Reinforcement learning over a frozen reasoner is a common recipe for teaching a policy which external tools to invoke. In specialist scientific settings where the full tool‑subset space is enumerable, this recipe becomes structurally mismatched. Only a small set of reusable computational capabilities covers the domain, so the combinatorial space of tool subsets is small enough to enumerate. GRPO (Group‑Normalized Policy Optimization) still estimates an action expectation from a handful of sampled rollouts, and the approximation error grows as training progresses. As the policy concentrates on preferred subsets, sampled rewards collide, the group‑normalized advantage vanishes, and the fraction of questions with no reward signal rises from 0.2% under a uniform reference policy to 20.8% after GRPO training on genomic reasoning tasks. To remedy this, we introduce FGPO (Full‑Group Policy Optimization) with two key ideas: (1) score every tool subset and optimize the exact action expectation, so each update sees the complete action space; (2) pre‑compute the reward for each question‑subset pair into an exhaustive table, removing frozen‑reasoner calls from the training loop entirely. Across five frozen reasoners and three genomic benchmarks, FGPO outperforms GRPO in all 15 settings by an average of 6.75 points and up to 14.20 points. A standard on‑demand GRPO schedule would require 2.4× as many frozen‑reasoner reward evaluations, and on GenomeQA FGPO reduces invoked tools per question from 2.36 to 1.40.
Review: FGPO achieves precise policy optimization by enumerating all tool subsets and pre‑computing rewards, delivering substantial gains in efficiency and performance for genomic reasoning, and highlighting the advantage of abandoning sampling when the action space is tractable.