arXiv Machine Learning By Andrew Gao, William Gao

bf16 Rounding Silently Discards Most RL Policy Updates: A Hidden Training-Inference Mismatch and an Unbiased One-Line Fix

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The paper identifies a hidden mismatch in reinforcement‑learning fine‑tuning of large language models: when training uses fp32 master weights but rollouts are served from a bf16 copy produced by round‑to‑nearest conversion, most per‑step updates are too small to affect the served weights, causing a lag of 50–150 steps. The authors propose Fair Cast, a one‑line change that exports the master weights with an unbiased rounding rule (stochastic rounding or error feedback) and computes the loss on the served copy, eliminating the lag without adding hyperparameters and incurring only a modest computational cost. Across multiple models and optimizers, Fair Cast consistently outperforms round‑to‑nearest, improves checkpoint consistency, and reveals the implicit regularization effect of the lag.

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