Multi-Time Scale Smoothed Functional With Nesterov’s Acceleration

Abstract

Smoothed functional (SF) algorithm estimates the gradient of the stochastic optimization problem by convolution with a smoothening kernel. This process helps the algorithm to converge to a global minimum or a point close to it. We study a two-time scale SF based gradient search algorithm with Nesterov’s acceleration for stochastic optimization problems. The main contribution of our work is to prove the convergence of this algorithm using the stochastic approximation theory. We propose a novel Lyapunov function to show the associated second-order ordinary differential equations’ (o.d.e.) stability for a non-autonomous system. We compare our algorithm with other smoothed functional algorithms such as Quasi-Newton SF, Gradient SF and Jacobi Variant of Newton SF on two different optimization problems: first, on a simple stochastic function minimization problem, and second, on the problem of optimal routing in a queueing network. Additionally, we compared the algorithms on real weather data in a weather prediction task. Experimental results show that our algorithm performs significantly better than these baseline algorithms.