Improved privacy-preserving methods for convex optimization with heavy-tailed data.
problem Privacy-preserving optimization of convex functions with heavy-tailed data.
method Developed algorithms for private mean estimation and convex optimization under concentrated differential privacy constraints.
result Achieved improved upper bounds on excess population risk for convex and strongly convex loss functions.
New algorithms for differentially private optimization in convex and non-convex settings with near-optimal rates.
problem Differentially private optimization in convex and non-convex settings.
method Developed algorithms for convex and non-convex settings with near-optimal excess population risk.
result Achieved near-optimal rates in near-linear time for convex settings and nearly dimension independent rates for non-convex settings.
Optimal private ERM and SCO with subquadratic gradient complexity.
problem Private optimization of non-smooth convex functions.
method Subquadratic gradient complexity algorithm using subsampling and smoothing.
result Achieved optimal excess empirical risk and population loss.
We study differentially private (DP) algorithms for stochastic convex optimization (SCO). In this problem the goal is to approximately minimize the population loss given i.i.d. samples from a distribution over convex and Lipschitz loss functions. A long line of existing work on private convex optimization focuses on th…
New approach achieves optimal rates for differentially private stochastic convex optimization with heavy-tailed gradients.
problem Differentially private stochastic convex optimization with heavy-tailed gradients.
method Reduction-based approach to achieve optimal rates.
result Achieved optimal rates up to logarithmic factors, nearly matching a lower bound.
New framework for DP-SMO with near-optimal privacy-loss trade-off.
problem Optimal trade-off between privacy and population loss in DP-SMO.
method General framework using Phased-ERM method and black-box optimization.
result Near-linear time algorithms with near-optimal guarantees.
Paper improves privacy in SGD with low noise, achieving optimal risk rates.
problem Privacy-preserving machine learning with good performance.
method Differentially private SGD with low-noise analysis.
result Achieves optimal excess risk rates for non-smooth losses.
Optimizes private learning with differential privacy for LASSO problems.
problem Private optimization of convex functions over ℓ 1 \ell_1 ℓ 1 -bounded domains. method Combines iterative localization with private regularized mirror descent and variance-reduced Frank-Wolfe algorithm.
result Achieves optimal excess population loss rates in ℓ 1 \ell_1 ℓ 1 geometry. Private adaptive methods improve on traditional SGD for convex optimization.
problem Differential privacy constraints in gradient optimization.
method Differentially private variants of SGD and AdaGrad with adaptive stepsizes and non-isotropic clipping.
result Private AdaGrad outperforms private SGD in high-dimensional problems.
Second-order methods improve differential privacy in convex optimization.
problem Improving differential privacy in convex optimization.
method Developed a private variant of the regularized cubic Newton method for strongly convex loss functions.
result Achieves quadratic convergence and optimal excess loss for strongly convex loss functions.
New algorithms achieve optimal DP convex optimization with linear time and gradient computations.
problem Private stochastic convex optimization with optimal excess loss.
method Two new techniques: variable batch sizes and localization with stable optimization.
result Achieves optimal bound on excess loss with O ( min { n , n 2 / d } ) O(\min\{n, n^2/d\}) O ( min { n , n 2 / d }) gradient computations. Paper revisits DP-SCO in Euclidean and ℓ p d \ell_p^d ℓ p d spaces, focusing on constrained and bounded sets.
problem Differentially private stochastic convex optimization in constrained and bounded sets in Euclidean and ℓ p d \ell_p^d ℓ p d spaces. method Proposes methods achieving excess population risks dependent on Gaussian width of the constraint set, and novel algorithms for unconstrained and heavy-tailed data.
result Theoretical results for DP-SCO in ℓ p d \ell_p^d ℓ p d spaces, including optimal bounds for strongly convex functions. New framework for private convex optimization in arbitrary norms.
problem Private optimization of convex functions in non-Euclidean settings.
method Regularized exponential mechanism based on localization tools from convex geometry.
result First optimal privacy-utility tradeoffs for ℓ p \ell_p ℓ p norms and Schatten- p p p norms. Gradient perturbation, widely used for differentially private optimization, injects noise at every iterative update to guarantee differential privacy. Previous work first determines the noise level that can satisfy the privacy requirement and then analyzes the utility of noisy gradient updates as in the non-private cas…
Improved DP algorithms for non-convex optimization with tighter generalization bounds.
problem Private stochastic non-convex optimization in high-dimensional spaces.
method Differential privacy techniques, including adaptive algorithms like DP RMSProp and DP Adam, combined with adaptive data analysis.
result Achieved a sharper rate of p 4 / n \sqrt[4]{p}/\sqrt{n} 4 p / n for population loss, improving upon previous bounds. New DP optimization methods for sparse gradients, improving on existing algorithms.
problem Differentially private optimization with sparse gradients in high-dimensional settings.
method Improved bounds for mean estimation, pure- and approximate-DP algorithms for stochastic convex optimization.
result First nearly dimension-independent rates for DP optimization with sparse gradients.
