# Adaptive Exact Learning of Decision Trees from Membership Queries

## TL;DR

This paper advances the adaptive learning of decision trees from membership queries by providing more query-efficient algorithms, improving upon previous randomized and deterministic methods for trees of bounded depth.

## Contribution

It introduces new randomized and deterministic algorithms with reduced query complexity for learning decision trees of bounded depth from membership queries.

## Key findings

- Improved randomized algorithm with $ ilde O(2^{2d}) + 2^{d} ext{log} n$ queries.
- Enhanced deterministic algorithm with $2^{5.83d}+2^{2d+o(d)} ext{log} n$ queries.
- Both algorithms operate in polynomial time and outperform prior methods.

## Abstract

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.