### Abstract

Given a sampling budget M, stochastic approximation (SA) schemes for constrained stochastic convex programs generally utilize a single sample for each projection, requiring an effort ofM projection operations, each of possibly significant complexity. We present an extragradient-based variable sample-size SA scheme (eg-VSSA) that uses Nk samples at step k where ϵk Nk > M. We make the following contributions: (i) In strongly convex regimes, the expected error decays linearly in the number of projection steps; (ii) In convex settings, if the sample-size is increased at suitable rates and the steplength is optimally chosen, the error diminishes at δ(1=K-d1) and δ(1/ √M), requiring O(M1/(2-d2)) steps, where K denotes the number of steps and d1;d2 > 0 can be made arbitrarily small. Preliminary numerics reveal that increasing sample-size schemes provide solutions of similar accuracy to SA schemes but with effort reduced by factors as high as 20.

Original language | English (US) |
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Title of host publication | 2016 Winter Simulation Conference |

Subtitle of host publication | Simulating Complex Service Systems, WSC 2016 |

Editors | Theresa M. Roeder, Peter I. Frazier, Robert Szechtman, Enlu Zhou |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 690-701 |

Number of pages | 12 |

ISBN (Electronic) | 9781509044863 |

DOIs | |

State | Published - Jul 2 2016 |

Event | 2016 Winter Simulation Conference, WSC 2016 - Arlington, United States Duration: Dec 11 2016 → Dec 14 2016 |

### Publication series

Name | Proceedings - Winter Simulation Conference |
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Volume | 0 |

ISSN (Print) | 0891-7736 |

### Other

Other | 2016 Winter Simulation Conference, WSC 2016 |
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Country | United States |

City | Arlington |

Period | 12/11/16 → 12/14/16 |

### All Science Journal Classification (ASJC) codes

- Software
- Modeling and Simulation
- Computer Science Applications

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## Cite this

*2016 Winter Simulation Conference: Simulating Complex Service Systems, WSC 2016*(pp. 690-701). [7822133] (Proceedings - Winter Simulation Conference; Vol. 0). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/WSC.2016.7822133