Randomized-direction Stochastic Approximation Algorithms Using Deterministic Sequences

We study the convergence and asymptotic normality of a generalized form of stochastic approximation algorithm with deterministic perturbation sequences. Both one-simulation and two-simulation methods are considered. Assuming a special structure of deterministic sequence, we establish sufficient condition on the noise sequence for a.s. convergence of the algorithm. Construction of such a special structure of deterministic sequence follows the discussion of asymptotic normality. Finally we discuss ideas on further research in analysis and design of the deterministic perturbation sequences.