2015/07/15 by Matthew Hale, Hale, Matthew, Magnus Egerstedt +1
Computer Science · #Privacy-Preserving Technologies in Data #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1507.04371
We present an optimization framework for solving multi-agent nonlinear\nprograms subject to inequality constraints while keeping the agents' state\ntrajectories private. Each agent has an objective function depending only upon\nits own state and the agents are collectively subject to global constraints.\nThe agents do not directly communicate with each other but instead route\nmessages through a trusted cloud computer. The cloud computer adds noise to\ndata being sent to the agents in accordance with the framework of differential\nprivacy in order to keep each agent's state trajectory private from all other\nagents and any eavesdroppers. This private problem can be viewed as a\nstochastic variational inequality and is solved using a projection-based method\nfor solving variational inequalities that resembles a noisy primal-dual\ngradient algorithm. Convergence of the optimization algorithm in the presence\nof noise is proven and a quantifiable trade-off between privacy and convergence\nis extracted from this proof. Simulation results are provided that demonstrate\nnumerical convergence for both \ε-differential privacy and (\ε,\n\δ)-differential privacy.\n