Policy learning under action constraints plays a central role in ensuring safe behaviors in various robot control and resource allocation applications. In this paper, we study a new problem setting termed Action-Constrained Imitation Learning (ACIL), where an action-constrained imitator aims to learn from a demonstrative expert with larger action space. The fundamental challenge of ACIL lies in the unavoidable mismatch of occupancy measure between the expert and the imitator caused by the action constraints. We tackle this mismatch through trajectory alignment and propose DTWIL, which replaces the original expert demonstrations with a surrogate dataset that follows similar state trajectories while adhering to the action constraints. Specifically, we recast trajectory alignment as a planning problem and solve it via Model Predictive Control, which aligns the surrogate trajectories with the expert trajectories based on the Dynamic Time Warping (DTW) distance. Through extensive experiments, we demonstrate that learning from the dataset generated by DTWIL significantly enhances performance across multiple robot control tasks and outperforms various benchmark imitation learning algorithms in terms of sample efficiency.

Network embedding that maps nodes in a graph to vectors in a Euclidean space is a very powerful method to address various tasks on a graph. However, most network embedding algorithms, in particular, graph neural networks (GNNs), are difficult to interpret and do not scale well to handle millions of nodes. In this article, we tackle the problem from a new perspective based on the equivalence of three constrained optimization problems: the network embedding problem, the trace maximization problem of the modularity matrix in a sampled graph, and the matrix factorization problem of the modularity matrix in a sampled graph. The optimal solutions to these three problems are the dominant eigenvectors of the modularity matrix. We propose two unsupervised learning algorithms that belong to a special class of graph convolutional networks (GCNs) for solving these problems: 1) Clustering As Feature Embedding (CAFE) and 2) Sphere. Both algorithms are stable trace maximization algorithms and yield good approximations of dominant eigenvectors. Moreover, there are linear-time implementations for sparse graphs. Various experiments are conducted to evaluate our algorithms and show that our proposed algorithms outperform several baseline methods.