Efficient Quantum Agnostic Improper Learning of Decision Trees

TL;DR

This paper introduces the first polynomial-time quantum algorithm for agnostic decision tree learning without membership queries, leveraging quantum boosting and a quantum Goldreich-Levin approach to improve learning efficiency.

Contribution

It presents a novel quantum agnostic learning framework for decision trees, including a weak learner, a boosting algorithm, and extensions to realizable and noisy settings.

Findings

First polynomial-time quantum algorithm for agnostic decision tree learning without membership queries.

Quantum boosting algorithm with improved bias dependence and classical speedup in VC dimension.

Quantum algorithms for decision trees in realizable and noisy classification settings.

Abstract

The agnostic setting is the hardest generalization of the PAC model since it is akin to learning with adversarial noise. In this paper, we give a poly$(n,t,{\frac{1}{\varepsilon}})$ quantum algorithm for learning size $t$ decision trees with uniform marginal over instances, in the agnostic setting, without membership queries. Our algorithm is the first algorithm (classical or quantum) for learning decision trees in polynomial time without membership queries. We show how to construct a quantum agnostic weak learner by designing a quantum version of the classical Goldreich-Levin algorithm that works with strongly biased function oracles. We show how to quantize the agnostic boosting algorithm by Kalai and Kanade (NIPS 2009) to obtain the first efficient quantum agnostic boosting algorithm. Our quantum boosting algorithm has a polynomial improvement in the dependence of the bias of the weak learner over all adaptive quantum boosting algorithms while retaining the standard speedup in the VC dimension over classical boosting algorithms. We then use our quantum boosting algorithm to boost the weak quantum learner we obtained in the previous step to obtain a quantum agnostic learner for decision trees. Using the above framework, we also give quantum decision tree learning algorithms for both the realizable setting and random classification noise model, again without membership queries.