Zhang, T. T., Lee, B. D., Ziemann, I., Pappas, G. J., & Matni, N. (2024). Guarantees for Nonlinear Representation Learning: Non-identical Covariates, Dependent Data, Fewer Samples. arXiv preprint arXiv:2410.11227.
This paper investigates the statistical guarantees of learning a shared nonlinear representation across multiple tasks for improved generalization, particularly when the data from each task exhibits non-identical distributions and potential sequential dependencies.
The authors analyze a two-stage empirical risk minimization (ERM) scheme for learning a shared representation g from T source tasks and a task-specific linear head f on a target task. They leverage concepts of task-diversity and hypercontractivity to derive generalization bounds on the excess risk of the learned predictor on the target task.
The study provides theoretical support for the effectiveness of multi-task representation learning in more realistic scenarios with non-identical distributions and dependent data, demonstrating its potential for broader applications in domain generalization and sequential decision-making.
This work significantly extends the theoretical understanding of multi-task representation learning by relaxing key assumptions made in prior work, making the results applicable to a wider range of practical problems.
The analysis primarily focuses on the statistical properties of ERM. Exploring computationally efficient algorithms for this setting and investigating the stability of task-diversity for practical applications are promising directions for future research.
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