Train for Many, Update with One: Improving Multi-Sample Reasoning via Fenchel-Bregman Posterior Learning
Multi-sample reasoning measures candidate coverage, the probability that at least one of $K$ candidates is correct. However, minimizing the average loss of individual attempts does not directly optimize candidate coverage. We therefore formulate finite-$K$ posterior learning, which trains a distribution over solver parameters to reduce the probability that all $K$ independently generated candidates fail. To optimize this objective efficiently, we propose a Fenchel-Bregman (FB) approach that requires only one posterior draw per update, rather than the $K$ used by direct Monte Carlo optimization. FB first uses an exact Fenchel reformulation to separate problem-specific weights from the post...
| Authors | Sungjun Lim, Adrian Robert Minut, Nico Carlsen Daheim et al. |
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| Primary category | cs.LG |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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