Abstract
This paper proves convergence of a sample-path based stochastic gradient-descent algorithm for optimizing expected-value performance measures in discrete event systems. The algorithm uses increasing precision at successive iterations, and it moves against the direction of a generalized gradient of the computed sample performance function. Two convergence results are established: one, for the case where the expected-value function is continuously differentiable; and the other, when that function is nondifferentiable but the sample performance functions are convex. The proofs are based on a version of the uniform law of large numbers which is provable for many discrete event systems where infinitesimal perturbation analysis is known to be strongly consistent.
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Communicated by W. B. Gong
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Shapiro, A., Wardi, Y. Convergence analysis of gradient descent stochastic algorithms. J Optim Theory Appl 91, 439–454 (1996). https://doi.org/10.1007/BF02190104
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DOI: https://doi.org/10.1007/BF02190104