Optimal partition selection with Rényi differential privacy

• URL: http://arxiv.org/abs/2603.09167v2
• Date: Wed, 11 Mar 2026 01:42:51 GMT
• Title: Optimal partition selection with Rényi differential privacy
• Abstract summary: We present an extension of our optimal algorithm tuned for $L2$ bounded partition selection.<n>We show that our primitive can be easily plugged into state of the art partition selection algorithms.
• Score: 24.85689199092059
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A common problem in private data analysis is the partition selection problem, where each user holds a set of partitions (e.g. keys in a GROUP BY operation) from a possibly unbounded set. The challenge here is in maximizing the set of released partitions while respecting a differential privacy constraint. Previous work [Desfontaines et al., PoPETS 2022] presented an optimal $(\varepsilon, δ)$-DP algorithm when each user submits only a single partition. We generalize this approach to find the optimal algorithm under $δ$-approximate $(α, \varepsilon)$-Rényi differential privacy (RDP), which allows much tighter analysis under composition. Motivated by the non-existence of a general optimality result in the case where users submit multiple partitions each, we present an extension of our optimal algorithm tuned for $L^2$ bounded weighted partition selection which can be used as a drop-in improvement over the Gaussian mechanism any time the partition frequency is not also needed. We show that our primitive can be easily plugged into state of the art partition selection algorithms (PolicyGaussian from [Gopi et al., ICML 2020] and MAD2R from [Chen et al., ICML 2025]), improving performance both for parallel and sequential adaptive algorithms. Finally, we show that there is an inherent cost to algorithms which do support releasing the frequency as well as the partitions. Specifically, we formulate a basic notion of optimal approximate RDP algorithm for partition selection using additive noise, and show that there is a numerical separation between additive and non-additive noise mechanisms for this problem.

Related papers

• Multinoulli Extension: A Lossless Continuous Relaxation for Partition-Constrained Subset Selection [60.07018090570548]
  We introduce a novel algorithm titled MultinoulliSCG, which is parameterfree and can achieve the same approximation guarantees as the distorted local-search methods.<n>We also present two novel online algorithms, namely, Multinoulli-CG and Multinoulli-GAGA, for the unexplored online subset selection problems over partition constraints.
  arXiv  Detail & Related papers  (2026-03-23T02:30:01Z)
• Optimized Tradeoffs for Private Prediction with Majority Ensembling [59.99331405291337]
  We introduce the Data-dependent Randomized Response Majority (DaRRM) algorithm.<n>DaRRM is parameterized by a data-dependent noise function $gamma$, and enables efficient utility optimization over the class of all private algorithms.<n>We show that DaRRM provably enjoys a privacy gain of a factor of 2 over common baselines, with fixed utility.
  arXiv  Detail & Related papers  (2024-11-27T00:48:48Z)
• Individualized Privacy Accounting via Subsampling with Applications in Combinatorial Optimization [55.81991984375959]
  In this work, we give a new technique for analyzing individualized privacy accounting via the following simple observation. We obtain several improved algorithms for private optimization problems, including decomposable submodular and set algorithm cover.
  arXiv  Detail & Related papers  (2024-05-28T19:02:30Z)
• Some Constructions of Private, Efficient, and Optimal $K$-Norm and Elliptic Gaussian Noise [54.34628844260993]
  Differentially private computation often begins with a bound on some $d$-dimensional statistic's sensitivity. For pure differential privacy, the $K$-norm mechanism can improve on this approach using a norm tailored to the statistic's sensitivity space. This paper solves both problems for the simple statistics of sum, count, and vote.
  arXiv  Detail & Related papers  (2023-09-27T17:09:36Z)
• A 2-opt Algorithm for Locally Optimal Set Partition Optimization [0.0]
  We develop an algorithm that can generate a locally optimal solution in at most $O(N2)$ time and $O(N)$ space. Our algorithm can handle arbitrary input precisions and does not require positive or integer inputs.
  arXiv  Detail & Related papers  (2023-03-14T20:25:56Z)
• Optimal Algorithms for Mean Estimation under Local Differential Privacy [55.32262879188817]
  We show that PrivUnit achieves the optimal variance among a large family of locally private randomizers. We also develop a new variant of PrivUnit based on the Gaussian distribution which is more amenable to mathematical analysis and enjoys the same optimality guarantees.
  arXiv  Detail & Related papers  (2022-05-05T06:43:46Z)
• Efficient Locally Optimal Number Set Partitioning for Scheduling, Allocation and Fair Selection [0.0]
  We show that our proposed algorithms can find a locally optimal solution in near linear time. Our algorithms require neither positive nor integer elements in the input set, hence, they are more widely applicable.
  arXiv  Detail & Related papers  (2021-09-10T11:53:34Z)
• No-Regret Algorithms for Private Gaussian Process Bandit Optimization [13.660643701487002]
  We consider the ubiquitous problem of gaussian process (GP) bandit optimization from the lens of privacy-preserving statistics. We propose a solution for differentially private GP bandit optimization that combines a uniform kernel approximator with random perturbations. Our algorithms maintain differential privacy throughout the optimization procedure and critically do not rely explicitly on the sample path for prediction.
  arXiv  Detail & Related papers  (2021-02-24T18:52:24Z)
• SGD with shuffling: optimal rates without component convexity and large epoch requirements [60.65928290219793]
  We consider the RandomShuffle (shuffle at the beginning of each epoch) and SingleShuffle (shuffle only once) We establish minimax optimal convergence rates of these algorithms up to poly-log factor gaps. We further sharpen the tight convergence results for RandomShuffle by removing the drawbacks common to all prior arts.
  arXiv  Detail & Related papers  (2020-06-12T05:00:44Z)
• Private Stochastic Convex Optimization: Optimal Rates in Linear Time [74.47681868973598]
  We study the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. has established the optimal bound on the excess population loss achievable given $n$ samples. We describe two new techniques for deriving convex optimization algorithms both achieving the optimal bound on excess loss and using $O(minn, n2/d)$ gradient computations.
  arXiv  Detail & Related papers  (2020-05-10T19:52:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.