Probe the Harness: Setup Checks for Stale-Data RL Comparisons in Language Models

Reinforcement learning from verifiable rewards assigns one terminal reward to an entire reasoning trajectory, obscuring how individual reasoning steps contributed to the outcome. GRPO broadcasts a group-normalized advantage to every response token, while finer-grained approaches often rely on dense auxiliary rollouts or branching schemes that can also alter the data used for policy updates. We cast the missing middle as budgeted measurement: with a limited rollout budget, which partial solutions should be evaluated, and how should their value estimates refine credit? ProbePO selects partial-solution states with a reward-free uncertainty score and estimates their expected verifier rewards under a capped continuation budget. ProbePO redistributes, rather than replaces, GRPO's trajectory-level advantage across tokens while preserving each trajectory's mean token-level advantage; probe continuations serve only as measurements. Across three DeepSeekMath and Qwen-family models spanning 1.5B-7B parameters, ProbePO consistently outperforms GRPO and achieves the highest accuracy among the four evaluated methods in 16 of 18 model-benchmark comparisons. Against dense-probing VinePPO on DeepSeekMath-7B, ProbePO achieves higher accuracy on all six benchmarks with 76% less end-to-end training time.

Production RL for language models lets the sampler fall behind the learner and repairs the resulting mismatch with a truncated importance weight. We ask how long the sampler can go without a refresh under that correction, and find a cliff: on Qwen2.5-Math-1.5B and GSM8K, importance-corrected GRPO refreshed every 192 updates learns well for 180 steps and then degrades severely in all three data seeds before the refresh arrives. Published remedies for staleness act on the update; we act on the sampler instead. Decoupled cooling draws samples at temperature 0.8 while the learner, the reference model and the importance weights stay at temperature 1, with the behaviour probability recorded from the tempered distribution, so the learner's objective is unchanged. All corresponding cooled runs are stable, and the longer interval keeps what the short one delivered: at the same update budget, a cooled sampler refreshed every 192 steps matches an uncooled sampler refreshed every 96 at the end of training (0.857 for both) and averaged over it (0.79), whereas lowering the learning rate to a safe value ends 3-7 points lower. On Qwen2.5-Math-7B the degradation points at interval 192 predict that an interval of 144 is fatal without cooling and survivable with it; on two data seeds the uncooled runs degrade before their first refresh and the cooled runs pass it and end at 92-93% against 68-81%, with one cooled run degrading transiently late in the second cycle. The benefit has a window: at three times the safe interval and in a high-mismatch MATH setting cooling delays degradation without preventing it, stronger cooling is not better, and cooling without the correction collapses. Sampling temperature is a control on staleness tolerance, and temperature and refresh interval should be chosen together.

We connect the spurious-reward paradox to a model's reachability and propose random-reward reinforcement learning (RL) as a useful tool for the probing enterprise, addressing a decade-long debate over what probing performance actually reveals about a model. There are two prevailing explanations for the surprising finding that even random rewards can improve the performance of large language models (LLMs): one attributes the gains to particular mechanisms within RL training; the other to data contamination. Our results motivate a different view: spurious-reward RL can probe a model's reachability, or what further training can attain from its current state under specified constraints, beyond what is reflected in its current performance. Two OLMo checkpoints with the same accuracy on synthetic arithmetic (3.5%), for example, reach 8.5% and 55% in their best runs under the same correctness-rewarded RL. Examining OLMo checkpoints across pre-training and mid-training reveals three distinct regimes of training response: early on, RL produces little improvement even when correct answers are rewarded; later in pre-training, rewarding correct answers becomes effective while random rewards remain weak; and, upon entering mid-training, even random rewards can produce large gains. A similar ordering appears in a number-masked supervised fine-tuning (SFT) analysis of these checkpoints, suggesting that the pattern is not specific to a particular RL mechanism. Moreover, RL with random rewards offers a distinctive perspective on what training can make an LLM do, since its reward signal supplies no information about which answers are correct. By asking what training can attain without correctness feedback, it addresses the label-leakage side of a central problem in decodability-based probing: whether a successful probe reveals the model's capabilities or learns the task itself.