TY - JOUR

T1 - Simultaneous private learning of multiple concepts

AU - Bun, Mark

AU - Nissim, Kobbi

AU - Stemmer, Uri

N1 - Publisher Copyright:
© 2019 Mark Bun and Kobbi Nissim and Uri Stemmer.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - We investigate the direct-sum problem in the context of differentially private PAC learning: What is the sample complexity of solving k learning tasks simultaneously under differential privacy, and how does this cost compare to that of solving k learning tasks without privacy? In our setting, an individual example consists of a domain element x labeled by k unknown concepts (c1; : : : ; ck). The goal of a multi-learner is to output k hypotheses (h1; : : : ; hk) that generalize the input examples. Without concern for privacy, the sample complexity needed to simultaneously learn k concepts is essentially the same as needed for learning a single concept. Under differential privacy, the basic strategy of learning each hypothesis independently yields sample complexity that grows polynomially with k. For some concept classes, we give multi-learners that require fewer samples than the basic strategy. Unfortunately, however, we also give lower bounds showing that even for very simple concept classes, the sample cost of private multi-learning must grow polynomially in k.

AB - We investigate the direct-sum problem in the context of differentially private PAC learning: What is the sample complexity of solving k learning tasks simultaneously under differential privacy, and how does this cost compare to that of solving k learning tasks without privacy? In our setting, an individual example consists of a domain element x labeled by k unknown concepts (c1; : : : ; ck). The goal of a multi-learner is to output k hypotheses (h1; : : : ; hk) that generalize the input examples. Without concern for privacy, the sample complexity needed to simultaneously learn k concepts is essentially the same as needed for learning a single concept. Under differential privacy, the basic strategy of learning each hypothesis independently yields sample complexity that grows polynomially with k. For some concept classes, we give multi-learners that require fewer samples than the basic strategy. Unfortunately, however, we also give lower bounds showing that even for very simple concept classes, the sample cost of private multi-learning must grow polynomially in k.

KW - Agnostic learning

KW - Differential privacy

KW - Direct-sum

KW - PAC learning

UR - http://www.scopus.com/inward/record.url?scp=85072616603&partnerID=8YFLogxK

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AN - SCOPUS:85072616603

SN - 1532-4435

VL - 20

JO - Journal of Machine Learning Research

JF - Journal of Machine Learning Research

ER -