On privacy vs. cooperation in multi-agent systems

ABSTRACT This paper considers distributed systems arising when multiple agents cooperatively solve a quadratic optimisation problem. To maintain privacy of their states over time, agents implement a noise-adding mechanism according to the classic differential privacy framework. We characterise how the noise due to the privacy mechanism degrades the performance of the multi-agent system. Interestingly, we show that depending on the desired level of privacy (and thus noise), the system performance is optimised by reducing the level of cooperation among the agents. The notion of cooperation level, which is formally introduced and defined in the paper, models the trust of an agent towards the information received from neighbouring agents. For the prototypical examples of consensus and centroidal Voronoi tessellations, we are able to characterise the optimum cooperation level that maximises the system performance while ensuring a desired privacy level. Our results suggest that for the class of problems we study, and in fact for a broad class of multi-agent systems, it is always beneficial for the agents to reduce their cooperation level when the privacy level increases.

[1]  R. Murray,et al.  Decentralized Multi-Agent Optimization via Dual Decomposition , 2011 .

[2]  Claudio Orlandi,et al.  Is multiparty computation any good in practice? , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[3]  Yehuda Lindell,et al.  Secure Multiparty Computation for Privacy-Preserving Data Mining , 2009, IACR Cryptol. ePrint Arch..

[4]  Tim Roughgarden,et al.  Privately Solving Linear Programs , 2014, ICALP.

[5]  Patrick D. McDaniel,et al.  Security and Privacy Challenges in the Smart Grid , 2009, IEEE Security & Privacy.

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

[7]  Yigang He,et al.  Distributed Finite-Time Cooperative Control of Multiple High-Order Nonholonomic Mobile Robots , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Wen-Chyuan Yueh.  EIGENVALUES OF SEVERAL TRIDIAGONAL MATRICES , 2005 .

[9]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[10]  R. Srikant,et al.  Opinion dynamics in social networks: A local interaction game with stubborn agents , 2012, 2013 American Control Conference.

[11]  N. F. Ota.  Differentially Private Convex Optimization with Piecewise Affine Objectives Using Projections and Average Subgradients , 2019 .

[12]  T. Tao.  Topics in Random Matrix Theory , 2012 .

[13]  Stephen P. Boyd,et al.  Distributed optimization for cooperative agents: application to formation flight , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[14]  Asuman E. Ozdaglar,et al.  Distributed Subgradient Methods for Multi-Agent Optimization , 2009, IEEE Transactions on Automatic Control.

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

[16]  Ufuk Topcu,et al.  Differentially private convex optimization with piecewise affine objectives , 2014, 53rd IEEE Conference on Decision and Control.

[17]  Stephen P. Boyd,et al.  Distributed average consensus with least-mean-square deviation , 2007, J. Parallel Distributed Comput..

[18]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[19]  Qiang Du,et al.  Centroidal Voronoi Tessellations: Applications and Algorithms , 1999, SIAM Rev..

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

[21]  Magnus Egerstedt,et al.  Cloud-Enabled Multi-Agent Optimization with Constraints and Differentially Private States , 2015 .

[22]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

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

[24]  Martin J. Wainwright,et al.  Network-Based Consensus Averaging With General Noisy Channels , 2008, IEEE Transactions on Signal Processing.

[25]  R. Rosenthal.  A class of games possessing pure-strategy Nash equilibria , 1973 .

[26]  Richard M. Murray,et al.  Privacy preserving average consensus , 2014, 53rd IEEE Conference on Decision and Control.

[27]  Geir E. Dullerud,et al.  Differentially private iterative synchronous consensus , 2012, WPES '12.