Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2510.05068

Multi-Agent Distributed Optimization With Feasible Set Privacy

Shreya Meel·Sennur Ulukus
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider the problem of decentralized constrained optimization with multiple agents $E_1,\ldots,E_N$ who jointly wish to learn the optimal solution set while keeping their feasible sets $\mathcal{P}_1,\ldots,\mathcal{P}_N$ private from each other. We assume that the objective function $f$ is known to all agents and each feasible set is a collection of points from a universal alphabet $\mathcal{P}_{alph}$. A designated agent (leader) starts the communication with the remaining (non-leader) agents, and is the first to retrieve the solution set. The leader searches for the solution by sending queries to and receiving answers from the non-leaders, such that the information on the individual feasible sets revealed to the leader should be no more than nominal, i.e., what is revealed from learning the solution set alone. We develop achievable schemes for obtaining the solution set at nominal information leakage, and characterize their communication costs under two communication setups between agents. In this work, we focus on two kinds of network setups: i) ring, where each agent communicates with two adjacent agents, and ii) star, where only the leader communicates with the remaining agents. We show that, if the leader first learns the joint feasible set through an existing private set intersection (PSI) protocol and then deduces the solution set, the information leaked to the leader is greater than nominal. Moreover, we draw connection of our schemes to threshold PSI (ThPSI), which is a PSI-variant where the intersection is revealed only when its cardinality is larger than a threshold value. Finally, for various realizations of $f$ mapped uniformly at random to a fixed range of values, our schemes are more communication-efficient with a high probability compared to retrieving the entire feasible set through PSI.

Explore related subjects

cs.ITcs.CRcs.DCcs.NIeess.SPmath.IT

Keep this discovery

BibTeXRIS

Shreya Meel, Sennur Ulukus. 2025-10-06. Multi-Agent Distributed Optimization With Feasible Set Privacy. https://arxiv.org/abs/2510.05068

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Mathematical Theory of Pragmatic Information

We propose a pragmatic information theory unifying communication, control, and decision-making. Its core is the isoteleia mapping, formalizing equifinality: distinct semantic paths leading to the same optimal action are pragmatically equivalent. This induces a three-tier hierarchy of syntactic, semantic, and pragmatic information, each abstraction discarding task-irrelevant distinctions. We develop pragmatic entropy, up/down mutual information, channel capacity, and rate-distortion, and prove three coding theorems generalizing Shannon's classical results. We introduce pragmatic value (VoI) and cost (CoI) of information as decision-theoretic duals to rate-distortion and capacity, respectively, and formulate a Lagrangian dual framework for cross-layer optimization. The pragmatic efficiency bound $\mathcal{E}_p(\lambda)=\sup_R[\Phi_p(R)-\lambda\,\mathrm{CoI}_p(R)]$ quantifies the maximum net utility any resource-constrained intelligent system can extract, thereby establishing a fundamental behavioral capacity limit---generalizing Shannon's symbol-level capacity to goal-directed action. Extensions to continuous messages yield closed-form Gaussian expressions, while dynamic settings are addressed via a Bellman equation for sequential decision-making. This framework provides a rigorous foundation for task-oriented communication, networked control, autonomous systems, and embodied AI, shifting focus from symbol fidelity to the effectiveness of information in guiding actions, and offers a unified mathematical language for next-generation intelligent systems.

cs.IT↗
arXiv2026

Data Protection in Function-Correcting Symbol-Pair Codes: Redundancy Bounds and Protection Profiles

In several storage systems, including DNA storage and flash memory, errors affect neighbouring symbols jointly, and the Hamming metric does not adequately capture such error patterns. The symbol-pair read channel, introduced by Cassuto and Blaum~\cite{cassuto2011codes}, addresses this by reading consecutive pairs of symbols rather than individual symbols. Motivated by this, we introduce function-correcting symbol-pair codes with data protection (FCSPC-DP), which guarantee reliable recovery of a desired function of the message while simultaneously protecting the message itself against symbol-pair errors. We derive bounds on the optimal redundancy of such codes and establish a relationship with joint-pair distance matrices. We also give explicit constructions of FCSPC-DP for locally pair-bounded functions and symbol-pair weight functions. We introduce the pair-separation constant of a function, the minimum symbol-pair distance between messages sharing a function value, and show that when it is sufficiently large, data protection requires no additional redundancy: the optimal redundancy coincides with that of the corresponding code without data protection. Considering the symbol-pair analogue of the $\alpha$-distance graph, we introduce two code invariants, the generation profile and the disconnection threshold, and use them to characterise a code's protection properties. Relating the two metrics through these invariants yields upper and lower bounds on the symbol-pair threshold in terms of its Hamming counterpart, both of which are attained. We further extend the classical Plotkin and sphere-packing bounds to this setting.

cs.IT↗
arXiv2026

Physics of Information Geometry - Part II: Small-Step Active Inference on the Probability Simplex

This paper is the second in a two-part investigation of the physics of information geometry. While Part I develops a physical foundation for distributional motion on the probability simplex, the present paper studies how that framework manifests in active inference. The treatment is fully self-contained and does not require familiarity with Part I. We focus in particular on active inference through small distributional steps and the geometric structure induced by such local motion. Starting from an initial distribution, an agent evolves its belief state toward a final target distribution through a sequence of constrained updates. We define a relative free energy functional with respect to the preferred distribution and extend it to a relative potential energy analogous to the Helmholtz/Gibbs free-energy decomposition. The evolution is subject to a per-step kinetic constraint expressed through the Kullback-Leibler (KL) divergence between consecutive distributions, which serves as a discrete kinetic energy on the probability simplex. Using the information-geometric Pythagorean theorem on KL balls, we show that sufficiently small local moves dominate large direct jumps, and that greedy maximization of free-energy reduction is globally optimal under the kinetic constraint. This leads to a sequential variational principle in which the optimal trajectory minimizes the associated Lagrangian of the optimization problem. Similar to classical mechanics, the Lagrangian takes on the form as the difference between the kinetic and potential terms, establishing a least-action principle for distributional motion on the simplex. The resulting optimal update admits a closed form as an exponentially tilted version of the current distribution toward the preferred distribution, parametrized by an inverse-temperature-like multiplier. We further extend the framework to incorporate state-dependent geodesic...

cs.IT↗