# Reinforcement Learning without Ground-Truth Solutions can Improve LLMs

arXiv: https://arxiv.org/abs/2606.27369 · HTML: https://mlsanity.com/paper/2606.27369/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 53 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 30 of 47)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [WebSailor: Navigating Super-human Reasoning for Web Agent](https://mlsanity.com/paper/2507.02592/) (2025)
- [WebDancer: Towards Autonomous Information Seeking Agency](https://mlsanity.com/paper/2505.22648/) (2025)
- [LLM Post-Training: A Deep Dive into Reasoning Large Language Models](https://mlsanity.com/paper/2502.21321/) (2025)
- [OpenCoder: The Open Cookbook for Top-Tier Code Large Language Models](https://mlsanity.com/paper/2411.04905/) (2024)
- [Learning to Discover at Test Time](https://mlsanity.com/paper/2601.16175/) (2026)
- [OctoThinker: Mid-training Incentivizes Reinforcement Learning Scaling](https://mlsanity.com/paper/2506.20512/) (2025)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [Watch Every Step! LLM Agent Learning via Iterative Step-Level Process Refinement](https://mlsanity.com/paper/2406.11176/) (2024)
- [Process Reward Model with Q-Value Rankings](https://mlsanity.com/paper/2410.11287/) (2024)
- [NPHardEval: Dynamic Benchmark on Reasoning Ability of Large Language Models via Complexity Classes](https://mlsanity.com/paper/2312.14890/) (2023)
- [Can Language Models Solve Olympiad Programming?](https://mlsanity.com/paper/2404.10952/) (2024)
- [On the Interplay of Pre-Training, Mid-Training, and RL on Reasoning Language Models](https://mlsanity.com/paper/2512.07783/) (2025)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) for training LLMs typically rely on ground-truth answers to assign rewards, limiting their applicability to tasks where the ground-truth solution is unknown. We introduce a Ranking-induced VERifiable framework (RiVER) that trains LLMs on score-based optimization tasks without ground-truth solutions, using deterministic execution feedback as continuous-valued supervision. When applying group-relative RL to such continuous rewards, we identify two key challenges: scale dominance, where uncalibrated score magnitudes across test instances distort policy updates, and frequency dominance, where repeatedly sampled suboptimal solutions can outweigh rare but stronger candidates. RiVER addresses these challenges with calibrated reward shaping that uses instance-wise comparisons and emphasizes top-ranked solvers while retaining bounded feedback for other valid solutions. We train on 12 AtCoder Heuristic Contest tasks and evaluate on Algorithm Engineering Benchmark (ALE-Bench), LiveCodeBench, and USACO. RiVER advances Qwen3-8B and GLM-Z1-9B-0414 by 8.9% and 9.4% in ALE rating rank. More importantly, despite training exclusively on score-based tasks without any ground-truth solutions, RiVER also improves the backbones across exact-solution benchmarks such as LiveCodeBench and USACO by an absolute average improvement of 2.4% and 3.5%. By contrast, baselines trained with raw execution scores improve ALE rating but fail to transfer to exact-solution benchmarks. These results suggest that score-based optimization tasks, combined with proper reward calibration, can serve as effective training environments for general coding ability without ground-truth solutions.