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A Representation Learning Perspective on the Importance of Train-Validation Splitting in Meta-Learning

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 Added by Nikunj Saunshi
 Publication date 2021
and research's language is English




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An effective approach in meta-learning is to utilize multiple train tasks to learn a good initialization for model parameters that can help solve unseen test tasks with very few samples by fine-tuning from this initialization. Although successful in practice, theoretical understanding of such methods is limited. This work studies an important aspect of these methods: splitting the data from each task into train (support) and validation (query) sets during meta-training. Inspired by recent work (Raghu et al., 2020), we view such meta-learning methods through the lens of representation learning and argue that the train-validation split encourages the learned representation to be low-rank without compromising on expressivity, as opposed to the non-splitting variant that encourages high-rank representations. Since sample efficiency benefits from low-rankness, the splitting strategy will require very few samples to solve unseen test tasks. We present theoretical results that formalize this idea for linear representation learning on a subspace meta-learning instance, and experimentally verify this practical benefit of splitting in simulations and on standard meta-learning benchmarks.



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231 - Yu Bai , Minshuo Chen , Pan Zhou 2020
Meta-learning aims to perform fast adaptation on a new task through learning a prior from multiple existing tasks. A common practice in meta-learning is to perform a train-validation split (emph{train-val method}) where the prior adapts to the task on one split of the data, and the resulting predictor is evaluated on another split. Despite its prevalence, the importance of the train-validation split is not well understood either in theory or in practice, particularly in comparison to the more direct emph{train-train method}, which uses all the per-task data for both training and evaluation. We provide a detailed theoretical study on whether and when the train-validation split is helpful in the linear centroid meta-learning problem. In the agnostic case, we show that the expected loss of the train-val method is minimized at the optimal prior for meta testing, and this is not the case for the train-train method in general without structural assumptions on the data. In contrast, in the realizable case where the data are generated from linear models, we show that both the train-val and train-train losses are minimized at the optimal prior in expectation. Further, perhaps surprisingly, our main result shows that the train-train method achieves a emph{strictly better} excess loss in this realizable case, even when the regularization parameter and split ratio are optimally tuned for both methods. Our results highlight that sample splitting may not always be preferable, especially when the data is realizable by the model. We validate our theories by experimentally showing that the train-train method can indeed outperform the train-val method, on both simulations and real meta-learning tasks.
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