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 does compute the optimal allocation of resources, avoiding each agent to reveal her private information (constraints and individual solution profile) neither to the central operator nor 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 (SMC). To obtain these cuts, we use an alternate projection method, which is implemented locally by each agent, preserving her privacy needs. We adress 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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一种优化分布式资源分配的隐私保护方法

我们考虑一个资源分配问题，它涉及大量具有受隐私约束的个体约束的代理，以及一个中央运营商，其目标是在满足代理的约束的同时优化全局的、可能是非凸的成本，例如一个能源运营商负责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，该算法确实计算资源的最佳分配，避免每个代理向中央运营商或第三方透露她的私人信息（约束和个人解决方案配置文件）。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，并逐渐确保存在分解，即满足代理的个人配置文件 私有约束，通过涉及生成多面体切割和安全多方计算 (SMC) 的协议。为了获得这些削减，我们使用了一种替代投影方法，该方法由每个代理在本地实施，以保护她的隐私需求。我们特别讨论了局部和全局约束定义运输多胞体的情况。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。我们特别讨论了局部和全局约束定义运输多胞体的情况。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。我们特别讨论了局部和全局约束定义运输多胞体的情况。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。