Contextual Search in the Presence of Adversarial Corruptions
This addresses the robustness issue in contextual search for applications like dynamic pricing, where existing methods fail under adversarial corruptions, representing a novel extension rather than an incremental improvement.
The paper tackles the problem of contextual search when some agents behave adversarially, inconsistent with the assumed response model, by proposing two algorithms that achieve near-optimal regret without corruptions and degrade gracefully with the number of adversarial agents.
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 response model 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.