  Open-Domain Conversational Question Answering (ODConvQA) aims at answering
questions through a multi-turn conversation based on a retriever-reader
pipeline, which retrieves passages and then predicts answers with them.
However, such a pipeline approach not only makes the reader vulnerable to the
errors propagated from the retriever, but also demands additional effort to
develop both the retriever and the reader, which further makes it slower since
they are not runnable in parallel. In this work, we propose a method to
directly predict answers with a phrase retrieval scheme for a sequence of
words, reducing the conventional two distinct subtasks into a single one. Also,
for the first time, we study its capability for ODConvQA tasks. However, simply
adopting it is largely problematic, due to the dependencies between previous
and current turns in a conversation. To address this problem, we further
introduce a novel contrastive learning strategy, making sure to reflect
previous turns when retrieving the phrase for the current context, by
maximizing representational similarities of consecutive turns in a conversation
while minimizing irrelevant conversational contexts. We validate our model on
two ODConvQA datasets, whose experimental results show that it substantially
outperforms the relevant baselines with the retriever-reader. Code is available
at: https://github.com/starsuzi/PRO-ConvQA.
