Active Learning for Decision Trees with Provable Guarantees

TL;DR

This paper provides a theoretical analysis of active learning for decision trees, introducing a new algorithm with provable guarantees that achieves near-optimal label complexity under specific assumptions.

Contribution

It offers the first analysis of the disagreement coefficient for decision trees and presents a new active learning algorithm with multiplicative error guarantees.

Findings

Disagreement coefficient analysis for decision trees under certain assumptions.

A new active learning algorithm achieving polylogarithmic label complexity.

Lower bounds showing near-optimal dependence on error tolerance.

Abstract

This paper advances the theoretical understanding of active learning label complexity for decision trees as binary classifiers. We make two main contributions. First, we provide the first analysis of the disagreement coefficient for decision trees-a key parameter governing active learning label complexity. Our analysis holds under two natural assumptions required for achieving polylogarithmic label complexity, (i) each root-to-leaf path queries distinct feature dimensions, and (ii) the input data has a regular, grid-like structure. We show these assumptions are essential, as relaxing them leads to polynomial label complexity. Second, we present the first general active learning algorithm for binary classification that achieves a multiplicative error guarantee, producing a $(1+\epsilon)$-approximate classifier. By combining these results, we design an active learning algorithm for decision trees that uses only a polylogarithmic number of label queries in the dataset size, under the stated assumptions. Finally, we establish a label complexity lower bound, showing our algorithm's dependence on the error tolerance $\epsilon$ is close to optimal.