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This paper argues that RL post-training of language models loses most small weight updates when fp32 master weights are converted to bf16 for rollouts, creating a lag between the policy generating data and the optimizer. The proposed fix swaps round-to-nearest for an unbiased rounding rule when exporting weights, reported as a one-line change with small export overhead. The evidence is a 25-seed-pair comparison across Qwen3 models of 0.6B to 4B, with a 6.1-point mean gain and a win on 18 of 25 pairs. Readers training RL policies should note that the results come from one model family and a limited set of benchmarks, so independent replication matters before adopting it.
bf16 Rounding Silently Discards Most RL Policy Updates: A Hidden Training-Inference Mismatch and an Unbiased One-Line Fix
arXiv:2610.41073v1 Announce Type: new Abstract: Reinforcement learning (RL) post-training of language models keeps fp32 master weights in the optimizer and serves rollouts from a bf16 copy produced by round-to-nearest conversion. At the learning rates in common use, most per-step updates are smaller than half a bf16 spacing and the conversion discards them: on Qwen3-1.7B only 0.4-0.5% of served weights change per step, and the policy that generates the training data lags the optimizer by 50-150 steps. Existing mismatch corrections cannot see this lag because they compare two copies downstream of the same rounding. We propose Fair Cast: export the master with an unbiased rounding rule (stochastic rounding or error feedback) and compute the training loss on the served copy. The change is one line at the export call, adds no hyperparameters and costs 22-38 ms per export of 1.7B parameters. Across 25 matched seed-pairs on Qwen3-0.6B to 4B with AdamW and Muon, Fair Cast is ahead on 18, tied on 6 and behind on 1, with a mean gain of 6.1 points; on zebra puzzles it reaches 0.57 +/- 0.16 over four runs where round-to-nearest collapses to 0.33 +/- 0.10. It also makes the saved fp32 checkpoint agree with the served model, and it exposes the implicit lag of round-to-nearest as a regularizer that can be restored explicitly when a task needs it.
Abstract:Reinforcement learning (RL) post-training of language models keeps fp32 master weights in the optimizer and serves rollouts from a bf16 copy produced by round-to-nearest conversion. At the learning rates in common use, most per-step updates are smaller than half a bf16 spacing and the conversion discards them: on Qwen3-1.7B only 0.4-0.5% of served weights change per step, and the policy that generates the training data lags the optimizer by 50-150 steps. Existing mismatch corrections cannot see this lag because they compare two copies downstream of the same rounding. We propose Fair Cast: export the master with an unbiased rounding rule (stochastic rounding or error feedback) and compute the training loss on the served copy. The change is one line at the export call, adds no hyperparameters and costs 22-38 ms per export of 1.7B parameters. Across 25 matched seed-pairs on Qwen3-0.6B to 4B with AdamW and Muon, Fair Cast is ahead on 18, tied on 6 and behind on 1, with a mean gain of 6.1 points; on zebra puzzles it reaches 0.57 +/- 0.16 over four runs where round-to-nearest collapses to 0.33 +/- 0.10. It also makes the saved fp32 checkpoint agree with the served model, and it exposes the implicit lag of round-to-nearest as a regularizer that can be restored explicitly when a task needs it.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.41073 [cs.LG]
(or arXiv:2610.41073v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.41073 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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