Publications · Journal article · J. Nonlinear Var. Anal. 2026
Accelerated gradient methods with biased gradient estimates: risk sensitivity, high-probability guarantees, and large deviation bounds
Journal of Nonlinear and Variational Analysis (special issue), 2026.
In brief
Studies accelerated methods when gradient estimates are biased as well as noisy. Computes the risk-sensitive index of generalized momentum methods via a Riccati-equation reduction, characterizes when it blows up, and derives a large deviation principle whose rate function is the convex conjugate of that index — turning rare-event behavior of the running suboptimality into a designable quantity, with finite-time high-probability guarantees beyond quadratics.
Cite
@article{gurbuzbalaban2026biased,
title = {Accelerated gradient methods with biased gradient estimates: risk sensitivity, high-probability guarantees, and large deviation bounds},
author = {Mert Gürbüzbalaban and Yasa Syed and Necdet Serhat Aybat},
year = {2026},
journal = {Journal of Nonlinear and Variational Analysis (special issue)},
note = {arXiv:2509.13628},
}Relatedsame topics