Multiple Importance Sampling for Guided Speculative Inference

We study an extension of the Guided Speculative Inference (GSI) algorithm for test-time-scaling of large language models (LLMs) to a novel setting where an ensemble of smaller LLMs proposes draft reasoning steps which are later verified by a larger base model and a process reward model. Using the established framework of multiple importance sampling (MIS), we introduce weighting schemes to aggregate samples from a diverse collection of proposal distributions. We provide new bounds on the KL divergence from the optimal reward-tilted target distribution and the expected reward degradation, then demonstrate that the well-known balance heuristic is optimal. Compared to GSI with a single well-tuned drafter, combining several diverse LLMs while retaining the same total number of samples maintains competitive pass-at-$N$ downstream performance while being mathematically robust to situations where the support of a single draft model does not cover that of the target, where GSI may fail.