  Centralized Training for Decentralized Execution, where training is done in a
centralized offline fashion, has become a popular solution paradigm in
Multi-Agent Reinforcement Learning. Many such methods take the form of
actor-critic with state-based critics, since centralized training allows access
to the true system state, which can be useful during training despite not being
available at execution time. State-based critics have become a common empirical
choice, albeit one which has had limited theoretical justification or analysis.
In this paper, we show that state-based critics can introduce bias in the
policy gradient estimates, potentially undermining the asymptotic guarantees of
the algorithm. We also show that, even if the state-based critics do not
introduce any bias, they can still result in a larger gradient variance,
contrary to the common intuition. Finally, we show the effects of the theories
in practice by comparing different forms of centralized critics on a wide range
of common benchmarks, and detail how various environmental properties are
related to the effectiveness of different types of critics.
