Efficient Quantum Agnostic Improper Learning of Decision Trees

Sagnik Chatterjee, Tharrmashastha SAPV, Debajyoti Bera
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:514-522, 2024.

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 $(n, t, 1/\epsilon)$ 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-chatterjee24a, title = { Efficient Quantum Agnostic Improper Learning of Decision Trees }, author = {Chatterjee, Sagnik and SAPV, Tharrmashastha and Bera, Debajyoti}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {514--522}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/chatterjee24a/chatterjee24a.pdf}, url = {https://proceedings.mlr.press/v238/chatterjee24a.html}, 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 $(n, t, 1/\epsilon)$ 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. } }
Endnote
%0 Conference Paper %T Efficient Quantum Agnostic Improper Learning of Decision Trees %A Sagnik Chatterjee %A Tharrmashastha SAPV %A Debajyoti Bera %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-chatterjee24a %I PMLR %P 514--522 %U https://proceedings.mlr.press/v238/chatterjee24a.html %V 238 %X 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.
APA
Chatterjee, S., SAPV, T. & Bera, D.. (2024). Efficient Quantum Agnostic Improper Learning of Decision Trees . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:514-522 Available from https://proceedings.mlr.press/v238/chatterjee24a.html.

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