Finite-sample bounds for waste-free SMC without spectral-gap assumptions

Establish finite-sample error bounds for waste-free Sequential Monte Carlo when the Markov kernels do not admit an L2 spectral gap, for example under warm-start mixing-time assumptions analogous to those used to analyze standard SMC with fast-mixing kernels such as MALA.

Background

The paper develops finite-sample guarantees for waste-free SMC under spectral-gap assumptions and provides mixing-time–based guarantees for standard SMC without requiring a spectral gap.

For tempering with fast-mixing kernels (e.g., MALA), the best complexity bounds are currently for standard SMC; whether analogous finite-sample bounds can be proven for waste-free SMC without spectral gaps is currently unresolved.