arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2312.02112cs.ITcs.CRcs.NIeess.SPmath.IT
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具有可行集隐私的分布式优化

Distributed Optimization with Feasible Set Privacy

Shreya Meel, Sennur Ulukus

AI总结:

本文针对两个智能体在不泄露各自可行集的情况下联合求解约束优化问题,提出基于SPIR的隐私检查方案并提取ThPSI协议,相比先求私有集合交集再寻优的方法,能以高概率实现更少信息泄露和更低下载代价。

摘要:

我们考虑一个带约束优化问题的场景,其中两个智能体 $E_1$ 和 $E_2$ 共同希望学习最优解集,同时彼此对各自的可行集 $\mathcal{P}_1$ 和 $\mathcal{P}_2$ 保持隐私。目标函数 $f$ 是全局已知的,每个可行集是来自全局字母表的一组点。我们采用顺序对称私有信息检索(SPIR)框架,其中一个智能体(例如 $E_1$)在 $\mathcal{P}_2$ 中私下检查仅受 $\mathcal{P}_1$ 约束的问题候选解是否存在,同时除了解本身之外不学习关于 $\mathcal{P}_2$ 的进一步信息。此外,我们从该方案中提取出一个信息论私密的阈值 PSI(ThPSI)协议,并刻画其下载代价。我们表明,与使用基于 SPIR 的私有集合交集(PSI)协议私下获取可行集 $\mathcal{P}_1\cap \mathcal{P}_2$ 并寻找最优解相比,我们的方案更好,因为它比前者产生更少的信息泄露和更少的下载代价。在 $f$ 到固定值域的所有可能均匀映射上,我们的方案以高概率优于前者。

英文摘要:

We consider the setup of a constrained optimization problem with two agents $E_1$ and $E_2$ who jointly wish to learn the optimal solution set while keeping their feasible sets $\mathcal{P}_1$ and $\mathcal{P}_2$ private from each other. The objective function $f$ is globally known and each feasible set is a collection of points from a global alphabet. We adopt a sequential symmetric private information retrieval (SPIR) framework where one of the agents (say $E_1$) privately checks in $\mathcal{P}_2$, the presence of candidate solutions of the problem constrained to $\mathcal{P}_1$ only, while learning no further information on $\mathcal{P}_2$ than the solution alone. Further, we extract an information theoretically private threshold PSI (ThPSI) protocol from our scheme and characterize its download cost. We show that, compared to privately acquiring the feasible set $\mathcal{P}_1\cap \mathcal{P}_2$ using an SPIR-based private set intersection (PSI) protocol, and finding the optimum, our scheme is better as it incurs less information leakage and less download cost than the former. Over all possible uniform mappings of $f$ to a fixed range of values, our scheme outperforms the former with a high probability.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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