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Adaptive Subgradient Methods for Online Learning and ...

Journal of Machine Learning Research 12 (2011) 2121-2159 Submitted 3/10; Revised 3/11; Published 7/11 Adaptive Subgradient Methods forOnline Learning and Stochastic Optimization John Science DivisionUniversity of California, BerkeleyBerkeley, CA 94720 USAElad - Israel Institute of TechnologyTechnion CityHaifa, 32000, IsraelYoram Amphitheatre ParkwayMountain View, CA 94043 USAE ditor:Tong ZhangAbstractWe present a new family of Subgradient Methods that dynamically incorporate knowledge of thegeometry of the data observed in earlier iterations to perform more informative gradient-basedlearning. Metaphorically, the adaptation allows us to find needles in haystacks in the form of verypredictive but rarely seen features.

tion, which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal function that can be chosen in hindsight. We give several efficient algorithms for empirical risk minimization probl ems with common and important regu-larization functions and domain constraints.

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