Rates of Convergence of Adaptive Step-Size of Stochastic Approximation Algorithms

We propose a new adaptive algorithm with decreasing step-size for stochastic approximations. The use of adaptive algorithms in various applications is widely spread across fields such as system identification and adaptive control. We analyze the rate of convergence of the proposed algorithms. An averaging algorithm, on its optimality of the rate of convergence, is used to control the step sizes. Our proofs are based on recent results in stochastic approximations and Gaussian Approximation Theorem.