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For a large family of penalized empirical risk minimization problems , our methods exploit data dependent local smoothness of the loss functions near the optimum , while maintaining convergence guarantees .
 used for: methods, penalized empirical risk minimization problems; used for: data dependent local smoothness, methods; feature of: data dependent local smoothness, loss functions
Given a phrase that describes the relationship between two words, extract the words and the lexical relationship between them. The output format should be "relation1: word1, word2; relation2: word3, word4". 
Option: conjunction, feature of, hyponym of, used for, part of, compare, evaluate for 
Text: {0} 
Answer:
 used for: methods, penalized empirical risk minimization problems; used for: data dependent local smoothness, methods; feature of: data dependent local smoothness, loss functions