  As humans, we often rely on language to learn language. For example, when
corrected in a conversation, we may learn from that correction, over time
improving our language fluency. Inspired by this observation, we propose a
learning algorithm for training semantic parsers from supervision (feedback)
expressed in natural language. Our algorithm learns a semantic parser from
users' corrections such as "no, what I really meant was before his job, not
after", by also simultaneously learning to parse this natural language feedback
in order to leverage it as a form of supervision. Unlike supervision with
gold-standard logical forms, our method does not require the user to be
familiar with the underlying logical formalism, and unlike supervision from
denotation, it does not require the user to know the correct answer to their
query. This makes our learning algorithm naturally scalable in settings where
existing conversational logs are available and can be leveraged as training
data. We construct a novel dataset of natural language feedback in a
conversational setting, and show that our method is effective at learning a
semantic parser from such natural language supervision.
