  Annealed Importance Sampling (AIS) moves particles along a Markov chain from
a tractable initial distribution to an intractable target distribution. The
recently proposed Differentiable AIS (DAIS) (Geffner and 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., 2017;
Naesseth et al., 2018; Le et al., 2018).
