Active Learning for Contextual Search with Binary Feedbacks
This work addresses efficient learning in applications like auctions and personalized experiments, offering a substantial improvement over passive methods, though it is incremental in the context of active learning research.
The paper tackles the problem of learning the mean value function in contextual search with binary feedbacks, proposing a tri-section search and margin-based active learning method that achieves ε-estimation accuracy with only O(1/ε²) queries, significantly reducing the sample complexity from at least Ω(1/ε⁴) in passive settings.
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 $ε$-estimation accuracy. This sample complexity significantly reduces the required sample complexity in the passive setting, at least $Ω(1/\varepsilon^4)$.