Contextual Search in the Presence of Adversarial Corruptions

• 成果类型: Article
• 署名作者: Krishnamurthy, Akshay; Lykouris, Thodoris; Podimata, Chara; Schapire, Robert
• 署名单位: Microsoft; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2365
• 发表日期: 2023
• 页码: 1120-1135
• 关键词: binary search; errors; MODEL

摘要

We study contextual search, a generalization of binary search in higher dimensions, which captures settings such as feature-based dynamic pricing. Standard formulations of this problem assume that agents act in accordance with a specific homogeneous response model. In practice, however, some responses may be adversarially corrupted. Existing algorithms heavily depend on the assumed responsemodel being (approximately) accurate for all agents and have poor performance in the presence of even a few such arbitrary misspecifications. We initiate the study of contextual search when some of the agents can behave in ways inconsistent with the underlying response model. In particular, we provide two algorithms, one based on multidimensional binary search methods and one based on gradient descent. We show that these algorithms attain near-optimal regret in the absence of adversarial corruptions and their performance degrades gracefully with the number of such agents, providing the first results for contextual search in any adversarial noise model. Our techniques draw inspiration from learning theory, game theory, high-dimensional geometry, and convex analysis.