Nicolas Markey

Résumé

This article focuses on the existence and synthesis of strategies in double-weighted Markov decision processes, which satisfy both a probability constraint over a weighted reachability condition, and a quantitative constraint on the expected value of a random variable defined using another reachability condition. This work generalizes a scheduling problem for energy consumption (typically the problem of charging electric vehicles). We study the set of values of a parameter (a threshold) for which the problem has a solution, and show how a partial characterization of this set can be obtained via two sequences of optimization problems. We also discuss the completeness and feasibility of the resulting approach.

@inproceedings{gretsi2019-GBLM,
  author =              {Gonz{\'a}lez, Mauricio and Bouyer, Patricia and
                         Lasaulce, Samson and Markey, Nicolas},
  title =               {Optimisation en pr\'esence de contraintes en
                         probabilit\'es et processus markoviens
                         contr\^ol\'es},
  booktitle =           {{A}ctes du 27{\`e}me {C}olloque du {G}roupe
                         d'{\'E}tudes du {T}raitement du {S}ignal et des
                         {I}mages ({GRETSI}'19)},
  acronym =             {{GRETSI}'19},
  year =                {2019},
  month =               aug,
  abstract =            {This article focuses on the existence and synthesis
                         of strategies in double-weighted Markov decision
                         processes, which satisfy both a probability
                         constraint over a weighted reachability condition,
                         and a quantitative constraint on the expected value
                         of a random variable defined using another
                         reachability condition. This work generalizes a
                         scheduling problem for energy consumption (typically
                         the problem of charging electric vehicles). We~study
                         the set of values of a parameter (a~threshold) for
                         which the problem has a solution, and show how a
                         partial characterization of this set can be obtained
                         via two sequences of optimization problems. We~also
                         discuss the completeness and feasibility of the
                         resulting approach.},
}