Sequential Monte Carlo Samplers (SMCS) constitute a widely used class of SMC algorithms that calculate normalizing constants and simulate complex multi-modal target distributions. Typically, SMCS utilizes a process known as annealing, which propagates solutions from a tractable reference distribution to the intractable target through a continuous path of increasingly complex distributions. SMCS delivers state-of-the-art performance when adequately tuned, although this can pose a challenge for current tuning methods, yielding a random run-time and compromising the normalizing constant's unbiasedness.

In this talk, we intend to describe all the components of an SMCS algorithm and their influence on the variance of the normalizing constant. Specifically, we will demonstrate that SMCS exhibits fundamentally different behaviour in large particle and dense schedule limits. The dense schedule limit reveals the natural geometry induced by annealing, which can pinpoint optimal performance and tune the number of particles, number of annealing distributions, annealing schedules, the resampling schedule, and the path. Lastly, we propose an efficient, black-box algorithm for tuning SMCS that delivers optimal performance within a fixed, user-specified computation budget, all while preserving the unbiasedness of the normalizing constant.