  Decentralized execution is one core demand in cooperative multi-agent
reinforcement learning (MARL). Recently, most popular MARL algorithms have
adopted decentralized policies to enable decentralized execution and use
gradient descent as their optimizer. However, there is hardly any theoretical
analysis of these algorithms taking the optimization method into consideration,
and we find that various popular MARL algorithms with decentralized policies
are suboptimal in toy tasks when gradient descent is chosen as their
optimization method. In this paper, we theoretically analyze two common classes
of algorithms with decentralized policies -- multi-agent policy gradient
methods and value-decomposition methods to prove their suboptimality when
gradient descent is used. In addition, we propose the Transformation And
Distillation (TAD) framework, which reformulates a multi-agent MDP as a special
single-agent MDP with a sequential structure and enables decentralized
execution by distilling the learned policy on the derived ``single-agent" MDP.
This approach uses a two-stage learning paradigm to address the optimization
problem in cooperative MARL, maintaining its performance guarantee.
Empirically, we implement TAD-PPO based on PPO, which can theoretically perform
optimal policy learning in the finite multi-agent MDPs and shows significant
outperformance on a large set of cooperative multi-agent tasks.
