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  • 1
    Electronic Resource
    Electronic Resource
    Epsilon efficiency (1986)
    Springer
    Journal of optimization theory and applications 49 (1986), S. 319-337 
    Details
    ISSN: 1573-2878
    Keywords: Efficient sets ; ε-efficiency ; weighting factors ; constrained objectives ; penalty functions ; ideal points ; Markov decision processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper considers the extension of ε-optimality for scalar problems to vector maximization problems, or efficiency problems, which havem objective functions defined on a set $$X \subseteq \mathbb{R}^n $$ . It is shown that the natural extension of the scalar ε-optimality concepts [viz, given ε〉0, given a solution setS, ifx∈S there exists an efficient solutiony with ∥f(x)−f(y)∥≦ε, and given an efficient solutiony, there exists anx∈S with ∥f(x)−f(y)∥≦ε] do not hold for some methods used. Six concepts of ε-efficient sets are introduced and examined, to a very limited extent, in the context of five methods used for generating efficient points or near efficient points. In doing so, a distinction is drawn between methods in which the surrogate optimizations are carried out exactly, and those where terminal ε-optimal solutions are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940762
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  • 2
    Electronic Resource
    Electronic Resource
    Computational approaches to variance-penalised Markov decision processes (1992)
    Springer
    OR spectrum 14 (1992), S. 79-83 
    Details
    ISSN: 1436-6304
    Keywords: Markov decision processes ; variance penalty ; parametric algorithms ; Markov-Entscheidungsprozesse ; Varianz-Strafkosten ; parametrische Verfahren
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Für ein Markov-Entscheidungsmodell, in dem der Durchschnittsgewinn um einen Teil der mittleren Varianz vermindert wird, werden drei Typen von Lösungsverfahren entwickelt, und zwar parametrische lineare Programmierung, parametrische Lagrange-Optimierung und parametrische Politik-Iterations-Algorithmen.
    Notes: Summary This paper develops three computational approaches for solving a variance-penalised Markov decision process, viz. parametric linear programming, parametric Lagrangean programming, and a parametric policy space approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01720350
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  • 3
    Electronic Resource
    Electronic Resource
    A mathematical programming approach to a problem in variance penalised Markov decision processes (1994)
    Springer
    OR spectrum 15 (1994), S. 225-230 
    Details
    ISSN: 1436-6304
    Keywords: Markov decision processes ; ɛ-optimal ; variance ; Markov'sche Entscheidungsprozesse ; ɛ-Optimalität ; Gewinnvarianz
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit geben wir drei Algorithmen zur Lösung eines stochastischen dynamischen Problems an. Dabei wird ein optimaler Ausgleich zwischen erwartetem Gewinn und Gewinnvarianz pro Zeiteinheit gesucht. Die Algorithmen liefern für beliebigesɛ〉0 jeweilsɛ-optimale Lösungen.
    Notes: Abstract In this paper we present three algorithms for solving a problem in which it is required to get an optimal compromise between the average expected reward per unit time and the variance of the reward per unit time. The algorithms lead to anɛ-optimal solution, whereɛ〉0 is arbitrary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01719453
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  • 4
    Electronic Resource
    Electronic Resource
    Mean, variance, and probabilistic criteria in finite Markov decision processes: A review (1988)
    Springer
    Journal of optimization theory and applications 56 (1988), S. 1-29 
    Details
    ISSN: 1573-2878
    Keywords: Markov decision processes ; infinite horizon ; finite horizon ; mean ; variance ; probabilistic criteria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is a survey of papers which make use of nonstandard Markov decision process criteria (i.e., those which do not seek simply to optimize expected returns per unit time or expected discounted return). It covers infinite-horizon nondiscounted formulations, infinite-horizon discounted formulations, and finite-horizon formulations. For problem formulations in terms solely of the probabilities of being in each state and taking each action, policy equivalence results are given which allow policies to be restricted to the class of Markov policies or to the randomizations of deterministic Markov policies. For problems which cannot be stated in such terms, in terms of the primitive state setI, formulations involving a redefinition of the states are examined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938524
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  • 5
    Electronic Resource
    Electronic Resource
    A superharmonic approach to solving infinite horizon partially observable Markov decision problems (1995)
    Springer
    Mathematical methods of operations research 41 (1995), S. 71-88 
    Details
    ISSN: 1432-5217
    Keywords: Markov decision processes ; partially observable ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we use an approach which uses a superharmonic property of a sequence of functions generated by an algorithm to show that these functions converge in a non-increasing manner to the optimal value function for our problem, and bounds are given for the loss of optimality if the computational process is terminated at any iteration. The basic procedure is to add an additional linear term at each iteration, selected by solving a particular optimisation problem, for which primal and dual linear programming formulations are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01415066
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