Optimal Stochastic Nonconvex Optimization with Bandit Feedback
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Abstract (arXiv)
In this paper, we analyze the continuous armed bandit problems for nonconvex cost functions under certain smoothness and sublevel set assumptions. We first derive an upper bound on the expected cumulative regret of a simple bin splitting method. We then propose an adaptive bin splitting method, which can significantly improve the performance. Furthermore, a minimax lower bound is derived, which shows that our new adaptive method achieves locally minimax optimal expected cumulative regret.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 9 of its 38 references that are in the map. First posted on arXiv 30 Mar 2021.
Builds on
9 of 38 references.
References · 9
- 2019Introduction to Multi-Armed Banditscited by 475
- 2016Kernel-based methods for bandit convex optimizationcited by 63
- 2016Highly-Smooth Zero-th Order Online Optimization Vianney Perchetcited by 22
- 2018Optimization of Smooth Functions with Noisy Observations: Local Minimax Ratescited by 14
- 2016On Sequential Elimination Algorithms for Best-Arm Identification in Multi-Armed Banditscited by 12
- 2019Minimax Optimal Algorithms for Adversarial Bandit Problem with Multiple Playscited by 11
- 2020Action-Manipulation Attacks Against Stochastic Bandits: Attacks and Defensecited by 8
- 2013Adaptive-treed banditscited by 6
- 2018Cost-aware Cascading Banditscited by 6
Built on by
Citing papers per year: 2023: 1.
1 paper.