  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.
