design exponential mechanism

This paper investigates the selection problem under differential privacy: whether the optimal error bound of the exponential mechanism can be approached using only adaptive calls to the Gaussian mechanism on low-sensitivity queries. The authors establish, for the first time, that relying solely on the Gaussian mechanism—without invoking the exponential mechanism or other complex primitives—and combining sensitivity analysis, adaptive query design, and optimized composition-theorem-based privacy budget allocation, achieves a selection error of $ ilde{O}(log |mathcal{Y}|)$. This improves upon the prior best bound of $O(log^{3/2} |mathcal{Y}|)$, nearly matching the theoretical lower bound. The result reveals the fundamental expressive power of the Gaussian mechanism for private selection tasks and establishes a new paradigm for designing lightweight, scalable differentially private algorithms.

Differential privacy (DP) mechanisms are commonly reported at a single $(varepsilon,delta)$ point, obscuring substantial differences in actual privacy risk among mechanisms sharing identical $(varepsilon,delta)$ parameters—leading to systematic underestimation of risk. Method: We propose a unified quantification framework grounded in $Delta$-divergence, integrating f-differential privacy, Bayesian privacy interpretations, and Blackwell order theory for the first time to establish a decision-theoretically principled paradigm for comparing DP mechanisms. Contribution/Results: By rigorously characterizing worst-case privacy vulnerability disparities, we expose non-negligible excess risk in mainstream noise mechanisms used in DP-SGD. Our framework yields a verifiable, ordinal privacy strength assessment tool—enabling rigorous, theoretically grounded selection of privacy-preserving mechanisms.

Multi-objective optimization under differential privacy remains challenging, particularly for sensitive data scenarios where conventional single-objective privacy mechanisms fail to balance competing utility objectives. Method: This paper proposes two ε-differentially private mechanisms—PrivPareto, which identifies the Pareto frontier via a novel Pareto scoring mechanism, and PrivAgg, which performs privacy-preserving weighted aggregation. We establish the first theoretical framework for composing local sensitivity of multi-objective utility functions, enabling rigorous privacy accounting beyond global sensitivity bounds. Contribution/Results: Evaluated on real-world tasks—influence maximization in social networks and cost-sensitive decision tree learning—our methods consistently outperform global-sensitivity baselines across ε ∈ [0.01, 1], delivering stable utility gains and practical deployability. The approach unifies multi-objective cooperative optimization with strict (ε, 0)-differential privacy guarantees, overcoming fundamental limitations of prior single-objective selection strategies.

Traditional differential privacy (DP) research adopts a “privacy-first” paradigm, whereas real-world applications often require “utility-first” design—minimizing privacy cost while guaranteeing a prescribed utility target. Existing approaches are restricted to Laplace/Gaussian mechanisms, lack support for general sequences of private estimators, and incur additional privacy overhead from hyperparameter tuning. Method: We generalize ex-post DP to arbitrary sequences of private estimators and propose an adaptive hyperparameter tuning scheme that incurs no extra privacy cost. We further extend this framework to Rényi DP. Contribution/Results: Our method enables optimal privacy budget allocation under flexible utility constraints. Empirically, it achieves up to 50% reduction in privacy cost while strictly satisfying the specified utility requirement—significantly enhancing the practicality and applicability of the privacy–utility trade-off.

Existing differentially private hyperparameter tuning methods under the white-box setting suffer from loose theoretical privacy bounds that significantly diverge from empirical observations. Method: This paper first uncovers intrinsic structural properties of the hyperparameter tuning process, breaking the tightness limitations of conventional private selection mechanisms. We propose a novel privacy analysis framework grounded in sensitivity reconstruction and white-box modeling, integrating rigorous differential privacy theory with empirical privacy auditing—without requiring additional assumptions—to precisely characterize actual privacy loss. Contribution/Results: Experiments demonstrate that our method substantially reduces privacy budget consumption (by 35–62% on average) while preserving model utility. It is broadly applicable across diverse hyperparameter spaces and model families, offering both tighter theoretical guarantees and practical tools for private machine learning.

This work addresses the fundamental challenge in privacy mechanism design: maximizing worst-case utility under strict privacy constraints while avoiding inefficient outputs. It introduces, for the first time, the novel privacy metric Pointwise Maximal Leakage (PML) to this setting and proposes a discrete privacy mechanism that optimizes worst-case utility under hard PML constraints. Crucially, the mechanism permits certain conditional probabilities to be exactly zero—a flexibility prohibited under differential privacy—thereby overcoming a key limitation of traditional approaches. By incorporating output support set constraints, the authors formulate a computationally efficient optimization framework. Experimental results demonstrate that the proposed mechanism consistently outperforms conventional differential privacy methods across multiple benchmarks, achieving superior utility-security trade-offs with low computational complexity.

This study addresses the trade-off between privacy preservation and targeting accuracy in resource allocation under differential privacy constraints. It presents the first systematic integration of private optimization and economic allocation theory, establishing a distribution-free analytical framework applicable to both individual-level and unit-level allocation policies. Theoretical analysis yields interpretable bounds that characterize the interplay among privacy, efficiency, and targeting precision, demonstrating that unit-level allocation achieves a superior balance between privacy and utility. Furthermore, the work quantifies the multidimensional trade-offs among these three competing objectives, offering principled insights for designing privacy-preserving allocation mechanisms.

This work addresses the design of optimal mechanisms for binary hypothesis testing under ε-local differential privacy (LDP). It proposes the Sort-Partition-Randomize (SPR) framework, which first orders input symbols by their likelihood ratios, partitions them into contiguous blocks, and then applies randomized response to the block labels. Leveraging this structure, the paper establishes the existence of an optimal mechanism for any privacy budget ε and any f-divergence–based utility objective—including total variation distance and KL divergence—and presents, for the first time, a dynamic programming algorithm that computes such a mechanism exactly in O(k³) time. This approach overcomes prior limitations restricted to asymptotic privacy regimes, enabling efficient computation of optimal mechanisms across the full range of privacy parameters.

This work addresses the problem of efficiently generating synthetic data under differential privacy for a given family of queries. By parameterizing the problem with the treewidth of the query family’s associated graph, the authors establish—for the first time—that the problem is fixed-parameter tractable. They propose a unified dynamic programming framework that integrates linear programming duality-based separation, subsampled private multiplicative weights, and Gibbs sampling techniques. This approach achieves theoretically optimal error rates across the full parameter regime, significantly enhancing both the scalability and practical utility of differentially private synthetic data generation.