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Annealed Importance Sampling (AIS) moves particles along a Markov chain froma tractable initial distribution to an intractable target distribution. Therecently proposed Differentiable AIS (DAIS) (Geffner and Domke, 2021; Zhang etal., 2021) enables efficient optimization of the transition kernels of AIS andof the distributions. However, we observe a low effective sample size in DAIS,indicating degenerate distributions. We thus propose to extend DAIS by aresampling step inspired by Sequential Monte Carlo. Surprisingly, we findempirically-and can explain theoretically-that it is not necessary todifferentiate through the resampling step which avoids gradient variance issuesobserved in similar approaches for Particle Filters (Maddison et al., 2017;Naesseth et al., 2018; Le et al., 2018).

Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplers