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.
| Subjects: | Machine Learning (cs.LG); Optimization and Control (math.OC) |
| Cite as: | arXiv:2605.00473 [cs.LG] |
| (or arXiv:2605.00473v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.00473 arXiv-issued DOI via DataCite (pending registration) |
From: ShiHong Ding [view email]
[v1]
Fri, 1 May 2026 07:22:01 UTC (122 KB)
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