Adaptive Exact Learning of Decision Trees from Membership Queries
This work addresses the query efficiency for learning decision trees, which is incremental as it builds on prior algorithms by Feldman and Kushilevitz-Mansour.
The paper tackles the problem of adaptively learning decision trees of depth at most d from membership queries, with applications in automated scientific discovery. It improves query complexity by providing a randomized algorithm with ~O(2^{2d}) + 2^d log n queries and a deterministic one with 2^{5.83d} + 2^{2d+o(d)} log n queries, reducing previous bounds.
In this paper we study the adaptive learnability of decision trees of depth at most $d$ from membership queries. This has many applications in automated scientific discovery such as drugs development and software update problem. Feldman solves the problem in a randomized polynomial time algorithm that asks $\tilde O(2^{2d})\log n$ queries and Kushilevitz-Mansour in a deterministic polynomial time algorithm that asks $ 2^{18d+o(d)}\log n$ queries. We improve the query complexity of both algorithms. We give a randomized polynomial time algorithm that asks $\tilde O(2^{2d}) + 2^{d}\log n$ queries and a deterministic polynomial time algorithm that asks $2^{5.83d}+2^{2d+o(d)}\log n$ queries.