Bayesian Optimal Active Search and Surveying

TL;DR

This paper introduces Bayesian optimal policies for active search and surveying, demonstrating that less-myopic strategies can outperform more-myopic ones and providing bounds to make implementation computationally feasible.

Contribution

It introduces the active surveying problem, extends active search theory with new optimality results, and offers practical bounds for efficient implementation.

Findings

Less-myopic policies can outperform more-myopic ones.

Bounds enable practical implementation of optimal policies.

The approach applies to real-world class discovery and proportion estimation.

Abstract

We consider two active binary-classification problems with atypical objectives. In the first, active search, our goal is to actively uncover as many members of a given class as possible. In the second, active surveying, our goal is to actively query points to ultimately predict the proportion of a given class. Numerous real-world problems can be framed in these terms, and in either case typical model-based concerns such as generalization error are only of secondary importance. We approach these problems via Bayesian decision theory; after choosing natural utility functions, we derive the optimal policies. We provide three contributions. In addition to introducing the active surveying problem, we extend previous work on active search in two ways. First, we prove a novel theoretical result, that less-myopic approximations to the optimal policy can outperform more-myopic approximations by any arbitrary degree. We then derive bounds that for certain models allow us to reduce (in practice dramatically) the exponential search space required by a naive implementation of the optimal policy, enabling further lookahead while still ensuring that optimal decisions are always made.