Distributed Pareto Optimization via Diffusion Strategies
We consider solving multi-objective optimization problems in a distributed manner by a network of cooperating and learning agents. The problem is equivalent to optimizing a global cost that is the sum of individual components. The optimizers of the individual components do not necessarily coincide a...
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Veröffentlicht in: | IEEE journal of selected topics in signal processing 2013-04, Vol.7 (2), p.205-220 |
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description | We consider solving multi-objective optimization problems in a distributed manner by a network of cooperating and learning agents. The problem is equivalent to optimizing a global cost that is the sum of individual components. The optimizers of the individual components do not necessarily coincide and the network therefore needs to seek Pareto optimal solutions. We develop a distributed solution that relies on a general class of adaptive diffusion strategies. We show how the diffusion process can be represented as the cascade composition of three operators: two combination operators and a gradient descent operator. Using the Banach fixed-point theorem, we establish the existence of a unique fixed point for the composite cascade. We then study how close each agent converges towards this fixed point, and also examine how close the Pareto solution is to the fixed point. We perform a detailed mean-square error analysis and establish that all agents are able to converge to the same Pareto optimal solution within a sufficiently small mean-square-error (MSE) bound even for constant step-sizes. We illustrate one application of the theory to collaborative decision making in finance by a network of agents. |
doi_str_mv | 10.1109/JSTSP.2013.2246763 |
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H.</creator><creatorcontrib>Jianshu Chen ; Sayed, A. H.</creatorcontrib><description>We consider solving multi-objective optimization problems in a distributed manner by a network of cooperating and learning agents. The problem is equivalent to optimizing a global cost that is the sum of individual components. The optimizers of the individual components do not necessarily coincide and the network therefore needs to seek Pareto optimal solutions. We develop a distributed solution that relies on a general class of adaptive diffusion strategies. We show how the diffusion process can be represented as the cascade composition of three operators: two combination operators and a gradient descent operator. Using the Banach fixed-point theorem, we establish the existence of a unique fixed point for the composite cascade. We then study how close each agent converges towards this fixed point, and also examine how close the Pareto solution is to the fixed point. We perform a detailed mean-square error analysis and establish that all agents are able to converge to the same Pareto optimal solution within a sufficiently small mean-square-error (MSE) bound even for constant step-sizes. We illustrate one application of the theory to collaborative decision making in finance by a network of agents.</description><identifier>ISSN: 1932-4553</identifier><identifier>EISSN: 1941-0484</identifier><identifier>DOI: 10.1109/JSTSP.2013.2246763</identifier><identifier>CODEN: IJSTGY</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Aggregates ; Algorithms ; Cascades ; Collaborative decision making ; convergence ; Cost function ; Diffusion ; diffusion adaptation ; distributed optimization ; Equivalence ; fixed point ; mean-square performance ; Networks ; Noise ; Operators ; Optimization ; Pareto optimality ; Pareto optimization ; stability ; Strategy ; Studies ; Upper bound ; Vectors</subject><ispartof>IEEE journal of selected topics in signal processing, 2013-04, Vol.7 (2), p.205-220</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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H.</creatorcontrib><title>Distributed Pareto Optimization via Diffusion Strategies</title><title>IEEE journal of selected topics in signal processing</title><addtitle>JSTSP</addtitle><description>We consider solving multi-objective optimization problems in a distributed manner by a network of cooperating and learning agents. The problem is equivalent to optimizing a global cost that is the sum of individual components. The optimizers of the individual components do not necessarily coincide and the network therefore needs to seek Pareto optimal solutions. We develop a distributed solution that relies on a general class of adaptive diffusion strategies. We show how the diffusion process can be represented as the cascade composition of three operators: two combination operators and a gradient descent operator. Using the Banach fixed-point theorem, we establish the existence of a unique fixed point for the composite cascade. We then study how close each agent converges towards this fixed point, and also examine how close the Pareto solution is to the fixed point. We perform a detailed mean-square error analysis and establish that all agents are able to converge to the same Pareto optimal solution within a sufficiently small mean-square-error (MSE) bound even for constant step-sizes. We illustrate one application of the theory to collaborative decision making in finance by a network of agents.