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Validation analysis of mirror descent stochastic approximation method

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Abstract

The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing stochastic approximation (SA) type algorithms. To this end we show that while running a Mirror Descent Stochastic Approximation procedure one can compute, with a small additional effort, lower and upper statistical bounds for the optimal objective value. We demonstrate that for a certain class of convex stochastic programs these bounds are comparable in quality with similar bounds computed by the sample average approximation method, while their computational cost is considerably smaller.

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Authors and Affiliations

  1. University of Florida, Gainesville, FL, 32611, USA

    Guanghui Lan

  2. Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Arkadi Nemirovski & Alexander Shapiro

Authors
  1. Guanghui Lan
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  2. Arkadi Nemirovski
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  3. Alexander Shapiro
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Corresponding author

Correspondence to Guanghui Lan.

Additional information

G. Lan research of this author was partly supported by the ONR Grant N000140811104 during his Ph.D. study. A. Nemirovski and A. Shapiro research of this author was partly supported by the NSF awards DMI-0619977 and DMS-0914785.

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Lan, G., Nemirovski, A. & Shapiro, A. Validation analysis of mirror descent stochastic approximation method. Math. Program. 134, 425–458 (2012). https://doi.org/10.1007/s10107-011-0442-6

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  • DOI: https://doi.org/10.1007/s10107-011-0442-6

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