A deterministic analysis of stochastic approximation with randomized directions

We study the convergence of two stochastic approximation algorithms with ra ndomized directions: the simultaneous perturbation stochastic approximation algorithm and the random direction Kiefer-Wolfowitz algorithm. We establis h deterministic necessary and sufficient conditions on the random direction s and noise sequences for both algorithms, and these conditions demonstrate the effect of the "random" directions on the "sample-path" behavior of the studied algorithms. We discuss ideas for further research in analysis and design of these algorithms.