  By transferring knowledge learned from seen/previous tasks, meta learning
aims to generalize well to unseen/future tasks. Existing meta-learning
approaches have shown promising empirical performance on various multiclass
classification problems, but few provide theoretical analysis on the
classifiers' generalization ability on future tasks. In this paper, under the
assumption that all classification tasks are sampled from the same
meta-distribution, we leverage margin theory and statistical learning theory to
establish three margin-based transfer bounds for meta-learning based multiclass
classification (MLMC). These bounds reveal that the expected error of a given
classification algorithm for a future task can be estimated with the average
empirical error on a finite number of previous tasks, uniformly over a class of
preprocessing feature maps/deep neural networks (i.e. deep feature embeddings).
To validate these bounds, instead of the commonly-used cross-entropy loss, a
multi-margin loss is employed to train a number of representative MLMC models.
Experiments on three benchmarks show that these margin-based models still
achieve competitive performance, validating the practical value of our
margin-based theoretical analysis.
