A simple condition for regularity in negative programming

1979 ◽  
Vol 16 (2) ◽  
pp. 305-318 ◽  
Author(s):  
P. Whittle
Keyword(s):  
Decision Problem ◽  
Loss Functions ◽  
Simple Condition ◽  
Markov Decision Problem ◽  
Domains Of Attraction ◽  
Section 8 ◽  
Counter Example ◽  
Regularity Properties ◽  
Markov Decision

A simple condition (the ‘bridging condition') is given for a Markov decision problem with non-negative costs to enjoy the regularity properties enunciated in Theorem 1. The bridging condition is sufficient for regularity, and is not far from being necessary, in a sense explained in Section 2. In Section 8 we consider the different classes of terminal loss functions (domains of attraction) associated with different solutions of (14). Some conjectures concerning these domains of attraction are either proved, or disproved by counter-example.

A simple condition for regularity in negative programming

1979 ◽  
Vol 16 (02) ◽  
pp. 305-318 ◽  
Author(s):  
P. Whittle
Keyword(s):  
Decision Problem ◽  
Loss Functions ◽  
Simple Condition ◽  
Markov Decision Problem ◽  
Domains Of Attraction ◽  
Section 8 ◽  
Counter Example ◽  
Regularity Properties ◽  
Markov Decision

A simple condition (the ‘bridging condition') is given for a Markov decision problem with non-negative costs to enjoy the regularity properties enunciated in Theorem 1. The bridging condition is sufficient for regularity, and is not far from being necessary, in a sense explained in Section 2. In Section 8 we consider the different classes of terminal loss functions (domains of attraction) associated with different solutions of (14). Some conjectures concerning these domains of attraction are either proved, or disproved by counter-example.

scholarly journals A Subjective Optimal Strategy for Transit Simulation Models

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Agostino Nuzzolo ◽  
Antonio Comi
Keyword(s):  
Optimal Strategy ◽  
Decision Problem ◽  
Simulation Models ◽  
Problem Solution ◽  
Markov Decision Problem ◽  
Behavioural Modelling ◽  
Transit Networks ◽  
Modelling Framework ◽  
Markov Decision ◽  
Choice Approach

A behavioural modelling framework with a dynamic travel strategy path choice approach is presented for unreliable multiservice transit networks. The modelling framework is especially suitable for dynamic run-oriented simulation models that use subjective strategy-based path choice models. After an analysis of the travel strategy approach in unreliable transit networks with the related hyperpaths, the search for the optimal strategy as a Markov decision problem solution is considered. The new modelling framework is then presented and applied to a real network. The paper concludes with an overview of the benefits of the new behavioural framework and outlines scope for further research.

scholarly journals Spinning plates and squad systems: policies for bi-directional restless bandits

2006 ◽  
Vol 38 (1) ◽  
pp. 95-115 ◽  
Author(s):  
K. D. Glazebrook ◽  
C. Kirkbride ◽  
D. Ruiz-Hernandez
Keyword(s):  
Decision Problem ◽  
Decision Processes ◽  
Optimal Management ◽  
Markov Decision Problem ◽  
Restless Bandits ◽  
The Family ◽  
Markov Decision ◽  
Necessary And Sufficient

This paper concerns two families of Markov decision problem that fall within the family of (bi-directional) restless bandits, an intractable class of decision processes introduced by Whittle. The spinning plates problem concerns the optimal management of a portfolio of reward-generating assets whose yields grow with investment but otherwise tend to decline. In the model of asset exploitation called the squad system, the yield from an asset tends to decline when it is used but will recover when the asset is at rest. In all cases, simply stated conditions are given that guarantee indexability of the problem, together with conditions necessary and sufficient for its strict indexability. The index heuristics for asset activation that emerge from the analysis are assessed numerically and found to perform very strongly.

Splitting in a finite Markov decision problem

2012 ◽  
Vol 39 (4) ◽  
pp. 38-38
Author(s):  
Eric V. Denardo ◽  
Eugene A. Feinberg ◽  
Uriel G. Rothblum
Keyword(s):  
Decision Problem ◽  
Markov Decision Problem ◽  
Markov Decision
Sign in / Sign up

Export Citation Format

Share Document