Stochastic Adaptive Optimization with Unreliable Inputs: A Unified Framework for High-Probability Complexity Analysis
Optimization and Control
2025-11-25 v1
Abstract
We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed noise. This setting captures challenging scenarios where both gradient and function value estimates can be unreliable, making it applicable to many real-world problems, which can have outliers and data anomalies. We introduce an algorithmic and analytical framework that provides high-probability bounds on iteration complexity for this setting. The analysis offers a unified approach, encompassing methods such as line search and trust region.
Cite
@article{arxiv.2511.19411,
title = {Stochastic Adaptive Optimization with Unreliable Inputs: A Unified Framework for High-Probability Complexity Analysis},
author = {Katya Scheinberg and Miaolan Xie},
journal= {arXiv preprint arXiv:2511.19411},
year = {2025}
}