Abstract
We show that the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm with projection may exhibit slow convergence in constrained stochastic optimization problems when the optimum is situated on the constraints. The cause of the slow convergence is a geometric interaction between the projection operator and the SPSA gradient estimate. The effect of this interaction can be described as “bouncing of iterates against the constraints.” We describe this on two low dimensional noise-free examples, and present a new algorithm that does not exhibit the bouncing effect and the consequent slow convergence.
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