All Work And No Play Makes Jack a Dull Boy: Understanding and Preventing Catastrophic Strategy Collapse in RLVR

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving the reasoning ability of large language models. However, widely used RLVR algorithms, such as GRPO, often suffer from entropy collapse, leading to premature determinism and unstable optimization. Existing remedies, including entropy regularization and ratio-based clipping heuristics, either control entropy in a coarse-grained manner or rely on approximate on-policy training. In this paper, we revisit entropy collapse from a token-level entropy flow perspective. Our analysis reveals that entropy-decreasing tokens consistently outweigh entropy-increasing ones, resulting in a severely imbalanced entropy flow. This perspective provides a unified explanation of entropy collapse in existing RLVR algorithms and highlights the importance of balancing entropy dynamics. Motivated by this analysis, we propose On-Policy Entropy Flow Optimization (OPEFO), an adaptive entropy flow balancing mechanism that rescales entropy-increasing and entropy-decreasing updates according to their contributions to entropy change, while remaining strict on-policy. Experiments on six mathematical reasoning benchmarks demonstrate that OPEFO improves training stability and final performance. We will release the code and models upon publication.

Reinforcement learning with verifiable rewards (RLVR) has become a key approach for enhancing the reasoning abilities of large language models. However, RLVR often suffers from diversity collapse: Pass@$1$ improves while high-$k$ Pass@$k$ degrades, which is viewed as a narrowing of the model's reasoning boundary. We formalize this diversity collapse through the lens of overtraining: once a problem's contribution to the reference metric has effectively saturated, further updates no longer expand what the model can solve but still concentrate probability mass on the trajectories favored by on-policy sampling. Under a standard setup with few rollouts per problem, even a single observed success places a problem in a nearly saturated regime for high-$k$ Pass@$k$, so most updates in standard RLVR are overtraining from the boundary perspective. This perspective also suggests a reading of whether RLVR can expand the model's reasoning abilities beyond the base model: since RLVR is structurally biased against high-$k$ Pass@$k$, its aggregate decline does not by itself mean that no new reasoning gains occurred. Interventionally, restricting updates to problems with zero observed success lifts Pass@$256$ above the base model on difficult benchmarks; observationally, a non-trivial fraction of initially unsolvable problems become solvable during standard RLVR training. Building on these findings, we propose Bayesian Boundary Gating (BBG), which redirects optimization away from overtraining by estimating each problem's marginal contribution to the reasoning boundary. Across multiple reasoning benchmarks, BBG improves average Pass@$k$ across a wide range of $k$.

Reinforcement Learning from Verifiable Rewards (RLVR) is a key driver for Large Reasoning Models, but it is vulnerable to "zero-reward collapse", a training failure where a sudden increase in task difficulty causes the learning signal to vanish. We argue that the conventional approach of discarding these failed trajectories is wasteful, as they contain valuable diagnostic information about the model's cognitive gaps, a bright side that can be leveraged for recovery. Existing solutions, however, often regress to static, "off-policy-style" interventions like pre-defined hint libraries or perform post-hoc refinement, failing to provide the adaptive, forward-looking guidance needed to escape the collapse. To address this, we propose a paradigm shift towards on-policy pedagogical intervention and introduce MENTOR, a multi-agent framework that acts as a live mentor. MENTOR diagnoses the root cause of failure in real-time and dynamically generates targeted, instructional prompts to guide the learning agent's next attempt. As a plug-and-play module, MENTOR integrates seamlessly into existing policy optimization pipelines like GRPO without modifying the training infrastructure. Extensive experiments on math and code generation show that MENTOR effectively mitigates zero-reward collapse, outperforming state-of-the-art baselines. Notably, it achieves massive average relative gains of up to 78.3% on Llama-3.2-3B-Instruct over its base model.