Nonexpansive Markov Operators and Random Function Iterations for Stochastic Fixed Point Problems

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant mea- sure the stochastic fixed point problem. This generalizes earlier work studying the stochastic feasibility problem, namely, to find points that are, with probability 1, fixed points of … Read more

A Different Perspective on the Stochastic Convex Feasibility Problem

We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is meant for a point to approximately solve the constraints, determining bounds on the expected number of iterations reduces to … Read more