# Guaranteed Feasibility in Differentially Private Linearly Constrained Convex Optimization

arXiv: https://arxiv.org/abs/2409.08364 · HTML: https://mlsanity.com/paper/2409.08364/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2024.

## Built on by (most cited first, 2 of 2)

- [Deceptive Sequential Decision-Making via Regularized Policy Optimization](https://mlsanity.com/paper/2501.18803/) (2025)
- [Differential Privacy for Euclidean Jordan Algebra with Applications to Private Symmetric Cone Programming](https://mlsanity.com/paper/2509.16915/) (2025)

## Abstract (arXiv)

Convex programming with linear constraints plays an important role in the operation of a number of everyday systems. However, absent any additional protections, revealing or acting on the solutions to such problems may reveal information about their constraints, which can be sensitive. Therefore, in this paper, we introduce a method for solving convex programs while keeping linear constraints private. First, we prove that this method is differentially private and always generates a feasible optimization problem (i.e., one whose solution exists). Then we show that the solution to the privatized problem also satisfies the original, non-private constraints. Next, we bound the expected loss in performance from privacy, which is measured by comparing the cost with privacy to that without privacy. Simulation results apply this framework to constrained policy synthesis in a Markov decision process, and they show that a typical privacy implementation induces only an approximately 9% loss in solution quality.