Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering
This is an incremental improvement for applications like robot localization where evaluating emission probabilities is expensive.
The paper tackled the problem of improving particle filter accuracy by replacing random sampling with Frank-Wolfe optimization to optimize particle positions, resulting in better accuracy than random or quasi-Monte Carlo sampling in synthetic examples and a robot localization task.
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.