Conic Scalarization Method in Multiobjective Optimization and Relations with Other Scalarization Methods

Kasımbeyli, Refail; Öztürk, Zehra Kamışlı; Kasimbeyli, Nergiz; Yalçın, Gülçin Dinç; Icmen, Banu

doi:10.1007/978-3-319-18161-5_27

Cited by 5 publications

(1 citation statement)

References 19 publications

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“…Many single method techniques utilize scalarization functions in order to combine the multiple defined objectives into a single objective. Kasimbeyli, Ozturk, Kasimbeyli, Yalcin, and Icmen (2015) discussed the properties of different scalarization functions in solving multi-objective optimization problems. Moffaert, Drugan, and Nowé (2013) introduced a variant of the Q-learning algorithm (Watkins & Dayan, 1992) that utilizes the Chebyshev function for reward scalarization solving an MOMDP grid-world scenario.…”

Section: Related Workmentioning

confidence: 99%

A robust policy bootstrapping algorithm for multi-objective reinforcement learning in non-stationary environments

Abdelfattah

Kasmarik

2019

Adaptive Behavior

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Multi-objective Markov decision processes are a special kind of multi-objective optimization problem that involves sequential decision making while satisfying the Markov property of stochastic processes. Multi-objective reinforcement learning methods address this kind of problem by fusing the reinforcement learning paradigm with multi-objective optimization techniques. One major drawback of these methods is the lack of adaptability to non-stationary dynamics in the environment. This is because they adopt optimization procedures that assume stationarity in order to evolve a coverage set of policies that can solve the problem. This article introduces a developmental optimization approach that can evolve the policy coverage set while exploring the preference space over the defined objectives in an online manner. We propose a novel multi-objective reinforcement learning algorithm that can robustly evolve a convex coverage set of policies in an online manner in non-stationary environments. We compare the proposed algorithm with two state-of-the-art multi-objective reinforcement learning algorithms in stationary and non-stationary environments. Results showed that the proposed algorithm significantly outperforms the existing algorithms in non-stationary environments while achieving comparable results in stationary environments.

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Section: Related Workmentioning

confidence: 99%

A robust policy bootstrapping algorithm for multi-objective reinforcement learning in non-stationary environments

Abdelfattah

Kasmarik

2019

Adaptive Behavior

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Multi Objective Decision Making for Virtual Machine Placement in Cloud Computing

Attaoui

Sabir

Elbiaze

et al. 2021

Network Games, Control and Optimization

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A Unified Characterization of Nonlinear Scalarizing Functionals in Optimization

Bouza¹,

Quintana²,

Tammer³

2019

Vietnam J. Math.

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Over the years, several classes of scalarization techniques in optimization have been introduced and employed in deriving separation theorems, optimality conditions and algorithms. In this paper, we study the relationships between some of those classes in the sense of inclusion. We focus on three types of scalarizing functionals defined by Hiriart-Urruty, Drummond and Svaiter, Gerstewitz. We completely determine their relationships. In particular, it is shown that the class of the functionals by Gerstewitz is minimal in this sense. Furthermore, we define a new (and larger) class of scalarizing functionals that are not necessarily convex, but rather quasidifferentiable and positively homogeneous. We show that our results are connected with some of the set relations in set optimization.

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Conic Scalarization Method in Multiobjective Optimization and Relations with Other Scalarization Methods

Cited by 5 publications

References 19 publications

A robust policy bootstrapping algorithm for multi-objective reinforcement learning in non-stationary environments

A robust policy bootstrapping algorithm for multi-objective reinforcement learning in non-stationary environments

Multi Objective Decision Making for Virtual Machine Placement in Cloud Computing

A Unified Characterization of Nonlinear Scalarizing Functionals in Optimization

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