A Markov Chain Monte Carlo Method for Global Optimization using Non-reversible, Stochastic Acceptance Probabilities

In this paper, we present a novel Markov Chain Monte Carlo framework for solving global optimization problems in the continuous domain. At each iterate, our algorithm uses a globally reaching Markov kernel to generate a candidate point in the feasible region. This candidate point is then accepted according to a possibly non-reversible acceptance probability. We derive sufficient conditions on the acceptance probability that guarantee convergence in probability to the globally optimum function value for a continuous objective function defined on a compact feasible region. We show that well known algorithms such as simulated annealing are special cases of this approach. We then extend this result to the case where the acceptance probability is allowed to be stochastic. This situation may arise when we are optimizing the expected value of a stochastic performance measure by using random function value estimates to compute acceptance probabilities. We illustrate how our analysis can be used to derive sufficient conditions for convergence of simulated annealing when applied to problems with noisy objective functions.