Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplers

The recently proposed Differentiable AIS (DAIS) (Geffner & Domke, 2021; Zhang et al., 2021) enables efficient optimization of the transition kernels of AIS and of the distributions. However, we observe a low effective sample size in DAIS, indicating degenerate distributions. We thus propose to extend DAIS by a resampling step inspired by Sequential Monte Carlo. Surprisingly, we find empirically--and can explain theoretically--that it is not necessary to differentiate through the resampling step, which avoids gradient variance issues observed in similar approaches for Particle Filters (Maddison et al., 2017a; Naesseth et al., 2018; Le et al., 2018). Figure 1: ESS for DAIS and Related Work Differentiable PFs construct a lower bound on the DSMCS at epochs 100 and log marginal likelihood utilizing the filtering distribution (e.g.