Abstract
We study the rates of growth of the regret in online convex optimization. First, we show that a simple extension of the algorithm of Hazan et al eliminates the need for a priori knowledge of the lower bound on the second derivatives of the observed functions. We then provide an algorithm, Adaptive Online Gradient Descent, which interpolates between the results of Zinkevich for linear functions and of Hazan et al for strongly convex functions, achieving intermediate rates between √ T and log T. Furthermore, we show strong optimality of the algorithm. Finally, we provide an extension of our results to general norms.
| Original language | English (US) |
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| Title of host publication | Advances in Neural Information Processing Systems 20 - Proceedings of the 2007 Conference |
| State | Published - Dec 1 2009 |
| Externally published | Yes |
| Event | 21st Annual Conference on Neural Information Processing Systems, NIPS 2007 - Vancouver, BC, Canada Duration: Dec 3 2007 → Dec 6 2007 |
Other
| Other | 21st Annual Conference on Neural Information Processing Systems, NIPS 2007 |
|---|---|
| Country | Canada |
| City | Vancouver, BC |
| Period | 12/3/07 → 12/6/07 |
All Science Journal Classification (ASJC) codes
- Information Systems
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Cite this
Bartlett, P. L., Hazan, E. E., & Rakhlin, A. (2009). Adaptive online gradient descent. In Advances in Neural Information Processing Systems 20 - Proceedings of the 2007 Conference