Linear scalarization for Pareto front identification in stochastic environments

M.M. Drugan

doi:10.1007/978-3-319-15892-1_11

Linear scalarization for Pareto front identification in stochastic environments

M.M. Drugan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

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Abstract

Multi-objective multi-armed bandits (MOMAB) is a multiarm bandit variant that uses stochastic reward vectors. In this paper, we propose three MOMAB algorithms. The first algorithm uses a fixed set of linear scalarization functions to identify the Pareto front. Two topological approaches identify thePareto front using linearweighted combinations of reward vectors. The weight hyper-rectangle decomposition algorithm explores a convex shape Pareto front by grouping scalarization functions that optimise the same arm intoweight hyperrectangles. It is generally acknowledged that linear scalarization is not able to identify all the Pareto front for non-convex shapes. The hierarchical PAC algorithm iteratively decomposes the Pareto front into a set of convex shapes to identify the entire Pareto front. We compare the performance of these algorithms on a bi-objective stochastic environment inspired from a real life control application.

Original language	English
Title of host publication	Evolutionary Multi-Criterion Optimization
Subtitle of host publication	8th International Conference, EMO 2015, Guimarães, Portugal, March 29 - April 1, 2015. Proceedings, Part II
Editors	A. Gaspar-Cunha , C. Henggeler Antunes , C. Coello Coello
Place of Publication	Berlin
Publisher	Springer
Pages	156-171
Number of pages	16
ISBN (Electronic)	978-3-319-15892-1
ISBN (Print)	9783319158914
DOIs	https://doi.org/10.1007/978-3-319-15892-1_11
Publication status	Published - 2015
Externally published	Yes
Event	8th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2015) - Guimarães, Portugal Duration: 29 Mar 2015 → 1 Apr 2015 Conference number: 8

Publication series

Name	Lecture Notes in Computer Science
Volume	9019
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Conference

Conference	8th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2015)
Abbreviated title	EMO 2015
Country/Territory	Portugal
City	Guimarães
Period	29/03/15 → 1/04/15

Keywords

Multi-objective multi-armed bandits
Pareto front identification
Scalarization functions
Topological decomposition

Access to Document

10.1007/978-3-319-15892-1_11

Cite this

Drugan, M. M. (2015). Linear scalarization for Pareto front identification in stochastic environments. In A. Gaspar-Cunha , C. Henggeler Antunes , & C. Coello Coello (Eds.), Evolutionary Multi-Criterion Optimization : 8th International Conference, EMO 2015, Guimarães, Portugal, March 29 - April 1, 2015. Proceedings, Part II (pp. 156-171). (Lecture Notes in Computer Science; Vol. 9019). Springer. https://doi.org/10.1007/978-3-319-15892-1_11

Drugan, M.M. / Linear scalarization for Pareto front identification in stochastic environments. Evolutionary Multi-Criterion Optimization : 8th International Conference, EMO 2015, Guimarães, Portugal, March 29 - April 1, 2015. Proceedings, Part II. editor / A. Gaspar-Cunha ; C. Henggeler Antunes ; C. Coello Coello. Berlin : Springer, 2015. pp. 156-171 (Lecture Notes in Computer Science).

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title = "Linear scalarization for Pareto front identification in stochastic environments",

abstract = "Multi-objective multi-armed bandits (MOMAB) is a multiarm bandit variant that uses stochastic reward vectors. In this paper, we propose three MOMAB algorithms. The first algorithm uses a fixed set of linear scalarization functions to identify the Pareto front. Two topological approaches identify thePareto front using linearweighted combinations of reward vectors. The weight hyper-rectangle decomposition algorithm explores a convex shape Pareto front by grouping scalarization functions that optimise the same arm intoweight hyperrectangles. It is generally acknowledged that linear scalarization is not able to identify all the Pareto front for non-convex shapes. The hierarchical PAC algorithm iteratively decomposes the Pareto front into a set of convex shapes to identify the entire Pareto front. We compare the performance of these algorithms on a bi-objective stochastic environment inspired from a real life control application.",

