Off-Policy Learning to Reason Works Because It Is More Pessimistic Than You Think

Reinforcement learning (RL) has significantly enhanced the reasoning capabilities of large language models (LLMs), yet the training process remains notoriously fragile. In this work, we investigate a critical source of this instability: over-optimization, where models exploit training heuristics at the expense of generalizable reasoning. While reverse KL regularization is the standard defense against such degradation, our analysis reveals that it is often insufficient in this regime, as it fails to ensure comprehensive coverage of the reference distribution. To address this, we propose ARMOR (Anchor Rollout and Mixed Optimization for RL), a framework that shifts the paradigm from passive penalty to active sample stabilization. ARMOR comprises two key components: (1) Anchor Rollout, which leverages off-policy data from the reference policy to preserve established solution patterns; and (2) Mixed Optimization, which reformulates the policy objective to enable controlled exploration without relying on auxiliary losses. Extensive experiments on reasoning benchmarks validate that ARMOR effectively mitigates validation collapse, enabling sustained performance improvements over extended training horizons.

On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

Reinforcement learning (RL) has gained growing attention in large language model (LLM) post-training, yet RL training remains fragile and can suffer from instability or collapse. One vital cause is training-inference mismatch: LLM adopts separate inference and training engines for generation efficiency and training precision, which in practice exhibits inconsistent probabilities for the same trajectories on training and inference sides, even with synchronized model parameters. This naturally induces a special type of off-policyness ever existing and poisoning the training. Prior works have made various efforts in addressing the off-policyness to stabilize the training policies under the mismatch. In this paper, we point out the objective misalignment neglected by existing works that an effective update to the policy in the training engine not necessarily ensures the improvement of the inference policy, i.e., the one used in deployment. To this end, we propose a new policy optimization objective for LLM RL, named Monotonic Inference Policy Improvement (MIPI). Following this principle, we introduce Monotonic Inference Policy Update (MIPU), a two-step LLM RL framework that constructs sampler-referenced candidate updates and selectively accepts synchronized candidates using an inference-side gap proxy. Experiments conducted on two model scales under high mismatch show that MIPU improves average reasoning performance and training stability.