A Global Stochastic Optimization Particle Filter Algorithm

TL;DR

This paper presents G-PFSO, a novel online stochastic optimization algorithm that efficiently finds global maxima in multi-modal functions using particle filters and averaging techniques, with proven convergence properties.

Contribution

Introduces G-PFSO, a new particle filter-based algorithm for global stochastic optimization with theoretical convergence guarantees and practical effectiveness.

Findings

Successfully finds the highest mode of the objective function.

Converges to the global maximizer at the optimal rate.

Effective in challenging estimation problems.

Abstract

We introduce a new online algorithm for expected log-likelihood maximization in situations where the objective function is multi-modal and/or has saddle points, that we term G-PFSO. The key element underpinning G-PFSO is a probability distribution which (a) is shown to concentrate on the target parameter value as the sample size increases and (b) can be efficiently estimated by means of a standard particle filter algorithm. This distribution depends on a learning rate, where the faster the learning rate the quicker it concentrates on the desired element of the search space, but the less likely G-PFSO is to escape from a local optimum of the objective function. In order to achieve a fast convergence rate with a slow learning rate, G-PFSO exploits the acceleration property of averaging, well-known in the stochastic gradient literature. Considering several challenging estimation problems, the numerical experiments show that, with high probability, G-PFSO successfully finds the highest mode of the objective function and converges to its global maximizer at the optimal rate. While the focus of this work is expected log-likelihood maximization, the proposed methodology and its theory apply more generally for optimizing a function defined through an expectation.