Information constrained and finite-time distributed optimisation algorithms

This paper studies the delay-accuracy trade-off for an unconstrained quadratic Network Utility Maximization (NUM) problem, which is solved by a distributed, consensus based, constant step-size, gradient-descent algorithm. Information theoretic tools such as entropy power inequality are used to analyse the convergence rate of the algorithm under quantised inter-agent communication. A finite-time distributed algorithm is proposed to solve the problem under synchronised message passing. For a system with N agents, the algorithm reaches any desired accuracy within 2N iterations, by adjusting the step-size, α. However, if N is quite large or if the agents are constrained by their memory or computational capacities, asymptotic convergence algorithms are preferred to arrive within a permissible neighbourhood of the optimal solution. The analytical tools and algorithms developed shed light to delay-accuracy trade-off required for many real-time IoT applications, e.g., smart traffic control and smart grid. As an illustrative example, we use our algorithm to implement an intersection management application, where distributed computation and communication capabilities of smart vehicles and road side units increase the efficiency of an intersection.

[1]  Tansu Alpcan,et al.  Convergence analysis of quantized primal-dual algorithm in quadratic network utility maximization problems , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[2]  Angelia Nedic,et al.  Convergence Rate of Distributed Averaging Dynamics and Optimization in Networks , 2015, Found. Trends Syst. Control..

[3]  Qing Ling,et al.  On the Convergence of Decentralized Gradient Descent , 2013, SIAM J. Optim..

[4]  John N. Tsitsiklis,et al.  On distributed averaging algorithms and quantization effects , 2007, 2008 47th IEEE Conference on Decision and Control.

[5]  Le Yi Wang,et al.  Control of vehicle platoons for highway safety and efficient utility: Consensus with communications and vehicle dynamics , 2014, J. Syst. Sci. Complex..

[6]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[7]  John A. Stankovic,et al.  Research Directions for the Internet of Things , 2014, IEEE Internet of Things Journal.

[8]  Yiguang Hong,et al.  Quantized Subgradient Algorithm and Data-Rate Analysis for Distributed Optimization , 2014, IEEE Transactions on Control of Network Systems.

[9]  C.N. Hadjicostis,et al.  Finite-Time Distributed Consensus in Graphs with Time-Invariant Topologies , 2007, 2007 American Control Conference.

[10]  Robert D. Nowak,et al.  Quantized incremental algorithms for distributed optimization , 2005, IEEE Journal on Selected Areas in Communications.

[11]  Carlos Gershenson,et al.  Self-organizing traffic lights: A realistic simulation , 2006, Advances in Applied Self-organizing Systems.

[12]  Guoyuan Wu,et al.  Platoon-based multi-agent intersection management for connected vehicle , 2013, 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013).

[13]  Panganamala Ramana Kumar,et al.  Cyber–Physical Systems: A Perspective at the Centennial , 2012, Proceedings of the IEEE.

[14]  Robin J. Evans,et al.  Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates , 2004, SIAM J. Control. Optim..

[15]  Daniel Pérez Palomar,et al.  A tutorial on decomposition methods for network utility maximization , 2006, IEEE Journal on Selected Areas in Communications.