Exact information accounting for SGD methods
As an alternative to the standard geometric analyses, we give an exact, information-theoretic analysis of stochastic gradient descent (SGD) and its variants. We show that a preconditioned SGD step is the posterior-mean update of a Gaussian Bayes model, and that its one-step regret splits into an intrinsic-time cost and a change in comparator information. The split extends to an identity for the objective itself. Convex convergence, strict-saddle-point escape, the link between flatness and generalization, the standard learning-rate schedules, adaptive optimizers, and the noisy, momentum, heavy-tailed, and gradient-free variants of SGD each correspond to a term or a special case of this ide...
| Authors | Akshay Balsubramani |
|---|---|
| Primary category | cs.LG |
| Published | 30 September 2026 |
| Last updated at source | 30 September 2026 |
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