  Auxiliary particle filters (APFs) are a class of sequential Monte Carlo (SMC)
methods for Bayesian inference in state-space models. In their original
derivation, APFs operate in an extended state space using an auxiliary variable
to improve inference. In this work, we propose optimized auxiliary particle
filters, a framework where the traditional APF auxiliary variables are
interpreted as weights in an importance sampling mixture proposal. Under this
interpretation, we devise a mechanism for proposing the mixture weights that is
inspired by recent advances in multiple and adaptive importance sampling. In
particular, we propose to select the mixture weights by formulating a convex
optimization problem, with the aim of approximating the filtering posterior at
each timestep. Further, we propose a weighting scheme that generalizes previous
results on the APF (Pitt et al. 2012), proving unbiasedness and consistency of
our estimators. Our framework demonstrates significantly improved estimates on
a range of metrics compared to state-of-the-art particle filters at similar
computational complexity in challenging and widely used dynamical models.
