On W.P.1 Convergence of A Parallel Stochastic Approximation Algorithm

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Abstract
To find zeros or locate maximum values of a regression function with noisy measurements, a commonly used algorithm is the RM or KW procedure. In various applications, the dimensionality of the problems involved might be quite large. As a result, enormous memory space and extensive computation time may be needed. Motivated by the recent progress in stochastic approximation methods for decentralized and distributed computing, a parallel stochastic approximation algorithm is developed in this paper. The essence is to take advantage of state-space decompositions, and to exploit the opportunities provided by parallel processing and asynchronous communication. In lieu of utilizing a single processor as in the classical cases, a number of parallel processors are employed to solve the underlying problem in a cooperative way. First, the large dimensional vector is partitioned into a number of subvectors with relatively small dimension, then each of the subvectors is assigned to one of the processors. The processors compute and communicate in an asynchronous manner and at random times. Under rather weak conditions, the global convergence of the parallel algorithm is obtained via the methods of randomly varying truncations.