Near-optimal and Efficient First-Order Algorithm for Multi-Task Learning with Shared Linear Representation

• URL: http://arxiv.org/abs/2605.00473v2
• Date: Wed, 06 May 2026 11:29:43 GMT
• Title: Near-optimal and Efficient First-Order Algorithm for Multi-Task Learning with Shared Linear Representation
• Abstract summary: Multi-task learning (MTL) has emerged as a paradigm in machine learning by leveraging shared structures across related tasks.<n>This paper introduces an algorithm that jointly learns the parameters that jointly learn.
• Score: 6.903751783272732
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multi-task learning (MTL) has emerged as a pivotal paradigm in machine learning by leveraging shared structures across multiple related tasks. Despite its empirical success, the development of likelihood-based efficiently solvable algorithms--even for shared linear representations--remains largely underdeveloped, primarily due to the non-convex structure intrinsic to matrix factorization. This paper introduces a first-order algorithm that jointly learns a shared representation and task-specific parameters, with guaranteed efficiency. Notably, it converges in $\widetilde{\mathcal{O}}(1)$ iterations and attains a \emph{near-optimal} estimation error of $\widetilde{\mathcal{O}}(dk/(TN))$, \emph{improving} over existing likelihood-based methods by a factor of $k$, where $d$, $k$, $T$, $N$ denote input dimension, representation dimension, task count, and samples per task, respectively. Our results justify that likelihood-based first-order methods can efficiently solve the MTL problem.

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