Contextual search in the presence of irrational agents

Abstract

We study contextual search, a generalization of binary search in higher dimensions, which captures settings such as feature-based dynamic pricing. Standard game-theoretic formulations of this problem assume that agents act in accordance with a specific behavioral model. In practice, some agents may not subscribe to the dominant behavioral model or may act in ways that are seemingly arbitrarily irrational. Existing algorithms heavily depend on the behavioral model being (approximately) accurate for all agents and have poor performance even with a few arbitrarily irrational agents. We initiate the study of contextual search when some of the agents can behave in ways inconsistent with the underlying behavioral model. In particular, we provide two algorithms, one based on multidimensional binary search methods and one based on gradient descent. Our techniques draw inspiration from learning theory, game theory, high-dimensional geometry, and convex analysis.