Reinforcement Learning With Reward Machines in Stochastic Games

We investigate multi-agent reinforcement learning for stochastic games with complex tasks, where the reward functions are non-Markovian. We utilize reward machines to incorporate high-level knowledge of complex tasks. We develop an algorithm called Q-learning with reward machines for stochastic games (QRM-SG), to learn the best-response strategy at Nash equilibrium for each agent. In QRM-SG, we define the Q-function at a Nash equilibrium in augmented state space. The augmented state space integrates the state of the stochastic game and the state of reward machines. Each agent learns the Q-functions of all agents in the system. We prove that Q-functions learned in QRM-SG converge to the Q-functions at a Nash equilibrium if the stage game at each time step during learning has a global optimum point or a saddle point, and the agents update Q-functions based on the best-response strategy at this point. We use the Lemke-Howson method to derive the best-response strategy given current Q-functions. The three case studies show that QRM-SG can learn the best-response strategies effectively. QRM-SG learns the best-response strategies after around 7500 episodes in Case Study I, 1000 episodes in Case Study II, and 1500 episodes in Case Study III, while baseline methods such as Nash Q-learning and MADDPG fail to converge to the Nash equilibrium in all three case studies.

Learning Sparse and Continuous Graph Structures for Multivariate Time Series Forecasting

Accurate forecasting of multivariate time series is an extensively studied subject in finance, transportation, and computer science. Fully mining the correlation and causation between the variables in a multivariate time series exhibits noticeable results in improving the performance of a time series model. Recently, some models have explored the dependencies between variables through end-to-end graph structure learning without the need for pre-defined graphs. However, most current models do not incorporate the trade-off between effectiveness and flexibility and lack the guidance of domain knowledge in the design of graph learning algorithms. Besides, they have issues generating sparse graph structures, which pose challenges to end-to-end learning. In this paper, we propose Learning Sparse and Continuous Graphs for Forecasting (LSCGF), a novel deep learning model that joins graph learning and forecasting. Technically, LSCGF leverages the spatial information into convolutional operation and extracts temporal dynamics using the diffusion convolution recurrent network. At the same time, we propose a brand new method named Smooth Sparse Unit (SSU) to learn sparse and continuous graph adjacency matrix. Extensive experiments on three real-world datasets demonstrate that our model achieves state-of-the-art performances with minor trainable parameters.