When More Objectives Make Identification Easier: The Role of Preferences and Feedback
Best-arm identification (BAI) aims to identify the optimal arm using as few samples as possible.
ProofPaper ↗
Key points
- While most existing work focuses on a single objective, many real-world applications involve multiple criteria, which motivates the study of BAI in multi-objective bandits.
- For Gaussian bandits, we establish a characteristic-time lower bound for fixed-confidence identification that holds uniformly across preference orders.
- Through explicit comparisons under Pareto, linear, and lexicographic preferences, we reveal three phenomena: (i) identifying a larger optimal set can require fewer samples than identifying a unique optimum; (ii) the advantage of vector feedback over coordinate feedback depends fundamentally on the preference order; and (iii) multi-objective identification can require fewer samples than even the easiest corresponding single-objective problem.
- Finally, we propose Order-Aware Track-and-Stop (OATS), an algorithm that is correct at any prescribed confidence level and asymptotically matches the lower bound.
Sources (1)
- [1]When More Objectives Make Identification Easier: The Role of Preferences and FeedbackarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 13, 03:42 PM
Best-arm identification (BAI) aims to identify the optimal arm using as few samples as possible.
While most existing work focuses on a single objective, many real-world applications involve multiple criteria, which motivates the study of BAI in multi-objective bandits.
Extractive summary: sentences quoted from the sources.
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