In this paper we study the differentially private Empirical Risk Minimization (ERM) problem in different settings. For smooth (strongly) convex loss function with or without (non)-smooth regularization, we give algorithms that achieve either optimal or near optimal utility bounds with less gradient complexity compared with previous work. For ERM with smooth convex loss function in high-dimensional (p n) setting, we give an algorithm which achieves the upper bound with less gradient complexity than previous ones. At last, we generalize the expected excess empirical risk from convex loss functions to non-convex ones satisfying the Polyak-Lojasiewicz condition and give a tighter upper bound on the utility than the one in [34].

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

In this paper, we give a faster width-dependent algorithm for mixed packingcovering LPs. Mixed packing-covering LPs are fundamental to combinatorial optimization in computer science and operations research. Our algorithm finds a 1 ` ε approximate solution in time OpNw{εq, where N is number of nonzero entries in the constraint matrix, and w is the maximum number of nonzeros in any constraint. This algorithm is faster than Nesterov's smoothing algorithm which requires OpN? nw{εq time, where n is the dimension of the problem. Our work utilizes the framework of area convexity introduced in [Sherman-FOCS'17] to obtain the best dependence on ε while breaking the infamous l

In this paper we study the uncapacitated facility location problem in the model of differential privacy (DP) with uniform facility cost.

In this paper, we revisit the Empirical Risk Minimization problem in the noninteractive local model of differential privacy. In the case of constant or low dimensions (p n), we first show that if the loss function is (, T)-smooth, we can avoid a dependence of the sample complexity, to achieve error α, on the exponential of the dimensionality p with base 1/α (i.e., α

In this paper we study the differentially private Empirical Risk Minimization (ERM) problem in different settings. For smooth (strongly) convex loss function with or without (non)-smooth regularization, we give algorithms that achieve either optimal or near optimal utility bounds with less gradient complexity compared with previous work. For ERM with smooth convex loss function in high-dimensional (p n) setting, we give an algorithm which achieves the upper bound with less gradient complexity than previous ones. At last, we generalize the expected excess empirical risk from convex loss functions to non-convex ones satisfying the Polyak-Lojasiewicz condition and give a tighter upper bound on the utility than the one in [34].

In this paper, we revisit the Empirical Risk Minimization problem in the noninteractive local model of differential privacy. In the case of constant or low dimensions (p n), we first show that if the loss function is (, T)-smooth, we can avoid a dependence of the sample complexity, to achieve error α, on the exponential of the dimensionality p with base 1/α (i.e., α