# Why Sample What You Can Enumerate? Exact Policy Optimization for Genomic Tool Selection

arXiv: https://arxiv.org/abs/2609.10221 · HTML: https://mlsanity.com/paper/2609.10221/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 42 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 26 of 26)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [HuggingGPT: Solving AI Tasks with ChatGPT and its Friends in Hugging Face](https://mlsanity.com/paper/2303.17580/) (2023)
- [API-Bank: A Comprehensive Benchmark for Tool-Augmented LLMs](https://mlsanity.com/paper/2304.08244/) (2023)
- [InternLM2 Technical Report](https://mlsanity.com/paper/2403.17297/) (2024)
- [ToolRL: Reward is All Tool Learning Needs](https://mlsanity.com/paper/2504.13958/) (2025)
- [Chameleon: Plug-and-Play Compositional Reasoning with Large Language Models](https://mlsanity.com/paper/2304.09842/) (2023)
- [HyenaDNA: Long-Range Genomic Sequence Modeling at Single Nucleotide Resolution](https://mlsanity.com/paper/2306.15794/) (2023)
- [GeneGPT: Augmenting Large Language Models with Domain Tools for Improved Access to Biomedical Information](https://mlsanity.com/paper/2304.09667/) (2023)
- [Caduceus: Bi-Directional Equivariant Long-Range DNA Sequence Modeling](https://mlsanity.com/paper/2403.03234/) (2024)
- [VisualToolAgent (VisTA): A Reinforcement Learning Framework for Visual Tool Selection](https://mlsanity.com/paper/2505.20289/) (2025)
- [Expected Policy Gradients for Reinforcement Learning](https://mlsanity.com/paper/1801.03326/) (2018)
- [Expected Policy Gradients](https://mlsanity.com/paper/1706.05374/) (2017)
- [Mean Actor Critic](https://mlsanity.com/paper/1709.00503/) (2017)
- [How Many Tools Should an LLM Agent See? A Chance-Corrected Answer](https://mlsanity.com/paper/2605.24660/) (2026)
- [AuTAgent: A Reinforcement Learning Framework for Tool-Augmented Audio Reasoning](https://mlsanity.com/paper/2602.13685/) (2026)
- [GenomeQA: Benchmarking General Large Language Models for Genome Sequence Understanding](https://mlsanity.com/paper/2604.05774/) (2026)

## Abstract (arXiv)

Reinforcement learning over a frozen reasoner has become a common recipe for teaching a policy which external tools to invoke. We show that this recipe becomes structurally mismatched in specialist scientific settings where the complete tool-subset space is enumerable. There, a small set of recurring computational capabilities covers the domain, so the space of tool subsets is combinatorial yet small enough to enumerate, and GRPO still estimates an action expectation from a handful of sampled rollouts. Worse, the approximation degrades as training succeeds: as the policy concentrates on preferred subsets it resamples them, sampled rewards collide, and the group-normalized advantage vanishes. On genomic reasoning the fraction of questions yielding no reward signal rises from 0.2% under a uniform reference policy to 20.8% after GRPO training. As a remedy, we introduce FGPO (Full-Group Policy Optimization), which (1) scores every tool subset and optimizes the exact action expectation, so each update sees the complete action space, and (2) precomputes the reward of 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 6.75 points on average and up to 14.20, while a standard on-demand GRPO schedule would require 2.4 times as many frozen-reasoner reward evaluations and, on GenomeQA, FGPO cuts invoked tools per question from 2.36 to 1.40.