Model-agnostic meta-learning (MAML) has been recently put forth as a strategy to learn resource-poor languages in a sample-efficient fashion. Nevertheless, the properties of these languages are often not well represented by those available during training. Hence, we argue that the i.i.d. assumption ingrained in MAML makes it ill-suited for cross-lingual NLP. In fact, under a decision-theoretic framework, MAML can be interpreted as minimising the expected risk across training languages (with a uniform prior), which is known as Bayes criterion. To increase its robustness to outlier languages, we create two variants of MAML based on alternative criteria: Minimax MAML reduces the maximum risk across languages, while Neyman-Pearson MAML constrains the risk in each language to a maximum threshold. Both criteria constitute fully differentiable two-player games. In light of this, we propose a new adaptive optimiser solving for a local approximation to their Nash equilibrium. We evaluate both model variants on two popular NLP tasks, part-of-speech tagging and question answering. We report gains for their average and minimum performance across low-resource languages in zero- and few-shot settings, compared to joint multi-source transfer and vanilla MAML.
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