Abstract: Conversational query rewriting aims to reformulate a concise conversational query to a fully specified, context-independent query that can be effectively handled by existing information retrieval systems. This paper presents a few-shot generative approach to conversational query rewriting. We develop two methods, based on rules and self-supervised learning, to generate weak supervision data using large amounts of ad hoc search sessions, and to fine-tune GPT-2 to rewrite conversational queries. On the TREC Conversational Assistance Track, our weakly supervised GPT-2 rewriter improves the state-of-the-art ranking accuracy by 12