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A mirror descent algorithm for minimization of mean Poisson flow driven losses

  • Stochastic Systems, Queueing Systems
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Abstract

A problem of minimization of integral losses on given horizon is considered for stochastic system in continuous time. The losses occur in jump times of a Poisson process, and represent continuous convex function of control parameter on convex compact finite-dimensional set. At the jump times an oracle provide stochastically perturbed sub-gradient of the loss function, bounded in mean squares; the noise is additive and centered. Control strategy generated by Mirror Descent algorithm is suggested. For the strategy an explicit upper bound for integral loss discrepancy over its minimum is proved. Example of such strategy application to queueing model is examined.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    A. V. Nazin, S. V. Anulova & A. A. Tremba

Authors
  1. A. V. Nazin
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  2. S. V. Anulova
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  3. A. A. Tremba
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Correspondence to A. V. Nazin.

Additional information

Original Russian Text © A.V. Nazin, S.V. Anulova, A.A. Tremba, 2014, published in Avtomatika i Telemekhanika, 2014, No. 6, pp. 30–38.

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Nazin, A.V., Anulova, S.V. & Tremba, A.A. A mirror descent algorithm for minimization of mean Poisson flow driven losses. Autom Remote Control 75, 1010–1016 (2014). https://doi.org/10.1134/S0005117914060022

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  • DOI: https://doi.org/10.1134/S0005117914060022

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