Discrete optimization, SPSA and Markov chain Monte Carlo methods

L. Gerencser, S.D. Hill
Proceedings of the 41st IEEE Conference on Decision and Control, 2002.  
The minimization of a convex function defined over the grid Z Z p is considered. A few relevant mathematical devices such as integer convexity, Markov Chain Monte Carlo (MCMC) methods, including stochastic comparison (SC), and simultaneous perturbation stochastic approximation (SPSA)are summarized. A truncated fixed gain SPSA method is proposed and investigated in combination with devices borrowed from the MCMC literature. The main contribution of the paper is the development and testing a
more » ... and testing a number of devices that may eventually improve the convergence properties of the algorithm, such as various truncation techniques, averaging and choices of acceptance probabilities. The basis for comparison of performances is accuracy vs. number of function evaluations. We present experimental evidence for the superiority of an SC method allowing moves in wrong directions with small probability, where the underlying method is an SPSA method using averaging and adaptive truncation.
doi:10.1109/cdc.2002.1184883 fatcat:44tav7smdjajxcdvu64kdseese