Switch Updating in SPSA Algorithm for Stochastic Optimization with Inequality Constraints

Abstract: Simultaneous perturbation stochastic approximation (SPSA) is widely used in stochastic optimization due to its high efficiency, asymptotic stability, and reduced number of required loss function measurements. However, the standard SPSA algorithm needs to be modified to deal with constrained problems. In recent years, sequential quadratic programming (SQP)-based projection ideas and penalty ideas have been analyzed. Both ideas have convergence results and a potentially wide range of applications, but with some limitations in practical consideration, such as computation time, complexity, and feasibility guarantee. We propose an SPSA-based switch updating algorithm, which updates based on the loss function or the inequality constraints, depending on current feasibility in each iteration. We show convergence results for the algorithm, and analyze its properties relative to other methods. We also numerically compare the switch updating algorithm with the penalty function approach for two constrained examples.