Markov Decision Processes on Borel Spaces with Total Cost and Random Horizon

Cruz−Suárez, Hugo; Ilhuicatzi-Roldán, Rocio; Montes-de-Oca, Raúl

doi:10.1007/s10957-012-0262-8

Cited by 8 publications

(3 citation statements)

References 6 publications

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“…Furthermore, it is assumed that the random horizon is independent of the sequence of state-action pairs generated in each stage (see Assumption 3.1). Under this hypothesis in [3], we study the optimal control problem with total expected cost as performance criterion, which has been applied to optimal replacement problems ( [16]). Considering an independent random horizon of the control process can be used to represent various situations, for example, in finance, where there may be a drastic change of the investor's plan in the future with certain probability (see [2]).…”

Section: Introductionmentioning

confidence: 99%

Markov decision processes with time-varying discount factors and random horizon

Ilhuicatzi-Roldán¹,

Cruz−Suárez²,

Chávez-Rodríguez³

2017

Kybernetika

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This paper is related to Markov Decision Processes. The optimal control problem is to minimize the expected total discounted cost, with a non-constant discount factor. The discount factor is time-varying and it could depend on the state and the action. Furthermore, it is considered that the horizon of the optimization problem is given by a discrete random variable, that is, a random horizon is assumed. Under general conditions on Markov control model, using the dynamic programming approach, an optimality equation for both cases is obtained, namely, finite support and infinite support of the random horizon. The obtained results are illustrated by two examples, one of them related to optimal replacement.

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Section: Introductionmentioning

confidence: 99%

Markov decision processes with time-varying discount factors and random horizon

Ilhuicatzi-Roldán¹,

Cruz−Suárez²,

Chávez-Rodríguez³

2017

Kybernetika

Self Cite

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“…CAP ÍTULO 1. PRELIMINARES En los trabajos de Cruz Suárez, Ilhuicatzi y Montes de Oca, así como en el de Iida y Mori [2,6], utilizan un horizonte aleatorio el cual llaman horizonte aleatorio de planeación el cual emplean en Procesos de Decisión de Markov (MDP por sus siglas en inglés). Bajo ciertos supuestos, muestran la existencia de la estrategia óptima para la MDP con horizonte aleatorio y la obtienen proponiendo un algoritmo que se resuelve numéricamente.…”

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“…Los resultados dependen de la distribución propuesta para el horizonte. Además en [2] se trata con costos que pueden ser no acotados.…”

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Optimalidad de pruebas secuenciales para experimentos con horizonte aleatorio

Soto

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En este trabajo desarrollamos la teoría para caracterizar la estructura de las pruebas secuenciales óptimas para experimentos, introduciendo un horizonte aleatorio, a diferencia de un horizonte infinito como en la teoría clásica. Analizamos las pruebas secuenciales óptimas encontradas con horizonte aleatorio en términos de razón de probabilidades y al observar un caso particular tenemos una relación con las clásicas pruebas secuenciales de razón de probabilidades (SPRT).

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