A regularized adaptive steplength stochastic approximation scheme for monotone stochastic variational inequalities

Authors:
Farzad Yousefian;Angelia Nedić;Uday V. Shanbhag
Affiliations:
UIUC, S. Mathews, Urbana, IL;UIUC, S. Mathews, Urbana, IL;UIUC, S. Mathews, Urbana, IL
Venue:
Proceedings of the Winter Simulation Conference
Year:
2011

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Abstract

We consider the solution of monotone stochastic variational inequalities and present an adaptive steplength stochastic approximation framework with possibly multivalued mappings. Traditional implementations of SA have been characterized by two challenges. First, convergence ofstandard SA schemes requiresa strongly or strictly monotone single-valued mapping, a requirement that is rarely met. Second, while convergence requires that the steplength sequences need to satisfy Σk γk = ∞ and Σk γk2 γk = 1/k may often perform poorly in practice. Motivated by the minimization of a suitable error bound, a recursive rule for prescribing steplengths is proposed for strongly monotone problems. By introducing a regularization sequence, extensions to merely monotone regimes are proposed. Finally, an iterative smoothing extension is suggested for accommodating multivalued mappings. Preliminary numerical results suggest that the schemes prove effective.