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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 53128 (19)
- University: Sharif University of Technology
- Department: Computer Engineering
- Advisor(s): Jafari Siavoshani, Mahdi
- Abstract:
- As application demands for online convex optimization accelerate, the need for design-ing new methods that simultaneously cover a large class of convex functions and im-pose the lowest possible regret is highly rising. Known online optimization methods usually perform well only in specific settings, e.g., specific parameters such as the diam-eter of decision space, Lipschitz constant, and strong convexity coefficient, where their performance depends highly on the geometry of the decision space and cost functions. However, in practice, the lack of such geometric information leads to confusion in using the appropriate algorithm. To address these issues, some adaptive methods have been proposed that only focus on adaptively learning the aforementioned parameters. In this work, we propose a general-purpose framework that uses Bandit algorithms to track the best optimizer in a family of online optimization algorithms (in terms of regret bound). This framework accelerates some of the previous adaptive methods while can compete with the best optimizer. Finally, we support our theoretical findings by applying our pro-posed algorithm to the problem of learning the best regularizer on the simplex and $l_2$-ball in a multiclass learning problem.
- Keywords:
- Minimization ; Regularization ; Online Convex Optimization ; Online Learning ; Regret Minimization ; Large Scale Machine Learning
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