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Centralized Training for Decentralized Execution, where agents are trained offline in a centralized fashion and execute online in a decentralized manner, has become a popular approach in Multi-Agent Reinforcement Learning (MARL). In particular, it has become popular to develop actor-critic methods that train decentralized actors with a centralized critic where the centralized critic is allowed access to global information of the entire system, including the true system state. Such centralized critics are possible given offline information and are not used for online execution. While these methods perform well in a number of domains and have become a de facto standard in MARL, using a centralized critic in this context has yet to be sufficiently analyzed theoretically or empirically. In this paper, we therefore formally analyze centralized and decentralized critic approaches, and analyze the effect of using state-based critics in partially observable environments. We derive theories contrary to the common intuition: critic centralization is not strictly beneficial, and using state values can be harmful. We further prove that, in particular, state-based critics can introduce unexpected bias and variance compared to history-based critics. Finally, we demonstrate how the theory applies in practice by comparing different forms of critics on a wide range of common multi-agent benchmarks. The experiments show practical issues such as the difficulty of representation learning with partial observability, which highlights why the theoretical problems are often overlooked in the literature. 

Offline training in simulated partially observable environments allows reinforcement learning methods to exploit privileged state information through a mechanism known as asymmetry. Such privileged information has the potential to greatly improve the optimal convergence properties, if used appropriately. However, current research in asymmetric reinforcement learning is often heuristic in nature, with few connections to underlying theory or theoretical guarantees, and is primarily tested through empirical evaluation. In this work, we develop the theory of \emph{asymmetric policy iteration}, an exact model-based dynamic programming solution method, and then apply relaxations which eventually result in \emph{asymmetric DQN}, a model-free deep reinforcement learning algorithm. Our theoretical findings are complemented and validated by empirical experimentation performed in environments which exhibit significant amounts of partial observability, and require both information gathering strategies and memorization. 

Modern deep reinforcement learning methods have departed from the incremental learning required for eligibility traces, rendering the implementation of the λ-return difficult in this context. In particular, off-policy methods that utilize experience replay remain problematic because their random sampling of minibatches is not conducive to the efficient calculation of λ-returns. Yet replay-based methods are often the most sample efficient, and incorporating λ-returns into them is a viable way to achieve new state-of-the-art performance. Towards this, we propose the first method to enable practical use of λ-returns in arbitrary replay-based methods without relying on other forms of decorrelation such as asynchronous gradient updates. By promoting short sequences of past transitions into a small cache within the replay memory, adjacent λ-returns can be efficiently precomputed by sharing Q-values. Computation is not wasted on experiences that are never sampled, and stored λ-returns behave as stable temporal-difference (TD) targets that replace the target network. Additionally, our method grants the unique ability to observe TD errors prior to sampling; for the first time, transitions can be prioritized by their true significance rather than by a proxy to it. Furthermore, we propose the novel use of the TD error to dynamically select λ-values that facilitate faster learning. We show that these innovations can enhance the performance of DQN when playing Atari 2600 games, even under partial observability. While our work specifically focuses on λ-returns, these ideas are applicable to any multi-step return estimator.