In many real-world scenarios, a team of agents coordinate with each other to compete against an opponent. The challenge of solving this type of game is that the team's joint action space grows exponentially with the number of agents, which results in the inefficiency of the existing algorithms, e.g., Counterfactual Regret Minimization (CFR). To address this problem, we propose a new framework of CFR: CFR-MIX. Firstly, we propose a new strategy representation that represents a joint action strategy using individual strategies of all agents and a consistency relationship to maintain the cooperation between agents. To compute the equilibrium with individual strategies under the CFR framework, we transform the consistency relationship between strategies to the consistency relationship between the cumulative regret values. Furthermore, we propose a novel decomposition method over cumulative regret values to guarantee the consistency relationship between the cumulative regret values. Finally, we introduce our new algorithm CFR-MIX which employs a mixing layer to estimate cumulative regret values of joint actions as a non-linear combination of cumulative regret values of individual actions. Experimental results show that CFR-MIX outperforms existing algorithms on various games significantly.

With the rise of online e-commerce platforms, more and more customers prefer to shop online. To sell more products, online platforms introduce various modules to recommend items with different properties such as huge discounts. A web page often consists of different independent modules. The ranking policies of these modules are decided by different teams and optimized individually without cooperation, which might result in competition between modules. Thus, the global policy of the whole page could be sub-optimal. In this paper, we propose a novel multi-agent cooperative reinforcement learning approach with the restriction that different modules cannot communicate. Our contributions are three-fold. Firstly, inspired by a solution concept in game theory named correlated equilibrium, we design a signal network to promote cooperation of all modules by generating signals (vectors) for different modules. Secondly, an entropy-regularized version of the signal network is proposed to coordinate agents' exploration of the optimal global policy. Furthermore, experiments based on real-world e-commerce data demonstrate that our algorithm obtains superior performance over baselines.

Pirate syndicates capturing tankers to siphon oil, causing an estimated cost of $5 billion a year, has become a serious security issue for maritime traffic. In response to the threat, coast guards and navies deploy patrol boats to protect international oil trade. However, given the vast area of the sea and the highly time and space dependent behaviors of both players, it remains a significant challenge to find efficient ways to deploy patrol resources. In this paper, we address the research challenges and provide four key contributions. First, we construct a Stackelberg model of the oil-siphoning problem based on incident reports of actual attacks; Second, we propose a compact formulation and a constraint generation algorithm, which tackle the exponentially growth of the defender’s and attacker’s strategy spaces, respectively, to compute efficient strategies of security agencies; Third, to further improve the scalability, we propose an abstraction method, which exploits the intrinsic similarity of defender’s strategy space, to solve extremely large-scale games; Finally, we evaluate our approaches through extensive simulations and a detailed case study with real ship traffic data. The results demonstrate that our approach achieves a dramatic improvement of scalability with modest influence on the solution quality and can scale up to realistic-sized problems.