  Chatbots are designed to carry out human-like conversations across different
domains, such as general chit-chat, knowledge exchange, and persona-grounded
conversations. To measure the quality of such conversational agents, a dialogue
evaluator is expected to conduct assessment across domains as well. However,
most of the state-of-the-art automatic dialogue evaluation metrics (ADMs) are
not designed for multi-domain evaluation. We are motivated to design a general
and robust framework, MDD-Eval, to address the problem. Specifically, we first
train a teacher evaluator with human-annotated data to acquire a rating skill
to tell good dialogue responses from bad ones in a particular domain and then,
adopt a self-training strategy to train a new evaluator with teacher-annotated
multi-domain data, that helps the new evaluator to generalize across multiple
domains. MDD-Eval is extensively assessed on six dialogue evaluation
benchmarks. Empirical results show that the MDD-Eval framework achieves a
strong performance with an absolute improvement of 7% over the state-of-the-art
ADMs in terms of mean Spearman correlation scores across all the evaluation
benchmarks.
