Reinforcement Learning for Finite Space Mean-Field Type Games

Mean field type games (MFTGs) describe Nash equilibria between large coalitions: each coalition consists of a continuum of cooperative agents who maximize the average reward of their coalition while interacting non-cooperatively with a finite number of other coalitions. Although the theory has been extensively developed, we are still lacking efficient and scalable computational methods. Here, we develop reinforcement learning methods for such games in a finite space setting with general dynamics and reward functions. We start by proving that MFTG solution yields approximate Nash equilibria in finite-size coalition games. We then propose two algorithms. The first is based on quantization of the mean-field spaces and Nash Q-learning. We provide convergence and stability analysis. We then propose an deep reinforcement learning algorithm, which can scale to larger spaces. Numerical examples on 5 environments show the scalability and the efficiency of the proposed method.

CM-DQN: A Value-Based Deep Reinforcement Learning Model to Simulate Confirmation Bias

In human decision-making tasks, individuals learn through trials and prediction errors. When individuals learn the task, some are more influenced by good outcomes, while others weigh bad outcomes more heavily. Such confirmation bias can lead to different learning effects. In this study, we propose a new algorithm in Deep Reinforcement Learning, CM-DQN, which applies the idea of different update strategies for positive or negative prediction errors, to simulate the human decision-making process when the task's states are continuous while the actions are discrete. We test in Lunar Lander environment with confirmatory, disconfirmatory bias and non-biased to observe the learning effects. Moreover, we apply the confirmation model in a multi-armed bandit problem (environment in discrete states and discrete actions), which utilizes the same idea as our proposed algorithm, as a contrast experiment to algorithmically simulate the impact of different confirmation bias in decision-making process. In both experiments, confirmatory bias indicates a better learning effect. Our code can be found here https://github.com/Patrickhshs/CM-DQN.