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.
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 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. 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.
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.
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.
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.
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 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.
New algorithms optimize private convex optimization with faster rates for functions with κ-growth.
problem Optimizing private convex functions with varying difficulty and growth conditions.
method Adapts inverse sensitivity mechanism and localization techniques to achieve faster rates without knowing growth constant.
result Achieves faster privacy rates ( d / n ε ) f r a c κ κ − 1 ({\sqrt{d}}/{n\varepsilon})^{ fracκ{κ- 1}} ( d / n ε ) f r a c κ κ − 1 for functions with κ-growth. 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.
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. 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 …
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 ≤ ∞ . 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.
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.
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.
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. 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…
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…
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. One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and then exactly solves it. However, to date, analyses of this approach crucially rely …
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.
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. Study on gradient complexity of private optimization with private oracles.
problem Analyzing the efficiency of differentially private optimization algorithms.
method Lower bounds on the number of first-order oracle queries for private optimization.
result Lower bounds on the number of queries for private optimization algorithms, showing a dimension-dependent runtime penalty.
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…
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.
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.
Two private algorithms improve domain adaptation with privacy guarantees.
problem Improving predictions for a private target domain using public data.
method Two ( ε , δ ) (ε, δ) ( ε , δ ) -differentially private algorithms for supervised domain adaptation. result Private algorithms maintain performance close to non-private versions.
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 …
Paper tackles LDP bandits learning with improved results and sub-linear regret.
problem Contextual bandits learning with LDP privacy constraints.
method Simple black-box reduction frameworks for context-free bandits, extended to GLB.
result First result for BCO with multi-point feedback under LDP, sub-linear regret for GLB.
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. 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.
Improved ADMM for convex distributed learning with differential privacy.
problem Privacy concerns in distributed learning with sensitive data.
method Approximate multi-step ADMM with calibrated noise.
result Higher utility and error bounds asymptotic to state-of-the-art.
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 . 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.
New algorithm for differentially private distributed optimization of smooth, non-convex problems.
problem No differentially private distributed method for smooth, non-convex optimization problems.
method Smoothed normalization integrated with an error-feedback mechanism.
result Achieves superior convergence rate and first differentially private distributed optimization algorithm with provable convergence guarantees.
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.
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.
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.
In this paper we develop the first algorithms for online submodular minimization that preserve differential privacy under full information feedback and bandit feedback. A sequence of T T T submodular functions over a collection of n n n elements arrive online, and at each timestep the algorithm must choose a subset of $[n]…
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 for private non-convex optimization with optimal rates.
problem Private optimization of non-convex functions under KL condition.
method Variance-reduced gradient descent and proximal point method.
result Achieves nearly optimal rates for excess empirical risk.
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 . Private optimization faster on interpolation problems with quadratic growth.
problem Private optimization in interpolation problems.
method Adaptive algorithm with improved sample complexity.
result Exponential improvement in private sample complexity for quadratic growth.
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.
Efficiently learns private models using public data.
problem Improving private learning performance with public data.
method Proves computationally efficient algorithms for private learning with public data.
result First computationally efficient algorithms for private learning with public data.
Paper proposes DP-SGD and DP-NSGD for differentially private non-convex optimization.
problem Mitigating privacy risks in large model learning.
method Clip or normalize per-sample gradients and add noise for differential privacy.
result Achieved convergence rate of gradient norm for non-convex optimization.