differentially private algorithm design

This work addresses the problem of cardinality-constrained multi-objective submodular maximization under differential privacy, where the goal is to select at most $k$ elements from sensitive data to maximize the minimum of $d$ monotone submodular functions. The study introduces differential privacy into this setting for the first time and proposes two novel algorithms: one extends the classical greedy strategy with privacy guarantees, and the other integrates a function truncation technique. Both algorithms provide rigorous theoretical approximation guarantees. Empirical evaluations on maximum coverage and facility location tasks demonstrate that the proposed methods effectively balance utility and privacy, thereby bridging a critical gap in the intersection of differential privacy and multi-objective submodular optimization.

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.

This work studies the problem of maximizing submodular functions subject to a knapsack constraint under differential privacy, covering both monotone and non-monotone settings. The authors propose efficient approximation algorithms that achieve an optimal $(1-1/e)$-approximation ratio in the monotone case while significantly reducing additive error and query complexity. For the non-monotone setting, they present the first differentially private algorithm with theoretical guarantees, attaining an expected approximation ratio of $1/4$ and additive error comparable to the best-known monotone algorithms. Their approach integrates differential privacy mechanisms with submodular optimization techniques, knapsack constraint handling, and randomized sampling combined with noise injection.

This paper addresses privacy accounting for subsampling mechanisms—specifically Poisson and without-replacement sampling—in compositional settings under differential privacy (DP), identifying two prevalent misuses: (i) erroneously assuming the worst-case dataset for a single step suffices for adaptive composition analysis, and (ii) conflating the distinct privacy loss characteristics of the two sampling schemes. Method: We rigorously prove that privacy parameters for subsampled composition cannot be derived by naïvely composing single-step worst-case guarantees. Leveraging Rényi differential privacy and exact privacy loss distribution analysis, we develop a numerical accounting framework incorporating counterexample construction and tight theoretical bounds. Contribution/Results: We establish a decidable criterion for detecting and correcting such misuses, and demonstrate—under typical DP-SGD parameters—that ε values for Poisson and without-replacement sampling may differ by over an order of magnitude. Empirical evaluation confirms our framework prevents significant over- or under-estimation of privacy budgets, substantially improving the reliability of privacy guarantees.

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.

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 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.

This work addresses the challenge of precisely characterizing the overall privacy guarantee when composing mechanisms under multiple heterogeneous differential privacy (DP) constraints. The authors propose a general composition framework that, for the first time, enables an exact description of the resulting privacy region after composing an arbitrary number of mechanisms subject to diverse DP bounds. By constructing a binary hypothesis testing–based mixture model and integrating probabilistic mixing with f-DP approximation techniques, the framework yields an exact composition theorem for multiple DP constraints. Moreover, the approach naturally extends to the f-DP setting, significantly enhancing both the tightness and applicability of compositional privacy analysis.

This study addresses the problem of locally differentially private online learning in extensive-form bandits, where at each round a user observes only the rewards and information set they encounter while interacting with a memoryless adversary, all coordinated by a central server. We introduce local differential privacy into this setting for the first time and propose the first privacy-preserving algorithm with theoretical guarantees. Our approach combines strategy space compression with carefully calibrated privacy-preserving noise injection, enabling efficient learning under strict privacy constraints. The algorithm achieves a regret bound of Õ(√(A ln(S) T)/ε), where A denotes the maximum number of actions per information set, S the number of information sets, T the time horizon, and ε the privacy parameter. Its per-round computational complexity is nearly linear in the time required for the server to transmit the compressed strategy.

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.