Multitask Online Mirror Descent
Nicol\`o Cesa-Bianchi, Pierre Laforgue, Andrea Paudice, Massimiliano, Pontil

TL;DR
This paper introduces MT-OMD, a multitask online mirror descent algorithm that shares information across tasks, improving regret bounds when tasks are similar, with practical algorithms and experimental validation.
Contribution
The paper develops a multitask extension of Online Mirror Descent with theoretical regret bounds, closed-form updates, and empirical evidence of improved performance for similar tasks.
Findings
Regret bound of order √(1 + σ²(N-1))√T
Improved bounds when tasks are similar (σ² ≤ 1)
Algorithms with closed-form updates for practical use
Abstract
We introduce and analyze MT-OMD, a multitask generalization of Online Mirror Descent (OMD) which operates by sharing updates between tasks. We prove that the regret of MT-OMD is of order , where is the task variance according to the geometry induced by the regularizer, is the number of tasks, and is the time horizon. Whenever tasks are similar, that is , our method improves upon the bound obtained by running independent OMDs on each task. We further provide a matching lower bound, and show that our multitask extensions of Online Gradient Descent and Exponentiated Gradient, two major instances of OMD, enjoy closed-form updates, making them easy to use in practice. Finally, we present experiments which support our theoretical findings.
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Stochastic Gradient Optimization Techniques · Sparse and Compressive Sensing Techniques
