论文标题
连续武装匪徒：功能空间透视图
Continuum-Armed Bandits: A Function Space Perspective
论文作者
论文摘要
连续武装的土匪（又称Black-Box或$ 0^{Th} $ - 订单优化）涉及优化一个未知的目标函数，给定一个在查询点评估该功能的oracle，其目的是使用尽可能少的查询点。在最深思熟虑的情况下，假定目标函数是Lipschitz的连续，并且在嘈杂和嘈杂的环境中都知道了简单和累积遗憾的最小值。本文研究了目标函数，研究在更一般的平滑度条件下，在更一般的平滑度条件下，即平滑度条件。在嘈杂和嘈杂的条件下，我们在简单和累积的遗憾下得出了最小值。我们的结果表明，在BESOV空间中，最小值比目标功能相同，与最小的Hölder空间中BESOV空间嵌入的最小的Hölder空间中的目标功能相同。
Continuum-armed bandits (a.k.a., black-box or $0^{th}$-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 Hölder space into which the Besov space embeds.
