# PPO-HSC: An Exploratory Reinforcement Learning Framework Based on Wide-Area Policy Coverage Optimization

arXiv: https://arxiv.org/abs/2607.16206 · HTML: https://mlsanity.com/paper/2607.16206/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 6 of its 10 references that are in the map.
- First posted on arXiv 8 May 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 6 of 6)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Unifying Count-Based Exploration and Intrinsic Motivation](https://mlsanity.com/paper/1606.01868/) (2016)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)

## Abstract (arXiv)

This paper introduces PPO-HSC (Proximal Policy Optimization with High-order Sampling Coverage), an exploratory reinforcement learning framework designed to address the "Invisible Shackles" of mode collapse in Large Language Model (LLM) fine-tuning. While standard Reinforcement Learning from Verifiable Rewards (RLVR) effectively reinforces high-reward trajectories, it often leads models to over-optimize known solutions, sacrificing curiosity and the ability to explore broader solution manifolds. To overcome this, PPO-HSC incorporates a High-order Sampling Coverage (HSC) reward that incentivizes the discovery of "low-similarity yet high-validity" reasoning patterns. By maintaining a dynamic trajectory library of verified unique solutions, the framework provides a differentiable signal that rewards semantic novelty while ensuring structural rationality through a plausibility constraint. Empirical evaluations on mathematical reasoning (GSM8K, SVAMP) and code generation tasks demonstrate that PPO-HSC significantly enhances solution diversity and state-space coverage while maintaining or surpassing the accuracy and syntax integrity of state-of-the-art RL baselines.