keywords = "Multi-objective multi-armed bandits, Pareto front identification, Scalarization functions, Topological decomposition",

author = "M.M. Drugan",

year = "2015",

doi = "10.1007/978-3-319-15892-1_11",

language = "English",

isbn = "9783319158914",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "156--171",

editor = "{Gaspar-Cunha }, A. and {Henggeler Antunes }, C. and {Coello Coello}, C.",

booktitle = "Evolutionary Multi-Criterion Optimization",

address = "Germany",

note = "8th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2015), EMO 2015 ; Conference date: 29-03-2015 Through 01-04-2015",

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Drugan, MM 2015, Linear scalarization for Pareto front identification in stochastic environments. in A Gaspar-Cunha , C Henggeler Antunes & C Coello Coello (eds), Evolutionary Multi-Criterion Optimization : 8th International Conference, EMO 2015, Guimarães, Portugal, March 29 - April 1, 2015. Proceedings, Part II. Lecture Notes in Computer Science, vol. 9019, Springer, Berlin, pp. 156-171, 8th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2015), Guimarães, Portugal, 29/03/15. https://doi.org/10.1007/978-3-319-15892-1_11

Linear scalarization for Pareto front identification in stochastic environments. / Drugan, M.M.

Evolutionary Multi-Criterion Optimization : 8th International Conference, EMO 2015, Guimarães, Portugal, March 29 - April 1, 2015. Proceedings, Part II. ed. / A. Gaspar-Cunha ; C. Henggeler Antunes ; C. Coello Coello. Berlin : Springer, 2015. p. 156-171 (Lecture Notes in Computer Science; Vol. 9019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - Multi-objective multi-armed bandits (MOMAB) is a multiarm bandit variant that uses stochastic reward vectors. In this paper, we propose three MOMAB algorithms. The first algorithm uses a fixed set of linear scalarization functions to identify the Pareto front. Two topological approaches identify thePareto front using linearweighted combinations of reward vectors. The weight hyper-rectangle decomposition algorithm explores a convex shape Pareto front by grouping scalarization functions that optimise the same arm intoweight hyperrectangles. It is generally acknowledged that linear scalarization is not able to identify all the Pareto front for non-convex shapes. The hierarchical PAC algorithm iteratively decomposes the Pareto front into a set of convex shapes to identify the entire Pareto front. We compare the performance of these algorithms on a bi-objective stochastic environment inspired from a real life control application.

AB - Multi-objective multi-armed bandits (MOMAB) is a multiarm bandit variant that uses stochastic reward vectors. In this paper, we propose three MOMAB algorithms. The first algorithm uses a fixed set of linear scalarization functions to identify the Pareto front. Two topological approaches identify thePareto front using linearweighted combinations of reward vectors. The weight hyper-rectangle decomposition algorithm explores a convex shape Pareto front by grouping scalarization functions that optimise the same arm intoweight hyperrectangles. It is generally acknowledged that linear scalarization is not able to identify all the Pareto front for non-convex shapes. The hierarchical PAC algorithm iteratively decomposes the Pareto front into a set of convex shapes to identify the entire Pareto front. We compare the performance of these algorithms on a bi-objective stochastic environment inspired from a real life control application.

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Drugan MM. Linear scalarization for Pareto front identification in stochastic environments. In Gaspar-Cunha A, Henggeler Antunes C, Coello Coello C, editors, Evolutionary Multi-Criterion Optimization : 8th International Conference, EMO 2015, Guimarães, Portugal, March 29 - April 1, 2015. Proceedings, Part II. Berlin: Springer. 2015. p. 156-171. (Lecture Notes in Computer Science). doi: 10.1007/978-3-319-15892-1_11

Linear scalarization for Pareto front identification in stochastic environments

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