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Since its inception, the modus operandi of multi-task learning (MTL) has beento minimize the task-wise mean of the empirical risks. We introduce ageneralized loss-compositional paradigm for MTL that includes a spectrum offormulations as a subfamily. One endpoint of this spectrum is minimax MTL: anew MTL formulation that minimizes the maximum of the tasks' empirical risks.Via a certain relaxation of minimax MTL, we obtain a continuum of MTLformulations spanning minimax MTL and classical MTL. The full paradigm itselfis loss-compositional, operating on the vector of empirical risks. Itincorporates minimax MTL, its relaxations, and many new MTL formulations asspecial cases. We show theoretically that minimax MTL tends to avoid worst caseoutcomes on newly drawn test tasks in the learning to learn (LTL) test setting.The results of several MTL formulations on synthetic and real problems in theMTL and LTL test settings are encouraging.

Minimax Multi-Task Learning and a Generalized Loss-Compositional Paradigm for MTL