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Recent work has shown that language models (LMs) trained with multi-task \textit{instructional learning} (MTIL) can solve diverse NLP tasks in zero- and few-shot settings with improved performance compared to prompt tuning. MTIL illustrates that LMs can extract and use information about the task from instructions beyond the surface patterns of the inputs and outputs. This suggests that meta-learning may further enhance the utilization of instructions for effective task transfer. In this paper we investigate whether meta-learning applied to MTIL can further improve generalization to unseen tasks in a zero-shot setting. Specifically, we propose to adapt meta-learning to MTIL in three directions: 1) Model Agnostic Meta Learning (MAML), 2) Hyper-Network (HNet) based adaptation to generate task specific parameters conditioned on instructions, and 3) an approach combining HNet and MAML. Through extensive experiments on the large scale Natural Instructions V2 dataset, we show that our proposed approaches significantly improve over strong baselines in zero-shot settings. In particular, meta-learning improves the effectiveness of instructions and is most impactful when the test tasks are strictly zero-shot (i.e. no similar tasks in the training set) and are "hard" for LMs, illustrating the potential of meta-learning for MTIL for out-of-distribution tasks.