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Alternating Direction Method of Multipliers (ADMM) has become a widely usedoptimization method for convex problems, particularly in the context of datamining in which large optimization problems are often encountered. ADMM hasseveral desirable properties, including the ability to decompose large problemsinto smaller tractable sub-problems and ease of parallelization, that areessential in these scenarios. The most common form of ADMM is the two-block, inwhich two sets of primal variables are updated alternatingly. Recent years haveseen advances in multi-block ADMM, which update more than two blocks of primalvariables sequentially. In this paper, we study the empirical question: {\em Istwo-block ADMM always comparable with sequential multi-block ADMM solving anequivalent problem?} In the context of optimization problems arising inmulti-task learning, through a comprehensive set of experiments we surprisinglyshow that multi-block ADMM consistently outperformed two-block ADMM onoptimization performance, and as a consequence on prediction performance,across all datasets and for the entire range of dual step sizes. Our resultshave an important practical implication: rather than simply using the populartwo-block ADMM, one may considerably benefit from experimenting withmulti-block ADMM applied to an equivalent problem.

Two-block vs. Multi-block ADMM: An empirical evaluation of convergence