2024-04-18-chatterjee24a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Efficient Quantum Agnostic Improper Learning of Decision Trees	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 $(n, t, 1/\epsilon)$ quantum algorithm for learning size $t$ decision trees over $n$-bit inputs with uniform marginal over instances, in the agnostic setting, without membership queries (MQ). This is the first algorithm (classical or quantum) for efficiently learning decision trees without MQ. First, we construct a quantum agnostic weak learner by designing a quantum variant of the classical Goldreich-Levin algorithm that works with strongly biased function oracles. Next, we show how to quantize the agnostic boosting algorithm by Kalai and Kanade (2009) to obtain the first efficient quantum agnostic boosting algorithm (that has a polynomial speedup over existing adaptive quantum boosting algorithms). We then use the quantum agnostic boosting algorithm to boost the weak quantum agnostic learner constructed previously to obtain a quantum agnostic learner for decision trees. Using the above framework, we also give quantum decision tree learning algorithms without MQ in weaker noise models.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	chatterjee24a	0	Efficient Quantum Agnostic Improper Learning of Decision Trees	514	522	514-522	514	false	Chatterjee, Sagnik and SAPV, Tharrmashastha and Bera, Debajyoti	given family Sagnik Chatterjee given family Tharrmashastha SAPV given family Debajyoti Bera	2024-04-18		Proceedings of The 27th International Conference on Artificial Intelligence and Statistics	238	inproceedings	date-parts 2024 4 18	https://proceedings.mlr.press/v238/chatterjee24a/chatterjee24a.pdf