Convergence analysis of gradient descent stochastic algorithms |
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Authors: | A Shapiro Y Wardi |
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Institution: | (1) School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia;(2) School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia |
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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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Keywords: | Gradient descent subdifferentials uniform laws of large numbers infinitesimal perturbation analysis discrete event dynamic systems |
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