Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds

@article{Bassily2014PrivateER,
  title={Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds},
  author={Raef Bassily and Adam D. Smith and Abhradeep Thakurta},
  journal={2014 IEEE 55th Annual Symposium on Foundations of Computer Science},
  year={2014},
  pages={464-473}
}
Convex empirical risk minimization is a basic tool in machine learning and statistics. We provide new algorithms and matching lower bounds for differentially private convex empirical risk minimization assuming only that each data point's contribution to the loss function is Lipschitz and that the domain of optimization is bounded. We provide a separate set of algorithms and matching lower bounds for the setting in which the loss functions are known to also be strongly convex. Our algorithms run… Expand
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References

SHOWING 1-10 OF 56 REFERENCES
(Near) Dimension Independent Risk Bounds for Differentially Private Learning
TLDR
This paper shows that under certain assumptions, variants of both output and objective perturbation algorithms have no explicit dependence on p; the excess risk depends only on the L2-norm of the true risk minimizer and that of training points. Expand
Private Convex Empirical Risk Minimization and High-dimensional Regression
We consider differentially private algorithms for convex empirical risk minimization (ERM). Differential privacy (Dwork et al., 2006b) is a recently introduced notion of privacy which guarantees thatExpand
The geometry of differential privacy: the sparse and approximate cases
TLDR
The connection between the hereditary discrepancy and the privacy mechanism enables the first polylogarithmic approximation to the hereditary discrepancies of a matrix A to be derived. Expand
(Nearly) Optimal Algorithms for Private Online Learning in Full-information and Bandit Settings
TLDR
The technique leads to the first nonprivate algorithms for private online learning in the bandit setting, and in many cases, the algorithms match the dependence on the input length of the optimal nonprivate regret bounds up to logarithmic factors in T. Expand
On the geometry of differential privacy
TLDR
The lower bound is strong enough to separate the concept of differential privacy from the notion of approximate differential privacy where an upper bound of O(√{d}/ε) can be achieved. Expand
Stochastic Convex Optimization
TLDR
Stochastic convex optimization is studied, and it is shown that the key ingredient is strong convexity and regularization, which is only a sufficient, but not necessary, condition for meaningful non-trivial learnability. Expand
Differentially Private Feature Selection via Stability Arguments, and the Robustness of the Lasso
TLDR
This work designs differentially private algorithms for statistical model selection and gives sufficient conditions for the LASSO estimator to be robust to small changes in the data set, and shows that these conditions hold with high probability under essentially the same stochastic assumptions that are used in the literature to analyze convergence of the LassO. Expand
Differentially Private Empirical Risk Minimization
TLDR
This work proposes a new method, objective perturbation, for privacy-preserving machine learning algorithm design, and shows that both theoretically and empirically, this method is superior to the previous state-of-the-art, output perturbations, in managing the inherent tradeoff between privacy and learning performance. Expand
Differentially Private Online Learning
TLDR
This paper provides a general framework to convert the given algorithm into a privacy preserving OCP algorithm with good (sub-linear) regret, and shows that this framework can be used to provide differentially private algorithms for offline learning as well. Expand
Sample Complexity Bounds for Differentially Private Learning
TLDR
An upper bound on the sample requirement of learning with label privacy is provided that depends on a measure of closeness between and the unlabeled data distribution and applies to the non-realizable as well as the realizable case. Expand
...
1
2
3
4
5
...