Information constrained and finite-time distributed optimisation algorithms

• Published in: 2017 IEEE 56th Annual Conference on Decision and Control (CDC) pp. 4588 - 4593
• Main Authors: Philip, Bigi Varghese, Alpcan, Tansu, Jiong Jin, Palaniswami, Marimuthu
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2017
• Subjects: Algorithm design and analysis; Australia; Convergence; Entropy; Optimization; Quantization (signal); Real-time systems
• DOI: 10.1109/CDC.2017.8264337

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.