FBI method trains for Pass@K with one sample per update at 12.3% of the cost
EmtiyazKhan · x · 2026-10-16
A RIKEN AIP-led preprint (arXiv 2610.17735) introduces finite-K posterior learning with a Fenchel–Bregman IVON (FBI) optimizer.
- Motivation: with K inference attempts, what matters is at least one correct candidate in the pool; training individual attempts doesn't target that, and directly optimizing the K-candidate objective needs K sampled solvers per update.
- Core idea: learn a distribution over solver parameters trained for pool coverage (Pass@K); a Fenchel reformulation splits the objective into a weighted posterior step plus failure tracking, requiring only one parameter draw per update.
- Results: on Maze-Hard, FBI matches Direct-10 on Pass@10 (91.3% vs 91.0%) at 0.0692s vs 0.5614s per update — 12.3% of the training time — and beats GRPO and DMPO on average Pass@K.
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