Meta-control of an interacting-particle algorithm for global optimization

A common issue for stochastic global optimization algorithms is how to set the parameters of the sampling distribution (e.g. temperature, mutation/cross-over rates, selection rate, etc.) so that the samplings converge to the optimum effectively and efficiently. We consider an interacting-particle algorithm and develop a meta-control methodology which analytically guides the inverse temperature parameter of the algorithm to achieve desired performance characteristics (e.g. quality of the final outcome, algorithm running time, etc.). The main aspect of our meta-control methodology is to formulate an optimal control problem where the fractional change in the inverse temperature parameter is the control variable. The objectives of the optimal control problem are set according to the desired behavior of the interacting-particle algorithm. The control problem considers particles’ average behavior, rather than treating the behavior of individual particles. The solution to the control problem provides feedback on the inverse temperature parameter of the algorithm.