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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.15526 |
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| _version_ | 1866917415738146816 |
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| author | Zhang, Shunzhi Liao, Shichen Han, Congying Guo, Tiande |
| author_facet | Zhang, Shunzhi Liao, Shichen Han, Congying Guo, Tiande |
| contents | We study unconstrained smooth convex optimization under stochastic first- and zeroth-order oracles subject only to finite-moment bounds, naturally admitting persistent bias and heavy-tailed noise. In this hostile environment, integrating momentum into \emph{adaptive step search} to secure acceleration poses an inherent structural challenge, because momentum propagates oracle errors across iterations, inevitably undermining the stabilizing effect of local search.
To address this difficulty, we propose \texttt{RAAS}, a robust accelerated adaptive search method with tunable momentum intervention. Theoretically, we develop a general high-probability framework for adaptive search methods under stochastic oracle feedback, and instantiate it through the strongly convex and general convex analyses of \texttt{RAAS}. This yields high-probability stopping-time complexity bounds for reaching the attainable precision neighborhood. The resulting guarantees also clarify how the algorithmic parameters trade off early-stage acceleration against late-stage stability, and motivate a simple switching heuristic that performs well empirically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15526 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust Accelerated Adaptive Search: High-Probability Complexity Bounds under Bounded-Moment Stochastic Oracles Zhang, Shunzhi Liao, Shichen Han, Congying Guo, Tiande Optimization and Control We study unconstrained smooth convex optimization under stochastic first- and zeroth-order oracles subject only to finite-moment bounds, naturally admitting persistent bias and heavy-tailed noise. In this hostile environment, integrating momentum into \emph{adaptive step search} to secure acceleration poses an inherent structural challenge, because momentum propagates oracle errors across iterations, inevitably undermining the stabilizing effect of local search. To address this difficulty, we propose \texttt{RAAS}, a robust accelerated adaptive search method with tunable momentum intervention. Theoretically, we develop a general high-probability framework for adaptive search methods under stochastic oracle feedback, and instantiate it through the strongly convex and general convex analyses of \texttt{RAAS}. This yields high-probability stopping-time complexity bounds for reaching the attainable precision neighborhood. The resulting guarantees also clarify how the algorithmic parameters trade off early-stage acceleration against late-stage stability, and motivate a simple switching heuristic that performs well empirically. |
| title | Robust Accelerated Adaptive Search: High-Probability Complexity Bounds under Bounded-Moment Stochastic Oracles |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.15526 |