider the application of projection-based stochastic approximation (SA) schemes. However, such techniques are characterized by a key shortcoming: in their traditional form, they can only accommodate strongly monotone mappings. In fact, standard extensions of SA schemes for merely monotone mappings require the solution of a sequence of related strongly monotone problems, a natively two-timescale scheme. Accordingly, we consider the development of single timescale techniques for computing equilibria when the associated gradient map does not admit strong monotonicity. We first show that, under suitable assumptions, standard projection schemes can indeed be extended to allow for strict, rather than strong monotonicity. Furthermore, we introduce a class of regularized SA schemes, in which the regularization parameter is updated at every step, leading to a single timescale method. The scheme is a stochastic extension of an iterative Tikhonov regularization method and its global convergence is established. To aid in networked implementations, we consider an extension to this result where players are allowed to choose their steplengths independently and show the convergence of the scheme if the deviation across their choices is suitably constrained.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages231-236
Number of pages6
DOIs
StatePublished - 2010
Externally publishedYes
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

Fingerprint

Stochastic Approximation
Approximation Scheme
Monotone
Time Scales
Game
Uncertainty
Monotone Mapping
Monotonicity
Strongly Monotone Mapping
Projection
Gradient
Iterative Regularization
Distributed Computation
Tikhonov Regularization
Regularization Parameter
Cartesian product
Regularization Method
Global Convergence
Variational Inequalities
Deviation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Koshal, J., Nedich, A., & Shanbhag, U. V. (2010). Single timescale regularized stochastic approximation schemes for monotone nash games under uncertainty. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 231-236). [5717489] https://doi.org/10.1109/CDC.2010.5717489

Single timescale regularized stochastic approximation schemes for monotone nash games under uncertainty. / Koshal, Jayash; Nedich, Angelia; Shanbhag, Uday V.

2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 231-236 5717489.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Koshal, J, Nedich, A & Shanbhag, UV 2010, Single timescale regularized stochastic approximation schemes for monotone nash games under uncertainty. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717489, pp. 231-236, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717489
Koshal J, Nedich A, Shanbhag UV. Single timescale regularized stochastic approximation schemes for monotone nash games under uncertainty. In 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 231-236. 5717489 https://doi.org/10.1109/CDC.2010.5717489
Koshal, Jayash ; Nedich, Angelia ; Shanbhag, Uday V. / Single timescale regularized stochastic approximation schemes for monotone nash games under uncertainty. 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. pp. 231-236
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