Regularized Iterative Stochastic Approximation Methods for Stochastic Variational Inequality Problems

Jayash Koshal, Angelia Nedic, Uday V. Shanbhag
2013 IEEE Transactions on Automatic Control  
We consider a Cartesian stochastic variational inequality problem with a monotone map. For this problem, we develop and analyze distributed iterative stochastic approximation algorithms. Monotone stochastic variational inequalities arise naturrally, for instance, from the equilibrium conditions of monotone stochastic Nash games over continuous strategy sets. We introduce two classes of stochastic approximation methods, each of which requires exactly one projection step at every iteration, and
more » ... ry iteration, and provide convergence analysis for them. Of these, the first is the stochastic iterative Tikhonov regularization method which necessitates the update of regularization parameter after every iteration. The second method is a stochastic iterative proximal-point method, where the centering term is updated after every iteration. Conditions are provided for recovering global convergence in limited coordination extensions of such schemes where agents are allowed to choose their steplength sequences, regularization and centering parameters independently, while meeting a suitable coordination requirement. We apply the proposed class of techniques and their limited coordination versions to a stochastic networked rate allocation problem.
doi:10.1109/tac.2012.2215413 fatcat:57euexu4jjfe3jhbwwgxm5uhxm