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One of the goals of natural language understanding is to develop models that map sentences into meaning representations. However, training such models requires expensive annotation of complex structures, which hinders their adoption. Learning to actively-learn(LTAL) is a recent paradigm for reducing the amount of labeled data by learning a policy that selects which samples should be labeled. In this work, we examine LTAL for learning semantic representations, such as QA-SRL. We show that even an oracle policy that is allowed to pick examples that maximize performance on the test set (and constitutes an upper bound on the potential of LTAL), does not substantially improve performance compared to a random policy. We investigate factors that could explain this finding and show that a distinguishing characteristic of successful applications of LTAL is the interaction between optimization and the oracle policy selection process. In successful applications of LTAL, the examples selected by the oracle policy do not substantially depend on the optimization procedure, while in our setup the stochastic nature of optimization strongly affects the examples selected by the oracle. We conclude that the current applicability of LTAL for improving data efficiency in learning semantic meaning representations is limited.