ACE: Cooperative Multi-agent Q-learning with Bidirectional Action-Dependency

Multi-agent reinforcement learning (MARL) suffers from the non-stationarity problem, which is the ever-changing targets at every iteration when multiple agents update their policies at the same time. Starting from first principle, in this paper, we manage to solve the non-stationarity problem by proposing bidirectional action-dependent Q-learning (ACE). Central to the development of ACE is the sequential decision-making process wherein only one agent is allowed to take action at one time. Within this process, each agent maximizes its value function given the actions taken by the preceding agents at the inference stage. In the learning phase, each agent minimizes the TD error that is dependent on how the subsequent agents have reacted to their chosen action. Given the design of bidirectional dependency, ACE effectively turns a multiagent MDP into a single-agent MDP. We implement the ACE framework by identifying the proper network representation to formulate the action dependency, so that the sequential decision process is computed implicitly in one forward pass. To validate ACE, we compare it with strong baselines on two MARL benchmarks. Empirical experiments demonstrate that ACE outperforms the state-of-the-art algorithms on Google Research Football and StarCraft Multi-Agent Challenge by a large margin. In particular, on SMAC tasks, ACE achieves 100% success rate on almost all the hard and super-hard maps. We further study extensive research problems regarding ACE, including extension, generalization, and practicability. Code is made available to facilitate further research.

Mixture Model Averaging for Clustering

In mixture model-based clustering applications, it is common to fit several models from a family and report clustering results from only the `best' one. In such circumstances, selection of this best model is achieved using a model selection criterion, most often the Bayesian information criterion. Rather than throw away all but the best model, we average multiple models that are in some sense close to the best one, thereby producing a weighted average of clustering results. Two (weighted) averaging approaches are considered: averaging the component membership probabilities and averaging models. In both cases, Occam's window is used to determine closeness to the best model and weights are computed within a Bayesian model averaging paradigm. In some cases, we need to merge components before averaging; we introduce a method for merging mixture components based on the adjusted Rand index. The effectiveness of our model-based clustering averaging approaches is illustrated using a family of Gaussian mixture models on real and simulated data.