Abstract: 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.