Correcting Stochastic Update Bias in Preconditioned Language Model Optimizers
Preconditioned optimizers are central to language model training, but their stochastic update rules are usually treated as direct approximations to population preconditioned descent. We show that this view misses two finite-sample biases. First, the gradient and preconditioner are typically estimated from the same minibatch, introducing gradient--preconditioner coupling bias. Second, even when the preconditioner estimate is unbiased, its inverse or inverse-root is generally biased because inversion is nonlinear. We propose a single-batch bias-correction framework that addresses both effects: cross-fitted preconditioning estimates the numerator and preconditioner from independent microbatc...
| Authors | Nikhil Nayak, Julia White, Urchade Zaratiana et al. |
|---|---|
| Primary category | cs.LG |
| Published | 20 May 2026 |
| Last updated at source | 20 May 2026 |
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