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Optimal Sampling for Simulated Annealing Under Noise

This paper proposes a simulated annealing variant for optimization problems in which the solution quality can only be estimated by sampling from a random distribution. The aim is to find the solution with the best expected performance, as, e.g., is typical for problems where solutions are evaluated using a stochastic simulation. Assuming Gaussian noise with known standard deviation, we derive a fully sequential sampling procedure and decision rule. The procedure starts with a single sample of the value of a proposed move to a neighboring solution and then continues to draw more samples until it is able to make a decision to accept or reject the move. Under constraints of equilibrium detailed balance at each draw, we find a decoupling between the acceptance criterion and the choice of the rejection criterion. We derive a universally optimal acceptance criterion in the sense of maximizing the acceptance probability per sample and thus the efficiency of the optimization process. We show that the choice of th...