无需预先知道函数平滑性，仍能高效寻找全局最优解。
Stochastic simultaneous optimistic optimization
- 基于乐观策略构建分层分区的置信上界，自适应选择采样点。
- 理论证明其性能接近已知平滑性的最优算法。
- 适合未知函数局部特性但需高精度优化的场景。
研究在噪声干扰下对函数 f 进行有限次评估以实现全局最大化的问题。假设函数在某个全局最大值附近具有局部光滑性（以某种半度量为基准），但无需事先知晓该半度量。与以往针对一般空间的带域问题工作相比，所提算法 StoSOO 不依赖于半度量信息。StoSOO 采用乐观策略，迭代构建函数定义域分层划分上的置信上界，以决定下一采样点。有限时间分析表明，尽管不掌握函数的局部光滑性，该算法性能几乎等同于专门调优的最优算法。
原文摘要 · Abstract (English)
We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect to some semi-metric, around one of its global maxima. Compared to previous works on bandits in general spaces (Kleinberg et al., 2008; Bubeck et al., 2011a) our algorithm does not require the knowledge of this semi-metric. Our algorithm, StoSOO, follows an optimistic strategy to iteratively construct upper confidence bounds over the hierarchical partitions of the function domain to decide which point to sample next. A finite-time analysis of StoSOO shows that it performs almost as well as the best specifically-tuned algorithms even though the local smoothness of the function is not known.
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