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By transferring knowledge learned from seen/previous tasks, meta learningaims to generalize well to unseen/future tasks. Existing meta-learningapproaches have shown promising empirical performance on various multiclassclassification problems, but few provide theoretical analysis on theclassifiers' generalization ability on future tasks. In this paper, under theassumption that all classification tasks are sampled from the samemeta-distribution, we leverage margin theory and statistical learning theory toestablish three margin-based transfer bounds for meta-learning based multiclassclassification (MLMC). These bounds reveal that the expected error of a givenclassification algorithm for a future task can be estimated with the averageempirical error on a finite number of previous tasks, uniformly over a class ofpreprocessing feature maps/deep neural networks (i.e. deep feature embeddings).To validate these bounds, instead of the commonly-used cross-entropy loss, amulti-margin loss is employed to train a number of representative MLMC models.Experiments on three benchmarks show that these margin-based models stillachieve competitive performance, validating the practical value of ourmargin-based theoretical analysis.

Margin-Based Transfer Bounds for Meta Learning with Deep Feature Embedding