Query Learning with Exponential Query Costs

In query learning, the goal is to identify an unknown object while minimizing the number of “yes” or “no” questions (queries) posed about that object. A well-studied algorithm for query learning is known as generalized binary search (GBS). We show that GBS is a greedy algorithm to optimize the expected number of queries needed to identify the unknown object. We also generalize GBS in two ways. First, we consider the case where the cost of querying grows exponentially in the number of queries and the goal is to minimize the expected exponential cost. Then, we consider the case where the objects are partitioned into groups, and the objective is to identify only the group to which the object belongs. We derive algorithms to address these issues in a common, information-theoretic framework. In particular, we present an exact formula for the objective function in each case involving Shannon or Renyi entropy, and develop a greedy algorithm for minimizing it. Our algorithms are demonstrated on two applications of query learning, active learning and emergency response.

💡 Research Summary

The paper revisits the classic problem of query learning, where an unknown object must be identified by asking a sequence of binary (yes/no) questions, and extends it in two important directions that reflect realistic constraints. First, it acknowledges that the cost of asking questions often grows faster than linearly—indeed, in many human‑in‑the‑loop or networked settings each additional query can impose an exponentially larger burden. To capture this, the authors introduce an exponential cost model C(t)=β^t with β>1, where t denotes the number of queries already asked. The objective becomes the minimization of the expected exponential cost E