Transcription of Introduction to Convex Optimization for Machine Learning
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Introduction to Convex Optimization for Machine Learning
Introduction to Convex Optimization for Machine Learning John Duchi University of California, Berkeley Practical Machine Learning , Fall 2009. Duchi (UC Berkeley) Convex Optimization for Machine Learning Fall 2009 1 / 53. Outline What is Optimization Convex Sets Convex Functions Convex Optimization Problems Lagrange Duality Optimization Algorithms Take Home Messages Duchi (UC Berkeley) Convex Optimization for Machine Learning Fall 2009 2 / 53. What is Optimization What is Optimization (and why do we care?)
Optimization is at the heart of many (most practical?) machine learning algorithms. Linear regression: minimize w kXw −yk2 Classification (logistic regresion or SVM): minimize w Xn i=1 log 1+exp(−yixT i w) or kwk2 +C Xn i=1 ξi s.t. ξi ≥ 1−yixTiw,ξi ≥ 0. Duchi (UC Berkeley) Convex Optimization for Machine Learning Fall 2009 5 / 53
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