# Continuum-Armed Bandits: A Function Space Perspective

arXiv: https://arxiv.org/abs/2010.08007 · HTML: https://mlsanity.com/paper/2010.08007/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Be More Diverse than the Most Diverse: Optimal Mixtures of Generative Models via Mixture-UCB Bandit Algorithms](https://mlsanity.com/paper/2412.17622/) (2024)
- [Permutation Search of Tensor Network Structures via Local Sampling](https://mlsanity.com/paper/2206.06597/) (2022)
- [Instance-Dependent Regret Analysis of Kernelized Bandits](https://mlsanity.com/paper/2203.06297/) (2022)
- [Online Algorithms for Hierarchical Inference in Deep Learning applications at the Edge](https://mlsanity.com/paper/2304.00891/) (2023)
- [Adaptation to Misspecified Kernel Regularity in Kernelised Bandits](https://mlsanity.com/paper/2304.13830/) (2023)
- [Consequences of Kernel Regularity for Bandit Optimization](https://mlsanity.com/paper/2512.05957/) (2025)
- [High-Dimensional Simulation Optimization via Brownian Fields and Sparse Grids](https://mlsanity.com/paper/2107.08595/) (2021)
- [Sparse Nonparametric Contextual Bandits](https://mlsanity.com/paper/2503.16382/) (2025)

## Abstract (arXiv)

Continuum-armed bandits (a.k.a., black-box or 0th-order optimization) involves optimizing an unknown objective function given an oracle that evaluates the function at a query point, with the goal of using as few query points as possible. In the most well-studied case, the objective function is assumed to be Lipschitz continuous and minimax rates of simple and cumulative regrets are known in both noiseless and noisy settings. This paper studies continuum-armed bandits under more general smoothness conditions, namely Besov smoothness conditions, on the objective function. In both noiseless and noisy conditions, we derive minimax rates under simple and cumulative regrets. Our results show that minimax rates over objective functions in a Besov space are identical to minimax rates over objective functions in the smallest H"older space into which the Besov space embeds.