Many real-world problems, such as network packet routing and the coordination of autonomous vehicles, are naturally modelled as cooperative multi-agent systems. There is a great need for new reinforcement learning methods that can efficiently learn decentralised policies for such systems. To this end, we propose a new multi-agent actor-critic method called counterfactual multi-agent (COMA) policy gradients. COMA uses a centralised critic to estimate the Q-function and decentralised actors to optimise the agents' policies. In addition, to address the challenges of multi-agent credit assignment, it uses a counterfactual baseline that marginalises out a single agent's action, while keeping the other agents' actions fixed. COMA also uses a critic representation that allows the counterfactual baseline to be computed efficiently in a single forward pass. We evaluate COMA in the testbed of StarCraft unit micromanagement, using a decentralised variant with significant partial observability. COMA significantly improves average performance over other multi-agent actor-critic methods in this setting, and the best performing agents are competitive with state-of-the-art centralised controllers that get access to the full state.

Navigation requires a sense of direction ('compass'), which in mammals is thought to be provided by head-direction cells, neurons that discharge when the animal's head points to a specific azimuth. However, it remains unclear whether a three-dimensional (3D) compass exists in the brain. Here we conducted neural recordings in bats, mammals well-adapted to 3D spatial behaviours, and found head-direction cells tuned to azimuth, pitch or roll, or to conjunctive combinations of 3D angles, in both crawling and flying bats. Head-direction cells were organized along a functional-anatomical gradient in the presubiculum, transitioning from 2D to 3D representations. In inverted bats, the azimuth-tuning of neurons shifted by 180°, suggesting that 3D head direction is represented in azimuth × pitch toroidal coordinates. Consistent with our toroidal model, pitch-cell tuning was unimodal, circular, and continuous within the available 360° of pitch. Taken together, these results demonstrate a 3D head-direction mechanism in mammals, which could support navigation in 3D space.

In the last few years, deep multi-agent reinforcement learning (RL) has become a highly active area of research. A particularly challenging class of problems in this area is partially observable, cooperative, multi-agent learning, in which teams of agents must learn to coordinate their behaviour while conditioning only on their private observations. This is an attractive research area since such problems are relevant to a large number of real-world systems and are also more amenable to evaluation than general-sum problems. Standardised environments such as the ALE and MuJoCo have allowed singleagent RL to move beyond toy domains, such as grid worlds. However, there is no comparable benchmark for cooperative multi-agent RL. As a result, most papers in this field use one-off toy problems, making it difficult to measure real progress. In this paper, we propose the StarCraft Multi-Agent Challenge (SMAC) as a benchmark problem to fill this gap. 1 SMAC is based on the popular real-time strategy game StarCraft II and focuses on micromanagement challenges where each unit is controlled by an independent agent that must act based on local observations. We offer a diverse set of challenge scenarios and recommendations for best practices in benchmarking and evaluations. We also open-source a deep multi-agent RL learning framework including state-of-the-art algorithms. 2 We believe that SMAC can provide a standard benchmark environment for years to come. Videos of our best agents for several SMAC scenarios are available at: https://youtu.be/VZ7zmQ_obZ0.

In many real-world settings, a team of agents must coordinate their behaviour while acting in a decentralised way. At the same time, it is often possible to train the agents in a centralised fashion in a simulated or laboratory setting, where global state information is available and communication constraints are lifted. Learning joint actionvalues conditioned on extra state information is an attractive way to exploit centralised learning, but the best strategy for then extracting decentralised policies is unclear. Our solution is QMIX, a novel value-based method that can train decentralised policies in a centralised end-to-end fashion. QMIX employs a network that estimates joint action-values as a complex non-linear combination of per-agent values that condition only on local observations. We structurally enforce that the joint-action value is monotonic in the per-agent values, which allows tractable maximisation of the joint action-value in off-policy learning, and guarantees consistency between the centralised and decentralised policies. We evaluate QMIX on a challenging set of StarCraft II micromanagement tasks, and show that QMIX significantly outperforms existing value-based multi-agent reinforcement learning methods.