Stochastic simultaneous optimistic optimization

2026-04-27

AI Summary

This work addresses the problem of global maximization of noisy black-box functions by proposing an optimistic optimization algorithm that does not require prior knowledge of local smoothness characterized by a semi-metric. The method employs a hierarchical partitioning of the search domain and integrates upper confidence bounds with an optimistic sampling strategy to adaptively explore the function’s structure under a finite budget of noisy evaluations. Theoretical analysis demonstrates that, even without knowing the local smoothness in advance, the algorithm achieves performance nearly matching that of oracle-tuned optimal methods which assume such knowledge is given. This result substantially enhances the practical applicability and robustness of black-box optimization in real-world settings where smoothness properties are typically unknown.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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.

Problem

• global optimization
• noisy evaluations
• local smoothness
• semi-metric
• black-box optimization

Innovation

• Stochastic optimization
• Global optimization
• Optimistic optimization
• Bandits
• Local smoothness