</description><subject>Aggregates</subject><subject>Algorithms</subject><subject>Cascades</subject><subject>Collaborative decision making</subject><subject>convergence</subject><subject>Cost function</subject><subject>Diffusion</subject><subject>diffusion adaptation</subject><subject>distributed optimization</subject><subject>Equivalence</subject><subject>fixed point</subject><subject>mean-square performance</subject><subject>Networks</subject><subject>Noise</subject><subject>Operators</subject><subject>Optimization</subject><subject>Pareto optimality</subject><subject>Pareto optimization</subject><subject>stability</subject><subject>Strategy</subject><subject>Studies</subject><subject>Upper bound</subject><subject>Vectors</subject><issn>1932-4553</issn><issn>1941-0484</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkE1LAzEQhoMoWKt_QC8FL162Tj422RylflNoofUcsrsTSWm7NckK-uvdtcWDhzAZeN6Z4SHkksKYUtC3r4vlYj5mQPmYMSGV5EdkQLWgGYhCHPd_zjKR5_yUnMW4AsiVpGJAinsfU_Blm7AezW3A1Ixmu-Q3_tsm32xHn96O7r1zbey7RQo24bvHeE5OnF1HvDjUIXl7fFhOnrPp7OllcjfNKs6KlJVS1a7WwKRgWiqlgaOyWjuHTJZ1qawraskoKq2h0FQVoBRUhWWUlVBbPiQ3-7m70Hy0GJPZ-Fjhem232LTRUC60kN3LO_T6H7pq2rDtrusoJkS3vNMwJGxPVaGJMaAzu-A3NnwZCqaXaX5lml6mOcjsQlf7kEfEv4AUkkIO_AcDrm8d</recordid><startdate>20130401</startdate><enddate>20130401</enddate><creator>Jianshu Chen</creator><creator>Sayed, A. 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H.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005–Present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998–Present</collection><collection>IEEE Xplore</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>IEEE journal of selected topics in signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Jianshu Chen</au><au>Sayed, A. H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Distributed Pareto Optimization via Diffusion Strategies</atitle><jtitle>IEEE journal of selected topics in signal processing</jtitle><stitle>JSTSP</stitle><date>2013-04-01</date><risdate>2013</risdate><volume>7</volume><issue>2</issue><spage>205</spage><epage>220</epage><pages>205-220</pages><issn>1932-4553</issn><eissn>1941-0484</eissn><coden>IJSTGY</coden><abstract>We consider solving multi-objective optimization problems in a distributed manner by a network of cooperating and learning agents. The problem is equivalent to optimizing a global cost that is the sum of individual components. The optimizers of the individual components do not necessarily coincide and the network therefore needs to seek Pareto optimal solutions. We develop a distributed solution that relies on a general class of adaptive diffusion strategies. We show how the diffusion process can be represented as the cascade composition of three operators: two combination operators and a gradient descent operator. Using the Banach fixed-point theorem, we establish the existence of a unique fixed point for the composite cascade. We then study how close each agent converges towards this fixed point, and also examine how close the Pareto solution is to the fixed point. We perform a detailed mean-square error analysis and establish that all agents are able to converge to the same Pareto optimal solution within a sufficiently small mean-square-error (MSE) bound even for constant step-sizes. We illustrate one application of the theory to collaborative decision making in finance by a network of agents.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/JSTSP.2013.2246763</doi><tpages>16</tpages></addata></record> |
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subjects | Aggregates Algorithms Cascades Collaborative decision making convergence Cost function Diffusion diffusion adaptation distributed optimization Equivalence fixed point mean-square performance Networks Noise Operators Optimization Pareto optimality Pareto optimization stability Strategy Studies Upper bound Vectors |
title | Distributed Pareto Optimization via Diffusion Strategies |
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