Particle Filter Optimization: A Bayesian Approach for Global Stochastic Optimization

Abstract

This paper proposes a novel global optimization algorithm, Particle Filter-Based Optimization (PFO), designed for a class of stochastic optimization problems in which the objective function lacks an analytical form and is subject to noisy evaluations. PFO utilizes the Bayesian inference framework of Particle Filters (PF) by reformulating the optimization task as a state estimation problem. In this context, evaluations of the objective function are interpreted as measurements, and a customized transition model based on covariance ellipsoids is introduced to guide particle propagation. This model serves as a surrogate for classical acquisition functions, equipping the PF framework with local search capabilities and supporting efficient exploration of the global optimum. To mitigate the adverse effects of measurement noise, the Unscented Transform (UT) is employed to approximate the underlying mean of the objective function, enhancing the accuracy of particle updates. The algorithm offers notable improvements over existing stochastic optimization algorithms for black-box multi-modal objective functions. First, PFO provides a fully probabilistic definition of particle weights, enhancing adaptability and robustness. Second, PFO integrates exploration and exploitation within a unified Bayesian framework, ensuring a non-zero probability of sampling from unexplored regions throughout the optimization process. This approach contrasts with traditional particle filter methods that are primarily used for state estimation, and heuristic optimization algorithms that lack theoretical guarantees. The novelty of PFO lies in its unique integration of particle filtering with a dynamic search space prediction, offering a theoretically grounded alternative to acquisition functions in Bayesian Optimization (BO).