Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering

TL;DR

This paper introduces a novel particle filtering method that uses Frank-Wolfe optimization to position particles more effectively, leading to improved accuracy over traditional sampling methods, especially when evaluations are costly.

Contribution

It proposes replacing random sampling in particle filters with Frank-Wolfe optimization for better particle placement, enhancing accuracy in expensive evaluation scenarios.

Findings

Improved accuracy over random and quasi-Monte Carlo sampling.

Effective in robot localization tasks.

Applicable when emission probability evaluations are costly.

Abstract

Recently, the Frank-Wolfe optimization algorithm was suggested as a procedure to obtain adaptive quadrature rules for integrals of functions in a reproducing kernel Hilbert space (RKHS) with a potentially faster rate of convergence than Monte Carlo integration (and "kernel herding" was shown to be a special case of this procedure). In this paper, we propose to replace the random sampling step in a particle filter by Frank-Wolfe optimization. By optimizing the position of the particles, we can obtain better accuracy than random or quasi-Monte Carlo sampling. In applications where the evaluation of the emission probabilities is expensive (such as in robot localization), the additional computational cost to generate the particles through optimization can be justified. Experiments on standard synthetic examples as well as on a robot localization task indicate indeed an improvement of accuracy over random and quasi-Monte Carlo sampling.