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Multicriteria Reinforcement Learning
, 1998
"... We consider multicriteria sequential decision making problems where the vectorvalued evaluations are compared by a given, fixed total ordering. Conditions for the optimality of stationary policies and the Bellman optimality equation are given. The analysis requires special care as the topology int ..."
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Cited by 19 (0 self)
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We consider multicriteria sequential decision making problems where the vectorvalued evaluations are compared by a given, fixed total ordering. Conditions for the optimality of stationary policies and the Bellman optimality equation are given. The analysis requires special care as the topology introduced by pointwise convergence and the ordertopology introduced by the preference order are in general incompatible. Reinforcement learning algorithms are proposed and analyzed. Preliminary computer experiments confirm the validity of the derived algorithms. It is observed that in the mediumterm multicriteria RL often converges to better solutions (measured by the first criterion) than their singlecriterion counterparts. These type of multicriteria problems are most useful when there are several optimal solutions to a problem and one wants to choose the one among these which is optimal according to another fixed criterion. Example applications include alternating games, when in addition...
Fast approximation schemes for multicriteria combinatorial Optimization
, 1994
"... The solution to an instance of the standard Shortest Path problem is a single shortest route in a directed graph. Suppose, however, that each arc has both a distance and a cost, and that one would like to find a route that is both short and inexpensive. In general, no single route will be both short ..."
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Cited by 8 (0 self)
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The solution to an instance of the standard Shortest Path problem is a single shortest route in a directed graph. Suppose, however, that each arc has both a distance and a cost, and that one would like to find a route that is both short and inexpensive. In general, no single route will be both shortest and cheapest; rather, the solution to an instance of this multicriteria problem will be a set of efficient or Pareto optimal routes. The (distance, cost) pairs associated with the efficient routes define an efficient frontier or tradeoff curve. An efficient set for a multicriteria problem can be exponentially large, even when the underlying singlecriterion;oblem is in P. This work therefore considers approximate solutions to rlulticriteria discrete optimization problems and investigates when they can be found quickly. This requires generalizing the notion of a fully polynomial time approximatiofi scheme to multicriteria problems. In this paper, necessary and sufficient conditions are developed for the existence of such a fast approximation scheme for a problem. Although the focus is multicriteria problems, the conditions are of interest even in the single criterion case. In addition, an appropriate form of problem reduction is introduced to facilitate the application of these conditions to a variety of problems. A companion paper uses the results of this paper to study the existence of fast approximation schemes for several interesting network flow, knapsack, and
Adaptive Differential Dynamic Programming for Multiobjective Optimal Control
, 1999
"... : An efficient numerical solution scheme entitled adaptive differential dynamic programming is developed in this paper for multiobjective optimal control problems with a general separable structure. For a multiobjective control problem with a general separable structure, the "optimal" weighting coef ..."
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Cited by 1 (0 self)
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: An efficient numerical solution scheme entitled adaptive differential dynamic programming is developed in this paper for multiobjective optimal control problems with a general separable structure. For a multiobjective control problem with a general separable structure, the "optimal" weighting coefficients for various performance indices are timevarying as the system evolves along any noninferior trajectory. Recognizing this prominent feature in multiobjective control, the proposed adaptive differential dynamic programming methodology combines a search process to identify an optimal timevarying weighting sequence with the solution concept in the conventional differential dynamic programming. Convergence of the proposed adaptive differential dynamic programming methodology is addressed. Key Words: Multiobjective optimal control, dynamic programming, multiobjective dynamic programming, differential dynamic programming, adaptive differential dynamic programming. Department of Mathem...
Multicriteria Reinforcement Learning
, 1998
"... We consider multicriteria sequential decision making problems where the vectorvalued evaluations are compared by a given, fixed total ordering. Conditions for the optimality of stationary policies and the Bellman optimality equation are given. The analysis requires special care as the topology int ..."
Abstract
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We consider multicriteria sequential decision making problems where the vectorvalued evaluations are compared by a given, fixed total ordering. Conditions for the optimality of stationary policies and the Bellman optimality equation are given. The analysis requires special care as the topology introduced by pointwise convergence and the ordertopology introduced by the preference order are in general incompatible. Reinforcement learning algorithms are proposed and analyzed. Preliminary computer experiments confirm the validity of the derived algorithms. It is observed that in the mediumterm multicriteria RL often converges to better solutions (measured by the first criterion) than their singlecriterion counterparts. These type of multicriteria problems are most useful when there are several optimal solutions to a problem and one wants to choose the one among these which is optimal according to another fixed criterion. Example applications include alternating games, when in addition...
