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We show a Talagrand-type of concentration inequality for MTL, using which we establish sharp excess risk bounds for Multi-Task Learning (MTL) in terms of distributionand data-dependent versions of the Local Rademacher Complexity (LRC). We also give a new bound on the LRC for strongly convex hypothesis classes, which applies not only to MTL but also to the standard i.i.d. setting. Combining both results, one can now easily derive fast-rate bounds on the excess risk for many prominent MTL methods, includingas we demonstrateSchatten-norm, group-norm, and graph-regularized MTL. The derived bounds reflect a relationship akeen to a conservation law of asymptotic convergence rates. This very relationship allows for trading off slower rates w.r.t. the number of tasks for faster rates with respect to the number of available samples per task, when compared to the rates obtained via a traditional, global Rademacher analysis.
Output:
Local Rademacher Complexity-based Learning Guarantees for Multi-Task Learning