{"ID":2837743,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.19411","arxiv_id":"2511.19411","title":"Stochastic Adaptive Optimization with Unreliable Inputs: A Unified Framework for High-Probability Complexity Analysis","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.","short_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...","url_abs":"https://arxiv.org/abs/2511.19411","url_pdf":"https://arxiv.org/pdf/2511.19411v1","authors":"[\"Katya Scheinberg\",\"Miaolan Xie\"]","published":"2025-11-24T18:48:36Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}