Perfect Dynamics for Neural Networks
"... this article we take another starting point and that is to consider perfect dynamics. We say that a recurrent ANN admits perfect dynamics if the dynamical system given by the update operator of the network has an attractor whose basin of attraction covers the set of all possible initial solution can ..."
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this article we take another starting point and that is to consider perfect dynamics. We say that a recurrent ANN admits perfect dynamics if the dynamical system given by the update operator of the network has an attractor whose basin of attraction covers the set of all possible initial solution candidates. One may wonder whether neural networks that admit perfect dynamics can be interesting in applications. In this article we show that there exist a family of such networks (or dynamics). We introduce
Associative Computing Ltd.
"... \Ve cOllf:iider multicriteria f:iequent,ial decision making problems where the vcctor"valucd evaluations arc compared by a given, fixed total ordering. Condit.ions for the opt.irnalit�y of statiOIl<l,r} ' p()lich�s;weI the Bellman optimalit,y equation are given for a. special, but. important cla ..."
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\Ve cOllf:iider multicriteria f:iequent,ial decision making problems where the vcctor"valucd evaluations arc compared by a given, fixed total ordering. Condit.ions for the opt.irnalit�y of statiOIl<l,r} ' p()lich�s;weI the Bellman optimalit,y equation are given for a. special, but. important class of problems ''v hell the evaluation of policies can be computed for the criteria, independently of each other. The anal)'sis requires special cafC as t.he t.opolag,Y int.roduced by polnL\visc convergence a.ncl the or<1crtopology introduced by the preference order arc in general incompatible. Reinforcement. learning algorithms are proposed and analY7,ed. Prelimina,ry computer experiments confirm t,he val idit.y of the derived algorithms. These type of multicriteria problem� are most useful,,,,hen t.here are several optimal solutions to a. problem and one 'VllIlt.S to choose the one among these,vhich is optimal according Lo another fixed criLerion. Possible application in robot.ics and repeat.ed ga.mes are outlined.
A DYNAMIC MULTIPLE STAGE, MULTIPLE OBJECTIVE OPTIMIZATION MODEL WITH AN APPLICATION TO A WASTEWATER TREATMENT SYSTEM
, 2008
"... I would not have made this far in the journey that I embarked upon in the spring of 2003 without the help and support of my supervising professors Drs. Chen and Corley. I want to thank you for not only providing constant inputs on my research but also coming through every time I needed and sought yo ..."
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I would not have made this far in the journey that I embarked upon in the spring of 2003 without the help and support of my supervising professors Drs. Chen and Corley. I want to thank you for not only providing constant inputs on my research but also coming through every time I needed and sought your help. I could not have asked for a better learning environment in terms of having an access to two people with different areas of expertise, perspectives, and supervising styles. I want to extend my thanks to Drs. Ferreira and Han for their inputs as my dissertation committee members. I would like to convey my appreciation to Drs. Jiang (Georgia Department of Natural Resources) and Beck (University of Georgia) for their quick responses to our frequent queries regarding wastewater treatment system. I would like to acknowledge IMSE faculty members for their positive influence. I would like to thank Drs. Imrhan and Rosenberger for their support and encouragement. I extend my gratitude to Dr. Liles for his support. I would also like to thank the IMSE staff for their constant help and support. At UTA, I met many wonderful people and had the privilege of knowing and befriending some of them. In particular, I would like to thank fellow COSMOSians for making this stay enjoyable and memorable. I am thankful to COSMOS graduates Durai,
Dynamic Programming: an overview by
"... Abstract: Dynamic programing is one of the major problemsolving methodologies in a number of disciplines such as operations research and computer science. It is also a very important and powerful tool of thought. But not all is well on the dynamic programming front. There is definitely lack of comme ..."
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Abstract: Dynamic programing is one of the major problemsolving methodologies in a number of disciplines such as operations research and computer science. It is also a very important and powerful tool of thought. But not all is well on the dynamic programming front. There is definitely lack of commercial software support and the situation in the classroom is not as good as it should be. In this paper we take a bird’s view of dynamic programming so as to identify ways to make it more accessible to students, academics and practitioners alike.