New DP algorithm improves privacy and efficiency for convex optimization.
problem Efficient, DP algorithms for convex optimization with strong excess risk bounds.
method Output perturbation for a broad class of tilted loss functions.
result Near optimal DP excess risk and runtime bounds for convex optimization.
Paper tackles private optimization for non-smooth objectives efficiently.
problem Private stochastic convex optimization for non-smooth objectives.
method Noisy mirror descent algorithm.
result Achieves optimal rates in statistical complexity and number of queries.
New method for differentially private optimization with general Lipschitz conditions.
problem Differentially private optimization under general Lipschitz conditions.
method Generalized Lipschitz condition for per-sample gradients, tuning clip norm based on minimum per-sample Lipschitz constant.
result Efficacy of the recommended clip norm tuning method verified on 8 datasets.
New algorithm achieves optimal privacy and efficiency in non-Euclidean convex optimization.
problem Optimizing convex functions while maintaining privacy in non-Euclidean settings.
method Developed a linear-time algorithm for ℓ p \ell_p ℓ p -setups, leveraging geometric properties. result Optimal excess risk achieved in linear time for 1 < p ≤ 2 1 < p \leq 2 1 < p ≤ 2 . Enhanced stability improves privacy in machine learning.
problem Improving privacy in machine learning training while maintaining accuracy.
method Study of stability in private empirical risk minimization, focusing on strongly-convex loss functions and uniform stability.
result An algorithm with uniform stability of β implies a bound of O(√β) on the scale of noise required for differential privacy.
The paper introduces a differentially private method for optimization on Riemannian manifolds.
problem Differential privacy in optimization constrained to Riemannian manifolds.
method Adding Gaussian noise to the Riemannian gradient on the tangent space, with privacy and utility guarantees.
result Privacy and utility guarantees for differentially private Riemannian optimization.
In this paper, we consider efficient differentially private empirical risk minimization from the viewpoint of optimization algorithms. For strongly convex and smooth objectives, we prove that gradient descent with output perturbation not only achieves nearly optimal utility, but also significantly improves the running …
New algorithms for private generalized linear contextual bandits.
problem Private estimation and optimization for generalized linear models under differential privacy.
method Developed algorithms for stochastic and adversarial contexts under shuffle and joint differential privacy.
result Achieved private regret bounds for generalized linear models, differing from non-private rates by factors of d / ε \sqrt{d/\varepsilon} d / ε and d / ε \sqrt{d/\varepsilon} d / ε respectively. Paper relaxes SGD privacy and generalization guarantees for non-smooth convex losses.
problem Privacy and generalization in SGD for non-smooth convex losses.
method Relaxes Lipschitz and strong smoothness assumptions to Hölder smoothness, proving ( ε , δ ) (ε,δ) ( ε , δ ) -DP and optimal excess risk. result Noisy SGD with α α α -Hölder smooth losses achieves optimal excess risk with linear gradient complexity for α ≥ 1 / 2 α \geq 1/2 α ≥ 1/2 . Study public-data assisted private stochastic optimization with labeled or unlabeled public data.
problem Limits and capability of public-data assisted differentially private (PA-DP) algorithms in stochastic convex optimization.
method Lower bounds for PA-DP mean estimation and novel methods for leveraging public data in private supervised learning.
result Achieved dimension independent rate for GLM with unlabeled public data, showing optimality.
New tool for parallel and private stochastic convex optimization reduces query complexity.
problem Parallel and private stochastic convex optimization with reduced query complexity.
method Reweighted Stochastic Query (ReSQue) estimator combined with ball oracle acceleration.
result Achieves state-of-the-art complexities for SCO in parallel and private settings.
Privacy affects how much data is needed for CVaR optimization.
problem Privacy constraints impact the effective sample size for CVaR optimization.
method Analyzes the privacy-relevant sample size and decomposes CVaR excess risk.
result The effective private tail sample size is εnτ, affecting CVaR learning rates.
Optimizes privacy-preserving optimization for heavy-tailed data.
problem Privacy-preserving optimization with heavy-tailed gradients.
method Pure ε-differential privacy framework for Lipschitz extensions.
result Minimax optimal excess-risk rate for pure ε-DP heavy-tailed SCO.
Novel algorithm reduces privacy noise in machine learning.
problem High privacy noise in machine learning algorithms.
method Robust statistics, specifically median and trimmed mean, to bound sensitivity of SGD iterates.
result Improved privacy-utility trade-off with reduced noise and computational efficiency.
