# Enhanced LLM Reasoning by Optimizing Reward Functions with Search-Driven Reinforcement Learning

arXiv: https://arxiv.org/abs/2605.02073 · HTML: https://mlsanity.com/paper/2605.02073/

## 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 27 of its 33 references that are in the map.
- First posted on arXiv 3 May 2026.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Eureka: Human-Level Reward Design via Coding Large Language Models](https://mlsanity.com/paper/2310.12931/) (2023)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Language to Rewards for Robotic Skill Synthesis](https://mlsanity.com/paper/2306.08647/) (2023)
- [Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning](https://mlsanity.com/paper/2502.14768/) (2025)
- [Reward Design with Language Models](https://mlsanity.com/paper/2303.00001/) (2023)
- [Inverse Reward Design](https://mlsanity.com/paper/1711.02827/) (2017)
- [Text2Reward: Reward Shaping with Language Models for Reinforcement Learning](https://mlsanity.com/paper/2309.11489/) (2023)
- [On Learning Intrinsic Rewards for Policy Gradient Methods](https://mlsanity.com/paper/1804.06459/) (2018)
- [Evolved Policy Gradients](https://mlsanity.com/paper/1802.04821/) (2018)
- [Automated Reinforcement Learning (AutoRL): A Survey and Open Problems](https://mlsanity.com/paper/2201.03916/) (2022)
- [A Large Language Model-Driven Reward Design Framework via Dynamic Feedback for Reinforcement Learning](https://mlsanity.com/paper/2410.14660/) (2024)
- [EAGER: Asking and Answering Questions for Automatic Reward Shaping in Language-guided RL](https://mlsanity.com/paper/2206.09674/) (2022)
- [REvolve: Reward Evolution with Large Language Models using Human Feedback](https://mlsanity.com/paper/2406.01309/) (2024)

## Abstract (arXiv)

Mathematical reasoning is a key benchmark for large language models. Reinforcement learning is a standard post-training mechanism for improving the reasoning capabilities of large language models, yet performance remains sensitive to the design of the reward function that drives policy optimization. This paper introduces a search-driven framework that treats the reward specification itself as an object of optimization. The setting of interest is one in which the base model is held fixed and the reward specification is the primary remaining design lever. Candidate reward functions are generated by a frontier language model, validated automatically, screened through 500-step Group Relative Policy Optimization (GRPO) training runs on a Llama-3.2-3B-Instruct base model with Low-Rank Adaptation (LoRA), and ranked by F1 on the GSM8K test set. Ranked summaries from prior rounds are then fed back into the next round of generation. Over five rounds, the search produces 50 candidate rewards. The mean F1 rises from 0.596 in Round 1 to 0.632 in Round 5, and the top individual reward reaches F1 = 0.787. Seven ensemble configurations of top-ranked rewards are evaluated. The best ensemble achieves F1 = 0.795 (95% bootstrap CI [0.756, 0.832]) and accuracy 0.660 [0.635, 0.686], a 0.19 absolute F1 gain over a base-rewards-only GRPO baseline (F1 = 0.609). Pairwise McNemar tests with Bonferroni correction show all five-or-more-reward configurations are statistically indistinguishable at α = 0.05/21. A three-seed re-training of the best ensemble yields F1 of 0.785. A randomly drawn 5-reward control collapses to F1 = 0.047, which shows that the ranked-feedback loop, not the additive signal of having more rewards, drives the gain.