We consider a general and realistic scenario involving non-stationary time series, consisting of several offline intervals with different distributions within a fixed offline time horizon, and an online interval that continuously receives new samples. For non-stationary time series, the data distribution in the current online interval may have appeared in previous offline intervals. We theoretically explore the feasibility of applying knowledge from offline intervals to the current online interval. To this end, we propose the Mixture of Online and Offline Experts (MOOE). MOOE learns static offline experts from offline intervals and maintains a dynamic online expert for the current online interval. It then adaptively combines the offline and online experts using a meta expert to make predictions for the samples received in the online interval. Specifically, we focus on theoretical analysis, deriving parameter convergence, regret bounds, and generalization error bounds to prove the effectiveness of the algorithm.

Efficient and collision-free navigation in multi-robot systems is fundamental to advancing mobility. Scenarios where the robots are restricted in observation and communication range call for decentralized solutions, whereby robots execute localized planning policies. From the point of view of an individual robot, however, its local decision-making system is incomplete, since other agents' unobservable states affect future values. The manner in which information is shared is crucial to the system's performance, yet is not well addressed by current approaches. To address these challenges, we propose a combined architecture, with the goal of learning a decentralized sequential action policy that yields efficient path plans for all robots. Our framework is composed of a convolutional neural network (CNN) that extracts adequate features from local observations, and a graph neural network (GNN) that communicates these features among robots. We train the model to imitate an expert algorithm, and use the resulting model online in decentralized planning involving only local communication. We evaluate our method in simulations involving teams of robots in cluttered workspaces. We measure the success rates and sum of costs over the planned paths. The results show a performance close to that of our expert algorithm, demonstrating the validity of our approach. In particular, we show our model's capability to generalize to previously unseen cases (involving larger environments and larger robot teams).