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Approximation of Lorenz-Optimal Solutions in Multiobjective Markov Decision Processes [article]

Patrice Perny, Paul Weng, Judy Goldsmith, Josiah Hanna
2013 arXiv   pre-print
This paper is devoted to fair optimization in Multiobjective Markov Decision Processes (MOMDPs).  ...  In this paper, we introduce methods to efficiently approximate the sets of Lorenz-non-dominated solutions of infinite-horizon, discounted MOMDPs.  ...  This problem is often represented by a Markov Decision Process (MDP) that provides a general formal framework for optimizing decisions in dynamic systems [2, 11] .  ... 
arXiv:1309.6856v1 fatcat:fqxtdqnspjbsll3b22mt5ajahe

From Preference-Based to Multiobjective Sequential Decision-Making [chapter]

Paul Weng
2016 Lecture Notes in Computer Science  
This link yields a new source of multiobjective sequential decision-making problems (i.e., when reward values are unknown) and justifies the use of solving methods developed in one setting in the other  ...  In this paper, we present a link between preference-based and multiobjective sequential decision-making.  ...  RL is based on the Markov decision process model (MDP) [21] . In the standard setting, both MDP and RL rely on scalar numeric evaluations of actions (and thus histories and policies).  ... 
doi:10.1007/978-3-319-49397-8_20 fatcat:bfgtkxulvjfxzenwbn6fgtmo74

Learning Fair Policies in Multi-Objective (Deep) Reinforcement Learning with Average and Discounted Rewards

Umer Siddique, Paul Weng, Matthieu Zimmer
2020 International Conference on Machine Learning  
During this analysis, we notably derive a new result in the standard RL setting, which is of independent interest: it states a novel bound on the approximation error with respect to the optimal average  ...  In this paper, we formulate this novel RL problem, in which an objective function, which encodes a notion of fairness that we formally define, is optimized.  ...  Acknowledgements This work is supported in part by the program of National Natural Science Foundation of China (No. 61872238), the program of the Shanghai NSF (No. 19ZR1426700), and a Yahoo FREP grant.  ... 
dblp:conf/icml/SiddiqueWZ20 fatcat:k5ef65ythbdi5fcuk7cdmkkfgq

Learning Fair Policies in Multiobjective (Deep) Reinforcement Learning with Average and Discounted Rewards [article]

Umer Siddique, Paul Weng, Matthieu Zimmer
2020 arXiv   pre-print
During this analysis, we notably derive a new result in the standard RL setting, which is of independent interest: it states a novel bound on the approximation error with respect to the optimal average  ...  In this paper, we formulate this novel RL problem, in which an objective function, which encodes a notion of fairness that we formally define, is optimized.  ...  Acknowledgements This work is supported in part by the program of National Natural Science Foundation of China (No. 61872238), the program of the Shanghai NSF (No. 19ZR1426700), and a Yahoo FREP grant.  ... 
arXiv:2008.07773v1 fatcat:dantx3awovavzoc7l3hm6fbiji

Decision making with multiple objectives using GAI networks

C. Gonzales, P. Perny, J.Ph. Dubus
2011 Artificial Intelligence  
We also provide results of numerical tests showing the practical efficiency of our procedures in various contexts such as compromise search and fair optimization in multicriteria or multiagent problems  ...  We first present two algorithms for the determination of Pareto-optimal elements. Then the second of these algorithms is adapted so as to directly focus on the preferred solutions.  ...  in multiobjective decision-making problems.  ... 
doi:10.1016/j.artint.2010.11.020 fatcat:ax5zd4resvbcli7cebhaobt6ty

An Efficient Primal-Dual Algorithm for Fair Combinatorial Optimization Problems [chapter]

Viet Hung Nguyen, Paul Weng
2017 Lecture Notes in Computer Science  
The numerical results show that our method outputs in a very short time efficient solutions giving lower bounds that CPLEX may take several orders of magnitude longer to obtain.  ...  We demonstrate the efficiency of our method by evaluating it against the exact solution of (IP) by CPLEX on several fair optimization problems related to matching.  ...  Conclusion We formulated the fair optimization with the Generalized Gini Index for a large class of combinatorial problem for which we proposed a primal-dual algorithm based on a Lagrangian decomposition  ... 
doi:10.1007/978-3-319-71150-8_28 fatcat:s7676fzadzg23bi2ak6rmtyepi

Multi-Objective Multi-Agent Decision Making: A Utility-based Analysis and Survey [article]

Roxana Rădulescu, Patrick Mannion, Diederik M. Roijers, Ann Nowé
2019 arXiv   pre-print
This allows us to offer a structured view of the field, to clearly delineate the current state-of-the-art in multi-objective multi-agent decision making approaches and to identify promising directions  ...  Starting from the execution phase, in which the selected policies are applied and the utility for the users is attained, we analyse which solution concepts apply to the different settings in our taxonomy  ...  This leads to the solution concept of Lorenz optimality [34] , which we will discuss in Section 5.2.4.  ... 
arXiv:1909.02964v1 fatcat:esizgbvjfbejfacjpwq5c4ujze

