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Private Rate-Constrained Optimization with Applications to Fair Learning

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.5Download Report PDF
differential privacyfairnessmachine learning
Abstract:

Many problems in trustworthy ML can be expressed as constraints on prediction rates across subpopulations, including group fairness constraints (demographic parity, equalized odds, etc.). In this work, we study such constrained minimization problems under differential privacy (DP). Standard DP optimization techniques like DP-SGD rely on objectives that decompose over individual examples, enabling per-example gradient clipping and noise addition. Rate constraints, however, depend on aggregate statistics across groups, creating inter-sample dependencies that violate this decomposability. To address this, we develop RaCO-DP, a DP variant of Stochastic Gradient Descent-Ascent (SGDA) that solves the Lagrangian formulation of rate constraint problems. We show that the additional privacy cost of incorporating these constraints reduces to privately estimating a histogram over the mini-batch at each step. We prove convergence of our algorithm through a novel analysis of SGDA that leverages the linear structure of the dual parameter. Empirical results show that our method Pareto-dominates existing private learning approaches under group fairness constraints and also achieves strong privacy–utility–fairness performance on neural networks.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper introduces RaCO-DP, a differentially private algorithm for optimization under rate constraints across subpopulations, with applications to group fairness. It resides in the 'Private Rate-Constrained Optimization and Fair Learning' leaf, which contains only this single paper in the taxonomy. This isolation suggests the specific combination of differential privacy with explicit rate constraints (e.g., demographic parity, equalized odds) represents a relatively sparse research direction within the broader field of private optimization, which spans 50 papers across 36 topics.

The taxonomy reveals dense activity in neighboring areas: Differentially Private Stochastic Convex Optimization (5 papers across 4 sub-branches) addresses foundational private learning theory, while Federated Learning with Privacy and Communication Constraints (26 papers) explores decentralized training with bandwidth limits. Distributed Optimization (13 papers) examines multi-agent coordination under privacy and communication constraints. The original work diverges by treating rate constraints as first-class optimization objectives rather than implementation details, bridging fairness-constrained learning with privacy mechanisms in a way that neighboring branches do not directly address.

Among 25 candidates examined, no papers clearly refute the three core contributions. The RaCO-DP algorithm (10 candidates examined, 0 refutable) appears novel in its approach to handling inter-sample dependencies via histogram privatization. The generalized rate constraints framework (10 candidates, 0 refutable) and convergence analysis for biased SGDA with linear dual structure (5 candidates, 0 refutable) similarly show no substantial prior overlap within the limited search scope. This suggests the specific technical combination—private Lagrangian formulation for rate constraints with provable convergence—has not been directly addressed in closely related work.

Based on the top-25 semantic matches and taxonomy structure, the work appears to occupy a genuinely underexplored niche at the intersection of fairness-constrained learning and differential privacy. However, the limited search scope means broader connections to fairness literature without privacy or privacy work without explicit rate constraints may exist beyond this analysis. The single-paper leaf status and absence of refuting candidates within examined work support a preliminary assessment of novelty, though exhaustive validation would require deeper exploration of fairness and constrained optimization communities.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
25
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: differentially private optimization under rate constraints. This field addresses the dual challenge of protecting sensitive data through differential privacy while operating under communication or bandwidth limitations. The taxonomy reveals a rich structure spanning seven main branches. Differentially Private Stochastic Convex Optimization establishes foundational theory for private learning with constrained resources, exemplified by works like Private Stochastic Convex[9]. Federated Learning with Privacy and Communication Constraints forms a dense branch exploring decentralized training scenarios where clients must balance privacy guarantees with limited upload capacity, as seen in Differential Privacy Federated[2] and Private Federated Bandwidth[8]. Distributed Optimization branches examine multi-agent coordination under privacy and rate limits, including consensus-based approaches like Privacy Consensus Dynamic[3] and Privacy ADMM Event-Triggered[5]. Private Rate-Constrained Optimization and Fair Learning tackles direct optimization problems where communication budgets interact with privacy mechanisms. Additional branches cover sparse distribution estimation under local privacy, privacy-preserving data aggregation for IoT and edge computing, and architectural reviews synthesizing theoretical frameworks. Particularly active lines of work explore trade-offs between privacy strength, communication efficiency, and convergence rates. Many studies in federated settings investigate gradient compression, quantization schemes as in Privacy Adaptive Quantization[43], and over-the-air aggregation methods like Private Over-the-Air Federated[24]. Contrasting approaches emerge between centralized privacy accounting versus local privacy models, and between synchronous versus event-triggered communication protocols. Private Rate-Constrained Optimization[0] sits within the branch addressing explicit rate constraints in optimization, closely related to works examining consensus under communication limits such as Privacy Consensus Dynamic[3] and distributed methods like Privacy ADMM Event-Triggered[5]. While neighboring papers often focus on iterative distributed algorithms, the original work emphasizes direct optimization formulations where rate budgets are first-class constraints rather than implementation details, offering a complementary perspective on how communication costs fundamentally shape achievable privacy-utility frontiers.

Claimed Contributions

RaCO-DP algorithm for private rate-constrained optimization

The authors introduce RaCO-DP, a differentially private algorithm that extends SGDA to handle rate-constrained optimization problems. The algorithm uses private histogram computation to enable per-sample gradient decomposition and constraint evaluation while maintaining differential privacy guarantees.

10 retrieved papers
Generalized rate constraints framework

The authors introduce a generalized formulation of rate constraints that extends beyond binary classification to multi-class settings and exploits shared structure through a global partition of the dataset. This formulation enables efficient private estimation while supporting a broad range of constraints including fairness, robust optimization, and cost-sensitive learning.

10 retrieved papers
Convergence analysis for biased SGDA with linear dual structure

The authors provide a novel convergence analysis for SGDA that handles biased gradient estimates and exploits the linear structure of the dual update to achieve faster convergence rates (1/T^(1/4) instead of 1/T^(1/6)). The analysis proves that RaCO-DP converges to an approximate stationary point even for non-convex problems.

5 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

RaCO-DP algorithm for private rate-constrained optimization

The authors introduce RaCO-DP, a differentially private algorithm that extends SGDA to handle rate-constrained optimization problems. The algorithm uses private histogram computation to enable per-sample gradient decomposition and constraint evaluation while maintaining differential privacy guarantees.

Contribution

Generalized rate constraints framework

The authors introduce a generalized formulation of rate constraints that extends beyond binary classification to multi-class settings and exploits shared structure through a global partition of the dataset. This formulation enables efficient private estimation while supporting a broad range of constraints including fairness, robust optimization, and cost-sensitive learning.

Contribution

Convergence analysis for biased SGDA with linear dual structure

The authors provide a novel convergence analysis for SGDA that handles biased gradient estimates and exploits the linear structure of the dual update to achieve faster convergence rates (1/T^(1/4) instead of 1/T^(1/6)). The analysis proves that RaCO-DP converges to an approximate stationary point even for non-convex problems.

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