(Bandit) Convex Optimization with Biased Noisy Gradient Oracles

Xiaowei Hu, Prashanth L.A., András György, Csaba Szepesvari
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:819-828, 2016.

Abstract

A popular class of algorithms for convex optimization and online learning with bandit feedback rely on constructing noisy gradient estimates, which are then used in place of the actual gradients in appropriately adjusted first-order algorithms. Depending on the properties of the function to be optimized and the nature of “noise” in the bandit feedback, the bias and variance of gradient estimates exhibit various tradeoffs. In this paper we propose a novel framework that replaces the specific gradient estimation methods with an abstract oracle model. With the help of the new framework we unify previous works, reproducing their results in a clean and concise fashion, while, perhaps more importantly, the framework also allows us to formally show that to achieve the optimal root-n rate either the algorithms that use existing gradient estimators, or the proofs have to go beyond what exists today.

Cite this Paper


BibTeX
@InProceedings{pmlr-v51-hu16b, title = {(Bandit) Convex Optimization with Biased Noisy Gradient Oracles}, author = {Hu, Xiaowei and L.A., Prashanth and György, András and Szepesvari, Csaba}, booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics}, pages = {819--828}, year = {2016}, editor = {Gretton, Arthur and Robert, Christian C.}, volume = {51}, series = {Proceedings of Machine Learning Research}, address = {Cadiz, Spain}, month = {09--11 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v51/hu16b.pdf}, url = {http://proceedings.mlr.press/v51/hu16b.html}, abstract = {A popular class of algorithms for convex optimization and online learning with bandit feedback rely on constructing noisy gradient estimates, which are then used in place of the actual gradients in appropriately adjusted first-order algorithms. Depending on the properties of the function to be optimized and the nature of “noise” in the bandit feedback, the bias and variance of gradient estimates exhibit various tradeoffs. In this paper we propose a novel framework that replaces the specific gradient estimation methods with an abstract oracle model. With the help of the new framework we unify previous works, reproducing their results in a clean and concise fashion, while, perhaps more importantly, the framework also allows us to formally show that to achieve the optimal root-n rate either the algorithms that use existing gradient estimators, or the proofs have to go beyond what exists today.} }
Endnote
%0 Conference Paper %T (Bandit) Convex Optimization with Biased Noisy Gradient Oracles %A Xiaowei Hu %A Prashanth L.A. %A András György %A Csaba Szepesvari %B Proceedings of the 19th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2016 %E Arthur Gretton %E Christian C. Robert %F pmlr-v51-hu16b %I PMLR %P 819--828 %U http://proceedings.mlr.press/v51/hu16b.html %V 51 %X A popular class of algorithms for convex optimization and online learning with bandit feedback rely on constructing noisy gradient estimates, which are then used in place of the actual gradients in appropriately adjusted first-order algorithms. Depending on the properties of the function to be optimized and the nature of “noise” in the bandit feedback, the bias and variance of gradient estimates exhibit various tradeoffs. In this paper we propose a novel framework that replaces the specific gradient estimation methods with an abstract oracle model. With the help of the new framework we unify previous works, reproducing their results in a clean and concise fashion, while, perhaps more importantly, the framework also allows us to formally show that to achieve the optimal root-n rate either the algorithms that use existing gradient estimators, or the proofs have to go beyond what exists today.
RIS
TY - CPAPER TI - (Bandit) Convex Optimization with Biased Noisy Gradient Oracles AU - Xiaowei Hu AU - Prashanth L.A. AU - András György AU - Csaba Szepesvari BT - Proceedings of the 19th International Conference on Artificial Intelligence and Statistics DA - 2016/05/02 ED - Arthur Gretton ED - Christian C. Robert ID - pmlr-v51-hu16b PB - PMLR DP - Proceedings of Machine Learning Research VL - 51 SP - 819 EP - 828 L1 - http://proceedings.mlr.press/v51/hu16b.pdf UR - http://proceedings.mlr.press/v51/hu16b.html AB - A popular class of algorithms for convex optimization and online learning with bandit feedback rely on constructing noisy gradient estimates, which are then used in place of the actual gradients in appropriately adjusted first-order algorithms. Depending on the properties of the function to be optimized and the nature of “noise” in the bandit feedback, the bias and variance of gradient estimates exhibit various tradeoffs. In this paper we propose a novel framework that replaces the specific gradient estimation methods with an abstract oracle model. With the help of the new framework we unify previous works, reproducing their results in a clean and concise fashion, while, perhaps more importantly, the framework also allows us to formally show that to achieve the optimal root-n rate either the algorithms that use existing gradient estimators, or the proofs have to go beyond what exists today. ER -
APA
Hu, X., L.A., P., György, A. & Szepesvari, C.. (2016). (Bandit) Convex Optimization with Biased Noisy Gradient Oracles. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 51:819-828 Available from http://proceedings.mlr.press/v51/hu16b.html.

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