Online Learning Meets Optimization in the Dual
We describe a novel framework for the design and analysis of online learning algorithms based on the notion of duality in constrained optimization. We cast a sub-family of universal online bounds as an optimization problem. Using the weak duality theorem we reduce the process of online learning to the task of incrementally increasing the dual objective function. The amount by which the dual increases serves as a new and natural notion of progress. We are thus able to tie the primal objective value and the number of prediction mistakes using and the increase in the dual. The end result is a general framework for designing and analyzing old and new online learning algorithms in the mistake bound model.
KeywordsOnline Learning Online Algorithm Dual Solution Dual Objective Bregman Divergence
Unable to display preview. Download preview PDF.
- 3.Cesa-Bianchi, N., Conconi, A., Gentile, C.: On the generalization ability of on-line learning algorithms. In: Advances in Neural Information Processing Systems 14, pp. 359–366 (2002)Google Scholar
- 4.Crammer, K., Dekel, O., Keshet, J., Shalev-Shwartz, S., Singer, Y.: Online passive aggressive algorithms. Technical report, The Hebrew University (2005)Google Scholar
- 5.Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000)Google Scholar
- 6.Dekel, O., Shalev-Shwartz, S., Singer, Y.: The Forgetron: A kernel-based perceptron on a fixed budget. In: Advances in Neural Information Processing Systems 18 (2005)Google Scholar
- 7.Gentile, C.: The robustness of the p-norm algorithms. Machine Learning 53(3) (2002)Google Scholar
- 13.Littlestone, N.: Learning when irrelevant attributes abound: A new linear-threshold algorithm. Machine Learning 2, 285–318 (1988)Google Scholar
- 14.Littlestone, N.: Mistake bounds and logarithmic linear-threshold learning algorithms. PhD thesis, U. C. Santa Cruz (March 1989)Google Scholar
- 15.Rosenblatt, F.: The perceptron: A probabilistic model for information storage and organization in the brain. Psychological Review 65, 386–407 (1958), Reprinted in Neurocomputing, MIT Press (1988)Google Scholar