Stochastic Adaptive Optimization with Unreliable Inputs: A Unified Framework for High-Probability Complexity Analysis Article Swipe

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YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2511.19411

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.

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Mathematical optimization Computer science Function (biology) Outlier Algorithm Term (time) Optimization problem Value (mathematics) Mathematics Gradient method Stochastic optimization Computational complexity theory Line (geometry) Bellman equation Variation (astronomy) Line search Optimization algorithm Measure (data warehouse) Iterative method Stochastic approximation Estimation theory Stochastic process Key (lock)

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Type: preprint
Landing Page: https://doi.org/10.48550/arxiv.2511.19411
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DOI: https://doi.org/10.48550/arxiv.2511.19411

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Title: Stochastic Adaptive Optimization with Unreliable Inputs: A Unified Framework for High-Probability Complexity Analysis

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Type: preprint

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Publication year: 2025

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Publication date: 2025-11-24

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Authors: Scheinberg, Katya, Xie, Miaolan

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Landing page: https://doi.org/10.48550/arxiv.2511.19411

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Concepts: Mathematical optimization, Computer science, Function (biology), Outlier, Algorithm, Term (time), Optimization problem, Value (mathematics), Mathematics, Gradient method, Stochastic optimization, Computational complexity theory, Line (geometry), Bellman equation, Variation (astronomy), Line search, Optimization algorithm, Measure (data warehouse), Iterative method, Stochastic approximation, Estimation theory, Stochastic process, Key (lock)

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