When All Rollouts Fail: Policy-Compatible Joint Decoding for Hard-Problem Reasoning

Reinforcement Learning with Verifiable Rewards (RLVR) derives its learning signal from binary rewards via on-policy exploration and becomes a powerful paradigm for improving the reasoning of large language models. Yet it faces a learning cliff on problems beyond model's current ability: when every rollout fails, the samples reveal nothing about a correct solution, and group-relative estimators (e.g., GRPO, RLOO) collapse the update to zero advantage. Expert trajectories offer a remedy, but they are incompatible with the current policy and often lie in the student's low-probability regions, so the surviving updates demand large parameter shifts and decay into surface-level imitation rather than transferable reasoning. We argue that a useful learning signal on hard problems must be both verifiably correct and sufficiently compatible with the current policy. We propose Policy-Compatible Reinforcement Learning (**PICO**), which performs distribution-constrained joint decoding: expert data guides decoding at the token level while preserving the student's relative token probabilities, and a dynamic top-k mechanism confines the sampling distribution under a finite divergence budget, yielding trajectories that are verified and policy-compatible by construction. These trajectories are optimized jointly with on-policy rollouts under a mixed-behavior objective that mitigates their distribution mismatch via importance sampling. Experiments across reasoning diverse datasets and agentic benchmarks demonstrate that PICO consistently outperforms standard RLVR and prior off-policy baselines.