RELTA-SGLD: Relative-Growth Localized Taming for Nonconvex Stochastic-Gradient Langevin Learning

Abstract:We introduce RELTA-SGLD, a taming scheme that stabilizes superlinear stochastic-gradient updates while reducing unnecessary suppression of the original learning drift. A threshold determines where the taming turns on, while a relative-growth principle derived from the one-step Lyapunov stability condition determines the required taming strength. Together, they produce a lighter $\lambda$-scale denominator and preserve a nonvanishing far-tail return. As a consequence, we prove polynomial moment stability and first-order stationary accuracy in both $W_1$ and $W_2$ for nonconvex SGLD with superlinearly growing stochastic-gradient oracles, improving the corresponding half-order and quarter-order bounds for comparable stochastic-gradient tamed schemes. On Fashion-MNIST under active stabilization pressure, RELTA improves the mean learning metrics over both untamed SGLD and TUSLA and remains competitive with a tuned AdamW reference. In an ordinary-training regime, its lighter localized denominator reduces unnecessary perturbation of the original update and maintains nearly untamed learning dynamics.

Machine Learning (stat.ML); Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2607.19544 [stat.ML]

(or arXiv:2607.19544v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2607.19544 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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