Multi-objective optimization of energy-efficient buffer allocation problem for non-homogeneous unreliable production lines

Yasmine Alaouchiche, Yassine Ouazene, Farouk Yalaoui
2021 IEEE Access  
The Pareto solutions obtained are trade-offs between the two objectives, enabling decision making that balances productivity maximization with energy economics in the design of production lines.  ...  The buffer allocation problem is of particular interest since buffers absorb disruptions in the production line.  ...  in multiobjective optimization can be found in [16] .  ... 
doi:10.1109/access.2021.3139954 fatcat:xoiusbl3rzeibly6pe3acc6kna

Search for Choquet-optimal paths under uncertainty [article]

Lucie Galand, Patrice Perny
2012 arXiv   pre-print
Choquet expected utility (CEU) is one of the most sophisticated decision criteria used in decision theory under uncertainty.  ...  In this paper, we investigate the use of CEU for path-planning under uncertainty with a special focus on robust solutions.  ...  In the future, it might be interesting to investigate the use of the Choquet integral in dynamic decision making problems e.g. decision trees or Markov decision processes.  ... 
arXiv:1206.5244v1 fatcat:3bkuvoyejvbihlukzo4t6hxjx4

Artificial Intelligence and Its Applications 2014

Yudong Zhang, Saeed Balochian, Praveen Agarwal, Vishal Bhatnagar, Orwa Jaber Housheya
2016 Mathematical Problems in Engineering  
Reproduction processes may generate infeasible solutions.  ...  Liu et al. proposed a modified version of hidden Markov model (HMM) classifier, called self-adaptive HMM, the parameters of which were optimized by particle swarm optimization algorithms.  ...  Reproduction processes may generate infeasible solutions. Previous research used repair processes that were applied after a population of chromosomes was generated.  ... 
doi:10.1155/2016/3871575 fatcat:irj62qjsdzfu7h4fdslkgy5hny

Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation

Jasper A. Vrugt, Cees G. H. Diks, Hoshin V. Gupta, Willem Bouten, Jacobus M. Verstraten
2005 Water Resources Research  
During this process, known as model calibration, the parameters are adjusted so that the behavior of the model approximates, as closely and consistently as possible, the observed response of the hydrologic  ...  Verstraten (2005), Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation, Water Resour.  ...  The constructive review comments of the Associate Editor, Peter Young, and Jean-Philippe Drecourt significantly improved the current version of this paper.  ... 
doi:10.1029/2004wr003059 fatcat:wj2soz2yzjbirhlllmkfkyz27i

Multi-objective decision-theoretic planning

Diederik M. Roijers
2016 AI Matters  
In this dissertation, we focus on decision-theoretic planning algorithms that produce the convex coverage set (CCS), which is the optimal solution set when either: 1) the user utility can be expressed  ...  In such complex decisionmaking tasks decision-theoretic agents, that can reason about their environments on the basis of mathematical models and produce policies that optimize the utility for their users  ...  (MOMDPs) and multi-objective partially observable Markov decision processes (MOPOMDPs).  ... 
doi:10.1145/3008665.3008670 fatcat:mpxluczzvje77h777quyj7tbdm

Mathematics as a Technology–Challenges for the next Ten Years [chapter]

H Neunzert
2005 Lecture Notes in Pure and Applied Mathematics  
Second, the set of Pareto optimal solutions is approximated by an adaptive grid of representatives that are found by a hybrid process of calculating extreme compromises and interpolation methods.  ...  For solving the problem (i. e. fi nding an approximation of the effi cient set) we develop a multiobjective evolutionary algorithm.  ...  In the second group of experiments numerical solution of real problems is presented.  ... 
doi:10.1201/9781420026511.pt1 fatcat:c6ni6noa3nambgkuftojudjbem

Joint location and dispatching decisions for Emergency Medical Services

Hector Toro-Díaz, Maria E. Mayorga, Sunarin Chanta, Laura A. McLay
2013 Computers & industrial engineering  
The ability of EMS systems to do this effectively is impacted by several resource allocation decisions including location of servers (ambulances), districting of demand zones and dispatching rules for  ...  The location decision is strategic while the  ...  Their suggestions helped to improve the readability and understanding of my  ... 
doi:10.1016/j.cie.2013.01.002 fatcat:47qfq4d42vafdexs4asuyudk3y

Multi-objective Bandits: Optimizing the Generalized Gini Index [article]

Robert Busa-Fekete, Balazs Szorenyi, Paul Weng, Shie Mannor
2017 arXiv   pre-print
The goal of the agent is to find a policy, which can optimize these objectives simultaneously in a fair way.  ...  We test our algorithm on synthetic data as well as on an electric battery control problem where the goal is to trade off the use of the different cells of a battery in order to balance their respective  ...  This research was supported in part by the European Communitys Seventh Framework Programme (FP7/2007(FP7/ -2013 under grant agreement 306638 (SUPREL).  ... 
arXiv:1706.04933v1 fatcat:wvmsftoeunfuhhymxjo7tz35fy
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