Differentiable Particle Filtering via Entropy-Regularized Optimal Transport
This addresses a key bottleneck in variational inference for non-linear state-space models, offering a more stable and efficient approach for practitioners in fields like robotics and signal processing, though it is incremental as it builds on existing optimal transport ideas.
The paper tackled the problem of non-differentiable loss functions and high variance gradient estimates in particle filtering due to traditional resampling methods, by introducing a differentiable particle filter using entropy-regularized optimal transport, which demonstrated improved performance in various applications.
Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF, necessary to obtain low variance likelihood and states estimates. However, traditional resampling methods result in PF-based loss functions being non-differentiable with respect to model and PF parameters. In a variational inference context, resampling also yields high variance gradient estimates of the PF-based evidence lower bound. By leveraging optimal transport ideas, we introduce a principled differentiable particle filter and provide convergence results. We demonstrate this novel method on a variety of applications.