Timezone: »
We study connections between Dykstra's algorithm for projecting onto an intersection of convex sets, the augmented Lagrangian method of multipliers or ADMM, and block coordinate descent. We prove that coordinate descent for a regularized regression problem, in which the penalty is a separable sum of support functions, is exactly equivalent to Dykstra's algorithm applied to the dual problem. ADMM on the dual problem is also seen to be equivalent, in the special case of two sets, with one being a linear subspace. These connections, aside from being interesting in their own right, suggest new ways of analyzing and extending coordinate descent. For example, from existing convergence theory on Dykstra's algorithm over polyhedra, we discern that coordinate descent for the lasso problem converges at an (asymptotically) linear rate. We also develop two parallel versions of coordinate descent, based on the Dykstra and ADMM connections.
Author Information
Ryan Tibshirani (Carnegie Mellon University)
More from the Same Authors
-
2019 Poster: Kalman Filter, Sensor Fusion, and Constrained Regression: Equivalences and Insights »
Maria Jahja · David Farrow · Roni Rosenfeld · Ryan Tibshirani -
2019 Poster: Conformal Prediction Under Covariate Shift »
Ryan Tibshirani · Rina Barber · Emmanuel Candes · Aaditya Ramdas -
2017 Poster: A Sharp Error Analysis for the Fused Lasso, with Application to Approximate Changepoint Screening »
Kevin Lin · James Sharpnack · Alessandro Rinaldo · Ryan Tibshirani -
2017 Poster: Higher-Order Total Variation Classes on Grids: Minimax Theory and Trend Filtering Methods »
Veeranjaneyulu Sadhanala · Yu-Xiang Wang · James Sharpnack · Ryan Tibshirani -
2016 Poster: The Multiple Quantile Graphical Model »
Alnur Ali · J. Zico Kolter · Ryan Tibshirani -
2016 Poster: Total Variation Classes Beyond 1d: Minimax Rates, and the Limitations of Linear Smoothers »
Veeranjaneyulu Sadhanala · Yu-Xiang Wang · Ryan Tibshirani -
2014 Workshop: Modern Nonparametrics 3: Automating the Learning Pipeline »
Eric Xing · Mladen Kolar · Arthur Gretton · Samory Kpotufe · Han Liu · Zoltán Szabó · Alan Yuille · Andrew G Wilson · Ryan Tibshirani · Sasha Rakhlin · Damian Kozbur · Bharath Sriperumbudur · David Lopez-Paz · Kirthevasan Kandasamy · Francesco Orabona · Andreas Damianou · Wacha Bounliphone · Yanshuai Cao · Arijit Das · Yingzhen Yang · Giulia DeSalvo · Dmitry Storcheus · Roberto Valerio