Recent progress in parallel stochastic approximations

Abstract

Parallel recursive algorithms of stochastic approximation type are discussed. The basic idea is to utilize a collection of parallel processors in lieu of using a single one alone as in the classical algorithms. The processors compute and communicate with each other asynchronously. By asynchronous implementations, we mean that each processor updates on its own pace, and uses the most recently received information from other processors. Several procedures are dealt with. These include distributed communicating schemes via convexifications, parallel algorithms with interacting processors and renewal type of computation times, and real time implementable procedures with pipeline arrangements. It appears that from the closed connection between real world applications and mathematical theories, the study of parallel stochastic approximation methods gains not only much of its special appeal, but also much of its intrinsic tension. The main emphasis and interest are the asymptotic properties of the algorithms. The parallel interacting algorithm and its variation are used as representatives for illustrating various limiting results. Convergence and rate of convergence issues are addressed, and robustness analysis is carried out.