  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.
