Semantic parsing over multiple knowledge bases enables a parser to exploit structural similarities of programs across the multiple domains. However, the fundamental challenge lies in obtaining high-quality annotations of (utterance, program) pairs across various domains needed for training such models. To overcome this, we propose a novel framework to build a unified multi-domain enabled semantic parser trained only with weak supervision (denotations). Weakly supervised training is particularly arduous as the program search space grows exponentially in a multi-domain setting. To solve this, we incorporate a multi-policy distillation mechanism in which we first train domain-specific semantic parsers (teachers) using weak supervision in the absence of the ground truth programs, followed by training a single unified parser (student) from the domain specific policies obtained from these teachers. The resultant semantic parser is not only compact but also generalizes better, and generates more accurate programs. It further does not require the user to provide a domain label while querying. On the standard OVERNIGHT dataset (containing multiple domains), we demonstrate that the proposed model improves performance by 20% in terms of denotation accuracy in comparison to baseline techniques.
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