### Abstract

We consider the solution of a stochastic convex optimization problem E[f(x;θ
^{lowast}
,ξ)] in x over a closed and convex set X in a regime where θ
^{lowast}
is unavailable. Instead, θ
^{lowast}
may be learnt by minimizing a suitable metric E[g(θη)] in θ over a closed and convex set Θ. We present a coupled stochastic approximation scheme for the associated stochastic optimization problem with imperfect information. The schemes are shown to be equipped with almost sure convergence properties in regimes where the function f is both strongly convex as well as merely convex. Rate estimates are provided in both a strongly convex as well as a merely convex regime, where the use of averaging facilitates the development of a bound.

Original language | English (US) |
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Title of host publication | Proceedings of the 2013 Winter Simulation Conference - Simulation |

Subtitle of host publication | Making Decisions in a Complex World, WSC 2013 |

Pages | 821-832 |

Number of pages | 12 |

DOIs | |

State | Published - Dec 1 2013 |

Event | 2013 43rd Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013 - Washington, DC, United States Duration: Dec 8 2013 → Dec 11 2013 |

### Publication series

Name | Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013 |
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### Other

Other | 2013 43rd Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013 |
---|---|

Country | United States |

City | Washington, DC |

Period | 12/8/13 → 12/11/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Modeling and Simulation

### Cite this

*Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013*(pp. 821-832). [6721474] (Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013). https://doi.org/10.1109/WSC.2013.6721474

}

*Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013.*, 6721474, Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013, pp. 821-832, 2013 43rd Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013, Washington, DC, United States, 12/8/13. https://doi.org/10.1109/WSC.2013.6721474

**On the solution of stochastic optimization problems in imperfect information regimes.** / Jiang, Hao; Shanbhag, Vinayak V.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - On the solution of stochastic optimization problems in imperfect information regimes

AU - Jiang, Hao

AU - Shanbhag, Vinayak V.

PY - 2013/12/1

Y1 - 2013/12/1

N2 - We consider the solution of a stochastic convex optimization problem E[f(x;θ lowast ,ξ)] in x over a closed and convex set X in a regime where θ lowast is unavailable. Instead, θ lowast may be learnt by minimizing a suitable metric E[g(θη)] in θ over a closed and convex set Θ. We present a coupled stochastic approximation scheme for the associated stochastic optimization problem with imperfect information. The schemes are shown to be equipped with almost sure convergence properties in regimes where the function f is both strongly convex as well as merely convex. Rate estimates are provided in both a strongly convex as well as a merely convex regime, where the use of averaging facilitates the development of a bound.

AB - We consider the solution of a stochastic convex optimization problem E[f(x;θ lowast ,ξ)] in x over a closed and convex set X in a regime where θ lowast is unavailable. Instead, θ lowast may be learnt by minimizing a suitable metric E[g(θη)] in θ over a closed and convex set Θ. We present a coupled stochastic approximation scheme for the associated stochastic optimization problem with imperfect information. The schemes are shown to be equipped with almost sure convergence properties in regimes where the function f is both strongly convex as well as merely convex. Rate estimates are provided in both a strongly convex as well as a merely convex regime, where the use of averaging facilitates the development of a bound.

UR - http://www.scopus.com/inward/record.url?scp=84894193510&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894193510&partnerID=8YFLogxK

U2 - 10.1109/WSC.2013.6721474

DO - 10.1109/WSC.2013.6721474

M3 - Conference contribution

AN - SCOPUS:84894193510

SN - 9781479939503

T3 - Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013

SP - 821

EP - 832

BT - Proceedings of the 2013 Winter Simulation Conference - Simulation

ER -