Differential privacy of populations in routing games

As our ground transportation infrastructure modernizes, the large amount of data being measured, transmitted, and stored motivates an analysis of the privacy aspect of these emerging cyber-physical technologies. In this paper, we consider privacy in the routing game, where the origins and destinations of drivers are considered private. This is motivated by the fact that this spatiotemporal information can easily be used as the basis for inferences for a person's activities. More specifically, we consider the differential privacy of the mapping from the amount of flow for each origin-destination pair to the traffic flow measurements on each link of a traffic network. We use a stochastic online learning framework for the population dynamics, which is known to converge to the Nash equilibrium of the routing game. We analyze the sensitivity of this process and provide theoretical guarantees on the convergence rates as well as differential privacy values for these models. We confirm these with simulations on a small example.

[1]  Benjamin Gerber,et al.  Conceptualizing privacy , 2010, CSOC.

[2]  Ufuk Topcu,et al.  Differentially Private Distributed Constrained Optimization , 2014, IEEE Transactions on Automatic Control.

[3]  Avrim Blum,et al.  Routing without regret: on convergence to nash equilibria of regret-minimizing algorithms in routing games , 2006, PODC '06.

[4]  Alexandre M. Bayen,et al.  Learning Nash Equilibria in Congestion Games , 2014, ArXiv.

[5]  Henrik Ohlsson,et al.  Fundamental limits of nonintrusive load monitoring , 2013, HiCoNS.

[6]  Gábor Lugosi,et al.  Prediction, learning, and games , 2006 .

[7]  William H. Sandholm,et al.  Potential Games with Continuous Player Sets , 2001, J. Econ. Theory.

[8]  John Darzentas,et al.  Problem Complexity and Method Efficiency in Optimization , 1983 .

[9]  Justin Hsu,et al.  Jointly Private Convex Programming , 2014, SODA.

[10]  Zeynep Tufekci,et al.  We Can’t Trust Uber , 2014 .

[11]  Zhenqi Huang,et al.  Differentially Private Distributed Optimization , 2014, ICDCN.

[12]  Umang Bhaskar,et al.  Routing games , 2012 .

[13]  Sébastien Bubeck,et al.  Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems , 2012, Found. Trends Mach. Learn..

[14]  Nina Taft,et al.  How to hide the elephant- or the donkey- in the room: Practical privacy against statistical inference for large data , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[15]  Parv Venkitasubramaniam.  Privacy in stochastic control: A Markov Decision Process perspective , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[16]  T. Roughgarden.  Algorithmic Game Theory: Routing Games , 2007 .

[17]  Martin J. Wainwright,et al.  Privacy Aware Learning , 2012, JACM.

[18]  H. Vincent Poor,et al.  Competitive privacy in the smart grid: An information-theoretic approach , 2011, 2011 IEEE International Conference on Smart Grid Communications (SmartGridComm).

[19]  George J. Pappas,et al.  Differentially Private Filtering , 2012, IEEE Transactions on Automatic Control.

[20]  Alexandre M. Bayen,et al.  Convergence of mirror descent dynamics in the routing game , 2015, 2015 European Control Conference (ECC).

[21]  Aaron Roth,et al.  The Algorithmic Foundations of Differential Privacy , 2014, Found. Trends Theor. Comput. Sci..

[22]  Alexandre M. Bayen,et al.  Online Learning of Nash Equilibria in Congestion Games , 2015, SIAM J. Control. Optim..

[23]  A. Juditsky,et al.  Solving variational inequalities with Stochastic Mirror-Prox algorithm , 2008, 0809.0815.

[24]  Cynthia Dwork,et al.  Differential Privacy , 2006, ICALP.

[25]  Marc Teboulle,et al.  Mirror descent and nonlinear projected subgradient methods for convex optimization , 2003, Oper. Res. Lett..