SIAM Journal on Optimization, Volume 30, Issue 3, Page 2303-2336, January 2020.
We consider a resource allocation problem involving a large number of agents with individual constraints subject to privacy, and a central operator whose objective is to optimize a global, possibly nonconvex, cost while satisfying the agents' constraints, for instance, an energy operator in charge of the management of energy consumption flexibilities of many individual consumers. We provide a privacy-preserving algorithm that computes the optimal allocation of resources, and in which each agent's private information (constraints and individual solution profile) is never revealed either to the central operator or to a third party. Our method relies on an aggregation procedure: we compute iteratively a global allocation of resources, and gradually ensure existence of a disaggregation, that is, individual profiles satisfying agents' private constraints, by a protocol involving the generation of polyhedral cuts and secure multiparty computations. To obtain these cuts, we use an alternate projection method, which is implemented locally by each agent, preserving her privacy needs. We address especially the case in which the local and global constraints define a transportation polytope. Then, we provide theoretical convergence estimates together with numerical results, showing that the algorithm can be effectively used to solve the allocation problem in high dimension, while addressing privacy issues.

中文翻译：

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一种保护分布式资源分配的隐私保护方法

SIAM优化杂志，第30卷，第3期，第2303-2336页，2020年1月。
我们考虑一个资源分配问题，该问题涉及到具有个体约束且受隐私约束的大量代理，目标是在满足代理约束的同时优化全局（可能是非凸）成本的中央运营商，例如负责能源的运营商管理许多个人消费者的能源消耗灵活性。我们提供了一种隐私保护算法，可以计算资源的最佳分配，并且其中每个代理的私有信息（约束和单独的解决方案配置文件）都不会泄露给中央运营商或第三方。我们的方法依赖于聚合过程：我们迭代地计算资源的全局分配，并逐步确保存在分类，即满足代理人需求的个人资料 私有约束，由涉及多面体切割和安全多方计算生成的协议组成。为了获得这些削减，我们使用了一种替代的投影方法，该方法由每个代理在本地实现，从而保留了她的隐私需求。我们特别解决了局部和全局约束定义运输多面体的情况。然后，我们提供了理论收敛估计和数值结果，表明该算法可以有效地解决高维分配问题，同时解决隐私问题。我们特别解决了局部和全局约束定义运输多面体的情况。然后，我们提供了理论上的收敛估计以及数值结果，表明该算法可以有效地解决高维分配问题，同时解决隐私问题。我们特别解决了局部和全局约束定义运输多面体的情况。然后，我们提供了理论收敛估计和数值结果，表明该算法可以有效地解决高维分配问题，同时解决隐私问题。