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.

arXiv:2509.13628

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.

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• Robust accelerated primal-dual methods for computing saddle points (SIAM J. Optim., 2024)