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Transferring knowledge across a sequence of related tasks is an important challenge in reinforcement learning (RL). Despite much encouraging empirical evidence, there has been little theoretical analysis. In this paper, we study a class of…

Machine Learning · Computer Science 2015-09-23 Emma Brunskill , Lihong Li

Studies addressing the question "Can a learner complete the learning securely?" have recently been spurred from the standpoints of fundamental theory and potential applications. In the relevant context of this question, we present a…

We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate…

Quantum Physics · Physics 2022-03-29 Dmytro Gavinsky

This Ph.D. thesis concerns the version of the classical coupon collector's problem, when a collector samples with replacement a set of $n\ge 2$ distinct coupons so that at each time any one of the $n$ coupons is drawn with the same…

Probability · Mathematics 2010-07-27 Anna Pósfai

We continue the study of the computational complexity of differentially private PAC learning and how it is situated within the foundations of machine learning. A recent line of work uncovered a qualitative equivalence between the private…

Machine Learning · Computer Science 2024-02-20 Mark Bun , Aloni Cohen , Rathin Desai

Despite years of effort, the quantum machine learning community has only been able to show quantum learning advantages for certain contrived cryptography-inspired datasets in the case of classical data. In this note, we discuss the…

Quantum Physics · Physics 2023-07-06 Casper Gyurik , Vedran Dunjko

Noise is often regarded as anathema to quantum computation, but in some settings it can be an unlikely ally. We consider the problem of learning the class of $n$-bit parity functions by making queries to a quantum example oracle. In the…

Quantum Physics · Physics 2015-08-05 Andrew W. Cross , Graeme Smith , John A. Smolin

We generalize the well-known Coupon Collector Problem (CCP) in combinatorics. Our problem is to find the minimum and expected number of draws, with replacement, required to recover $n$ distinctly labeled coupons, with each draw consisting…

Discrete Mathematics · Computer Science 2025-07-22 Andrew Tan , Oriel Limor , Daniella Bar-Lev , Ryan Gabrys , Zohar Yakhini , Paul H. Siegel

Quantum counting is the task of determining the dimension of the subspace of states that are accepted by a quantum verifier circuit. It is the quantum analog of counting the number of valid solutions to NP problems -- a problem well-studied…

Quantum Physics · Physics 2025-03-17 Mason L. Rhodes , Sam Slezak , Anirban Chowdhury , Yiğit Subaşı

In a work by Raz (J. ACM and FOCS 16), it was proved that any algorithm for parity learning on $n$ bits requires either $\Omega(n^2)$ bits of classical memory or an exponential number (in~$n$) of random samples. A line of recent works…

Quantum Physics · Physics 2023-03-02 Qipeng Liu , Ran Raz , Wei Zhan

We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from…

Probability · Mathematics 2015-11-25 Richard Arratia , Stephen DeSalvo

We study the problems of quantum tomography and shadow tomography using measurements performed on individual, identical copies of an unknown $d$-dimensional state. We first revisit a known lower bound due to Haah et al. (2017) on quantum…

Quantum Physics · Physics 2025-06-12 Angus Lowe , Ashwin Nayak

Despite significant effort, the quantum machine learning community has only demonstrated quantum learning advantages for artificial cryptography-inspired datasets when dealing with classical data. In this paper we address the challenge of…

Quantum Physics · Physics 2024-11-14 Casper Gyurik , Vedran Dunjko

This paper provides analysis to a generalized version of the coupon collector problem, in which the collector gets $d$ distinct coupons each run and she chooses the one that she has the least so far. On the asymptotic case when the number…

Information Theory · Computer Science 2019-07-10 Weiyu Xu , Ao Kevin Tang

This paper studies the sample complexity (aka number of comparisons) bounds for the active best-$k$ items selection from pairwise comparisons. From a given set of items, the learner can make pairwise comparisons on every pair of items, and…

Machine Learning · Computer Science 2021-08-02 Wenbo Ren , Jia Liu , Ness B. Shroff

Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…

Instance discriminative self-supervised representation learning has been attracted attention thanks to its unsupervised nature and informative feature representation for downstream tasks. In practice, it commonly uses a larger number of…

Machine Learning · Computer Science 2022-01-17 Kento Nozawa , Issei Sato

Quantum annealing (QA) has attracted research interest as a sampler and combinatorial optimization problem (COP) solver. A recently proposed sampling-based solver for QA significantly reduces the required number of qubits, being capable of…

Quantum Physics · Physics 2025-07-31 Ryo Hagiwara , Shunta Arai , Satoshi Takabe

The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…

Computational Complexity · Computer Science 2025-12-02 Guy Blanc , Caleb Koch , Jane Lange , Carmen Strassle , Li-Yang Tan

We study the collaborative PAC learning problem recently proposed in Blum et al.~\cite{BHPQ17}, in which we have $k$ players and they want to learn a target function collaboratively, such that the learned function approximates the target…

Machine Learning · Computer Science 2018-10-15 Jiecao Chen , Qin Zhang , Yuan Zhou