Robust parallel control in a random environment and data processing optimization (original) (raw)

Abstract

Consideration was given to the control of processing large amounts of data, provided that there are two alternative methods of processing with different and a priori unknown efficiencies. It was required to determine the most efficient method and maintain its preferable use. With the use of parallel processing this may be carried out in a relatively small number of steps and actually without losses in the control performance, that is, without increasing the minimax risk. An invariant equation with a solution containing a singularity at t = 0 was previously obtained to describe the control. This solution was represented as a product with one cofactor being the density of the normal distribution which is singular at t = 0 and the other, the nonsingular one, the solution to a new equation. Numerical experiments demonstrated that this new equation offers greater possibilities for calculations. In particular, it enabled one to improve the asymptotic estimates of the minimax risk.

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References

  1. Kolnogorov, A.V., Parallel Design of Robust Control in the Stochastic Environment (the Two-armed Bandit Problem), Autom. Remote Control, 2012, vol. 73, no. 4, pp. 689–701.
    Article MathSciNet Google Scholar
  2. Vogel, W., An Asymptotic Minimax Theorem for the Two-armed Bandit Problem, Ann. Math. Stat., 1960, vol. 31, pp. 444–451.
    Article MATH Google Scholar
  3. Nazin, A.V. and Poznyak, A.S., Adaptivnyi vybor variantov (Adaptive Selection of Variants), Moscow: Nauka, 1986.
    Google Scholar
  4. Poznyak, A.S. and Najim, K., Learning Automata and Stochastic Optimization, in Lect. Notes Control Inf. Sci., vol. 225, Berlin: Springer, 1997.
    Google Scholar
  5. Juditsky, A., Nazin, A.V., Tsybakov, A.B., et al., Gap-free Bounds for Stochastic Multi-Armed Bandit, in Proc. 17th World Congr. Int. Federation Autom. Control, Seoul, 2008, July 6–11, pp. 11560–11563.
  6. Witmer, J.A., Bayesian Multistage Decision Problems, Ann. Statist., 1986, vol. 14, pp. 283–297.
    Article MATH MathSciNet Google Scholar
  7. Lai, T.L., Levin, B., Robbins, H., et al., Sequential Medical Trials (Stopping Rules/Asymptotic Optimality), in Proc. Natl. Acad. Sci. USA, 1980, vol. 77, no. 6, pp. 3135–3138.
    Article MATH MathSciNet Google Scholar
  8. Kolnogorov, A.V., Problem of Two-armed Bandit for Systems with Parallel Data Processing, Probl. Peredachi Inf., 2012, vol. 48, no. 1, pp. 83–95.
    MathSciNet Google Scholar

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Authors and Affiliations

  1. Yaroslav-the-Wise State University, Novgorod, Russia
    A. V. Kolnogorov

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Correspondence toA. V. Kolnogorov.

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Original Russian Text © A.V. Kolnogorov, 2014, published in Avtomatika i Telemekhanika, 2014, No. 12, pp. 42–55.

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Kolnogorov, A.V. Robust parallel control in a random environment and data processing optimization.Autom Remote Control 75, 2124–2134 (2014). https://doi.org/10.1134/S0005117914120042

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