Active Learning for Contextual Search with Binary Feedbacks

TL;DR

This paper introduces an active learning algorithm for contextual search with binary feedback, significantly reducing the number of queries needed to accurately learn the underlying value function compared to passive methods.

Contribution

The paper proposes a novel tri-section search combined with margin-based active learning for contextual search, achieving lower sample complexity than passive approaches.

Findings

Requires only O(1/ε²) queries for ε-accuracy

Reduces sample complexity from Ω(1/ε⁴) in passive settings

Effective in applications like auctions and personalized medicine

Abstract

In this paper, we study the learning problem in contextual search, which is motivated by applications such as first-price auction, personalized medicine experiments, and feature-based pricing experiments. In particular, for a sequence of arriving context vectors, with each context associated with an underlying value, the decision-maker either makes a query at a certain point or skips the context. The decision-maker will only observe the binary feedback on the relationship between the query point and the value associated with the context. We study a PAC learning setting, where the goal is to learn the underlying mean value function in context with a minimum number of queries. To address this challenge, we propose a tri-section search approach combined with a margin-based active learning method. We show that the algorithm only needs to make $O(1/\varepsilon^2)$ queries to achieve an $\epsilon$-estimation accuracy. This sample complexity significantly reduces the required sample complexity in the passive setting, at least $\Omega(1/\varepsilon^4)$.