Optimal DP model training with public data improves privacy and accuracy.
problem Ensuring privacy while training models with public data.
method Proves optimal error rates for DP model training with public data, develops novel algorithms.
result Optimal error rates can be achieved by using public data or optimal DP algorithms.
Paper addresses DP-SCO on heavy-tailed data, providing methods and results.
problem Designing DP algorithms for SCO on heavy-tailed data.
method Sample-and-aggregate framework, gradient smoothing and trimming.
result Achieved DP guarantees for various loss functions with different excess population risks.
Paper addresses private online convex optimization with optimal algorithms in various geometries and high-dimensional bandits.
problem Private online convex optimization with streaming and continual release data.
method Proposes a private variant of online Frank-Wolfe algorithm with recursive gradients for variance reduction.
result Achieves optimal excess risk in linear time for 1 < p ≤ 2 1<p\leq 2 1 < p ≤ 2 and state-of-the-art excess risk for 2 < p ≤ ∞ 2<p\leq\infty 2 < p ≤ ∞ . We consider the problem of minimizing a convex risk with stochastic subgradients guaranteeing ε ε ε -locally differentially private ( ε ε ε -LDP). While it has been shown that stochastic optimization is possible with ε ε ε -LDP via the standard SGD (Song et al., 2013), its convergence rate largely depends on the learning rate, w…
Paper introduces a privacy-preserving line search method for optimization.
problem Optimization performance depends on step size tuning, which is difficult and privacy-sensitive.
method Introduces a stochastic adaptive line search algorithm that satisfies differential privacy.
result The algorithm efficiently uses privacy budget and outperforms existing private optimizers.
Study optimizes privacy in distributed optimization, balancing accuracy and communication.
problem Privacy-preserving distributed stochastic convex optimization.
method Distributed algorithm using Vaidya's plane cutting method, with privacy guarantees via differential privacy.
result Complete characterization of accuracy-communication-privacy trade-off.
New stability bounds for SGD on nonsmooth convex losses.
problem Understanding stability of SGD on nonsmooth convex losses.
method Sharp upper and lower bounds for SGD and full-batch GD on nonsmooth convex losses.
result SGD can be less stable but still useful for generalization bounds.
Optimizes differentially private kernel learning with random projection.
problem Privacy-preserving learning algorithms with optimal performance.
method Differentially private kernel ERM algorithm based on random projection in reproducing kernel Hilbert space.
result Achieves minimax-optimal excess risk rates for various loss functions.
Paper improves privacy-preserving optimization rates for convex functions.
problem Differentially private stochastic convex optimization.
method Algorithmic improvements for convex and strongly convex functions under TNC and non-negative loss.
result Excess population risk bounds for DP-SCO are faster than previous results.
Many commonly used learning algorithms work by iteratively updating an intermediate solution using one or a few data points in each iteration. Analysis of differential privacy for such algorithms often involves ensuring privacy of each step and then reasoning about the cumulative privacy cost of the algorithm. This is …
Develops a functional generalization of Eldan's stochastic localization for optimization and privacy.
problem Sampling under non-Euclidean geometries and optimization in differential privacy.
method Functional generalization of Eldan's stochastic localization, incorporating log-Laplace transform.
result Improves query complexities in zeroth-order differential private convex optimization.
Differential privacy is concerned about the prediction quality while measuring the privacy impact on individuals whose information is contained in the data. We consider differentially private risk minimization problems with regularizers that induce structured sparsity. These regularizers are known to be convex but they…
Optimizes private statistics with noisy methods.
problem Private inference in statistical models.
method Noisy optimization for M-estimators and confidence regions.
result Private estimators converge to non-private ones with high probability.
Zeroth-order optimization methods lack inherent privacy guarantees.
problem Ensuring differential privacy in zeroth-order optimization methods.
method Analyzing ZO-GD with and without random initialization for convex and strongly convex objectives.
result ZO-GD is not differentially private for strongly convex objectives and can have superlinear privacy loss.
While many solutions for privacy-preserving convex empirical risk minimization (ERM) have been developed, privacy-preserving nonconvex ERM remains a challenge. We study nonconvex ERM, which takes the form of minimizing a finite-sum of nonconvex loss functions over a training set. We propose a new differentially private…
We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex optimization, the sample complexity of our algorithms depends only on the margin of…
New private algorithms for online learning improve regret in high privacy regimes.
problem Private online learning from experts and convex optimization.
method Transformed lazy algorithms for differential privacy.
result Improved regret bounds for DP-OPE and DP-OCO.
The paper addresses differentially private learning for neural networks, focusing on risk bounds and algorithm feasibility.
problem Achieving differentially private learning for neural networks with theoretical guarantees.
method Developed algorithms and theoretical analysis for differentially private stochastic optimization of neural networks.
result Established theoretical bounds for excess population risk in differentially private learning of neural networks.