网络路由的微分私有随机凸优化算法
Differentially Private Stochastic Convex Optimization for Network Routing Applications
摘要：
网络路由问题在许多工程应用中很常见。计算最优路由策略需要关于网络需求的知识，即，网络中所有请求的来源和目的地（OD）。然而，隐私考虑使得共享计算最优策略所需的个体OD数据具有挑战性。在标准网络路由问题中，隐私可能特别具有挑战性，因为源和汇可以很容易地从流量守恒约束中识别出来，这使得可行性和隐私相互排斥。在本文中，我们提出了一个差分隐私算法的网络路由问题。的主要成分是一个重新制定的网络路由移动所有用户数据相关的参数的约束集，并进入目标函数。然后，我们提出了一个算法来解决这个配方的基础上的差异私人变量的随机梯度下降。在该算法中，差分隐私是通过注入噪声来实现的，人们可能会怀疑这种噪声注入是否会损害解决方案的质量。我们证明了我们的算法是差分私人和渐近最优的训练集的大小趋于无穷大。我们证实了理论结果与道路交通网络上的数值实验表明，我们的算法在实践中提供了不同的私人和接近最优的解决方案。
英文摘要：
Network routing problems are common across many engineering applications. Computing optimal routing policies requires knowledge about network demand, i.e., the origin and destination (OD) of all requests in the network. However, privacy considerations make it challenging to share individual OD data that would be required for computing optimal policies. Privacy can be particularly challenging in standard network routing problems because sources and sinks can be easily identified from flow conservation constraints, making feasibility and privacy mutually exclusive. In this paper, we present a differentially private algorithm for network routing problems. The main ingredient is a reformulation of network routing which moves all user data-dependent parameters out of the constraint set and into the objective function. We then present an algorithm for solving this formulation based on a differentially private variant of stochastic gradient descent. In this algorithm, differential privacy is achieved by injecting noise, and one may wonder if this noise injection compromises solution quality. We prove that our algorithm is both differentially private and asymptotically optimal as the size of the training set goes to infinity. We corroborate the theoretical results with numerical experiments on a road traffic network which show that our algorithm provides differentially private and near-optimal solutions in practice.
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