Dual-Directed Algorithm Design for Efficient Pure Exploration

Although experimental design often focuses on selecting the single best alternative from a finite set (e.g., in ranking and selection or best-arm identification), many pure-exploration problems pursue richer goals. Given a specific goal, adaptive experimentation aims to achieve it by strategically allocating sampling effort, with the underlying sample complexity characterized by a maximin optimization problem. By introducing dual variables, we derive necessary and sufficient conditions for an optimal allocation, yielding a unified algorithm design principle that extends the top-two approach beyond best-arm identification. This principle gives rise to information-directed selection, a hyperparameter-free rule that dynamically evaluates and chooses among candidates based on their current informational value. We prove that, when combined with information-directed selection, top-two Thompson sampling attains asymptotic optimality for Gaussian best-arm identification, resolving a notable open question in the pure-exploration literature. Furthermore, our framework produces asymptotically optimal algorithms for pure-exploration thresholding bandits and $\epsilon$-best-arm identification (i.e., ranking and selection with probability-of-good-selection guarantees), and more generally establishes a recipe for adapting Thompson sampling across a broad class of pure-exploration problems. Extensive numerical experiments highlight the efficiency of our proposed algorithms compared with existing methods.

Funding: W. You’s research is generously supported by the Hong Kong Research Grants Council [Grants ECS 26212320 and GRF 16212823].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results are available at https://doi.org/10.1287/opre.2023.0590.