Multi-resource allocation for federated settings: A non-homogeneous Markov chain model

In a federated setting, agents coordinate with a central agent or a server to solve an optimization problem in which agents do not share their information with each other. Wirth and his co-authors, in a recent paper, describe how the basic additive-increase multiplicative-decrease (AIMD) algorithm can be modified in a straightforward manner to solve a class of optimization problems for federated settings for a single shared resource with no inter-agent communication. The AIMD algorithm is one of the most successful distributed resource allocation algorithms currently deployed in practice. It is best known as the backbone of the Internet and is also widely explored in other application areas. We extend the singleresource algorithm to multiple heterogeneous shared resources that emerge in smart cities, sharing economy, and many other applications. Our main results show the convergence of the average allocations to the optimal values. We model the system as a non-homogeneous Markov chain with place-dependent probabilities. Furthermore, simulation results are presented to demonstrate the efficacy of the algorithms and to highlight the main features of our analysis.

[1]  Jérôme Lang,et al.  Efficiency and envy-freeness in fair division of indivisible goods: logical representation and complexity , 2005, IJCAI.

[2]  Hubert Eichner,et al.  Towards Federated Learning at Scale: System Design , 2019, SysML.

[3]  Robert Shorten,et al.  The Convergence of Finite-Averaging of AIMD for Distributed Heterogeneous Resource Allocations , 2020, ArXiv.

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

[5]  Raj Jain,et al.  Analysis of the Increase and Decrease Algorithms for Congestion Avoidance in Computer Networks , 1989, Comput. Networks.

[6]  Martin J. Wainwright,et al.  Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling , 2010, IEEE Transactions on Automatic Control.

[7]  Saraju P. Mohanty,et al.  Everything You Wanted to Know About Smart Cities , 2016, IEEE Consumer Electron. Mag..

[8]  Robert Shorten,et al.  Plug-and-Play Distributed Algorithms for Optimized Power Generation in a Microgrid , 2014, IEEE Transactions on Smart Grid.

[9]  Karl Henrik Johansson,et al.  Subgradient methods and consensus algorithms for solving convex optimization problems , 2008, 2008 47th IEEE Conference on Decision and Control.

[10]  Craig Boutilier,et al.  Social Choice : From Consensus to Personalized Decision Making , 2011 .

[11]  Blaise Agüera y Arcas,et al.  Communication-Efficient Learning of Deep Networks from Decentralized Data , 2016, AISTATS.

[12]  Robert Shorten,et al.  Stochastic Equilibria of AIMD Communication Networks , 2006, SIAM J. Matrix Anal. Appl..

[13]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[14]  J. Elton.  An ergodic theorem for iterated maps , 1987, Ergodic Theory and Dynamical Systems.

[15]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[16]  Richard Nock,et al.  Advances and Open Problems in Federated Learning , 2021, Found. Trends Mach. Learn..

[17]  Robert Shorten,et al.  A flexible distributed framework for realising electric and plug-in hybrid vehicle charging policies , 2012, Int. J. Control.

[18]  Julia Kastner.  Nonhomogeneous Matrix Products , 2016 .

[19]  Peter Richtárik,et al.  Federated Learning: Strategies for Improving Communication Efficiency , 2016, ArXiv.

[20]  Craig Boutilier,et al.  Optimal social choice functions: A utilitarian view , 2015, Artif. Intell..

[21]  Mung Chiang,et al.  Multiresource Allocation: Fairness–Efficiency Tradeoffs in a Unifying Framework , 2012, IEEE/ACM Transactions on Networking.

[22]  Vahab S. Mirrokni,et al.  Dual Mirror Descent for Online Allocation Problems , 2020, ICML.

[23]  Robert Shorten,et al.  Communication-efficient Distributed Multi-resource Allocation , 2018, 2018 IEEE International Smart Cities Conference (ISC2).

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

[25]  Piotr Faliszewski,et al.  On distance rationalizability of some voting rules , 2009, TARK '09.

[26]  Klaus-Robert Müller,et al.  Robust and Communication-Efficient Federated Learning From Non-i.i.d. Data , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[27]  John N. Tsitsiklis,et al.  Problems in decentralized decision making and computation , 1984 .

[28]  Benjamin Hindman,et al.  Dominant Resource Fairness: Fair Allocation of Multiple Resource Types , 2011, NSDI.

[29]  Robert Shorten,et al.  Nonhomogeneous Place-dependent Markov Chains, Unsynchronised AIMD, and Optimisation , 2019, J. ACM.

[30]  Robert Shorten,et al.  On the Design of Campus Parking Systems With QoS Guarantees , 2015, IEEE Transactions on Intelligent Transportation Systems.

[31]  Benjamin Sovacool,et al.  Electricity market design for the prosumer era , 2016, Nature Energy.

[32]  Angelia Nedic,et al.  Distributed Optimization Over Networks , 2018 .

[33]  Yi Zhou,et al.  Communication-efficient algorithms for decentralized and stochastic optimization , 2017, Mathematical Programming.

[34]  Burkhard Stiller,et al.  A Survey of the State-of-the-Art in Fair Multi-Resource Allocations for Data Centers , 2018, IEEE Transactions on Network and Service Management.

[35]  Sashank J. Reddi,et al.  SCAFFOLD: Stochastic Controlled Averaging for Federated Learning , 2019, ICML.

[36]  Robert Shorten,et al.  Modelling TCP congestion control dynamics in drop-tail environments , 2007, Autom..

[37]  Ziyang Meng,et al.  A survey of distributed optimization , 2019, Annu. Rev. Control..

[38]  Angelia Nedic,et al.  Asynchronous Broadcast-Based Convex Optimization Over a Network , 2011, IEEE Transactions on Automatic Control.

[39]  Tianjian Chen,et al.  Federated Machine Learning: Concept and Applications , 2019 .

[40]  Robert Shorten,et al.  Derandomized Distributed Multi-resource Allocation with Little Communication Overhead , 2018, 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[41]  Jianping Pan,et al.  Performance analysis of TCP-friendly AIMD algorithms for multimedia applications , 2005, IEEE Transactions on Multimedia.

[42]  R. Shorten,et al.  Analytics for the Sharing Economy: Mathematics, Engineering and Business Perspectives , 2020 .

[43]  Fabian R. Wirth,et al.  AIMD Dynamics and Distributed Resource Allocation , 2016 .

[44]  Lawrence G. Sager.  Handbook of Computational Social Choice , 2015 .

[45]  Anit Kumar Sahu,et al.  Federated Optimization in Heterogeneous Networks , 2018, MLSys.

[46]  M. Barnsley,et al.  Invariant measures for Markov processes arising from iterated function systems with place-dependent , 1988 .

[47]  Sneha A. Dalvi,et al.  Internet of Things for Smart Cities , 2017 .

[48]  Vivek S. Borkar,et al.  Controlling G-AIMD by index policy , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[49]  John N. Tsitsiklis,et al.  Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms , 1984, 1984 American Control Conference.