Stochastic approximation is a powerful class of algorithms with celebrated success. However, a large body of previous analysis focuses on stochastic approximations driven by contractive operators, which is not applicable in some important reinforcement learning settings like the average reward setting. This work instead investigates stochastic approximations with merely nonexpansive operators. In particular, we study nonexpansive stochastic approximations with Markovian noise, providing both asymptotic and finite sample analysis. Key to our analysis are novel bounds of noise terms resulting from the Poisson equation. As an application, we prove for the first time that classical tabular average reward temporal difference learning converges to a sample-path dependent fixed point.

Traditionally, reinforcement learning (RL) agents learn to solve new tasks by updating their neural network parameters through interactions with the task environment. However, recent works demonstrate that some RL agents, after certain pretraining procedures, can learn to solve unseen new tasks without parameter updates, a phenomenon known as in-context reinforcement learning (ICRL). The empirical success of ICRL is widely attributed to the hypothesis that the forward pass of the pretrained agent neural network implements an RL algorithm. In this paper, we support this hypothesis by showing, both empirically and theoretically, that when a transformer is trained for policy evaluation tasks, it can discover and learn to implement temporal difference learning in its forward pass.

The demand for collaborative and private bandit learning across multiple agents is surging due to the growing quantity of data generated from distributed systems. Federated bandit learning has emerged as a promising framework for private, efficient, and decentralized online learning. However, almost all previous works rely on strong assumptions of client homogeneity, i.e., all participating clients shall share the same bandit model; otherwise, they all would suffer linear regret. This greatly restricts the application of federated bandit learning in practice. In this work, we introduce a new approach for federated bandits for heterogeneous clients, which clusters clients for collaborative bandit learning under the federated learning setting. Our proposed algorithm achieves non-trivial sub-linear regret and communication cost for all clients, subject to the communication protocol under federated learning that at anytime only one model can be shared by the server.

Graph Convolutional Networks (GCNs) have fueled a surge of research interest due to their encouraging performance on graph learning tasks, but they are also shown vulnerability to adversarial attacks. In this paper, an effective graph structural attack is investigated to disrupt graph spectral filters in the Fourier domain, which are the theoretical foundation of GCNs. We define the notion of spectral distance based on the eigenvalues of graph Laplacian to measure the disruption of spectral filters. We realize the attack by maximizing the spectral distance and propose an efficient approximation to reduce the time complexity brought by eigen-decomposition. The experiments demonstrate the remarkable effectiveness of the proposed attack in both black-box and white-box settings for both test-time evasion attacks and training-time poisoning attacks. Our qualitative analysis suggests the connection between the imposed spectral changes in the Fourier domain and the attack behavior in the spatial domain, which provides empirical evidence that maximizing spectral distance is an effective way to change the graph structural property and thus disturb the frequency components for graph filters to affect the learning of GCNs.

This paper studies a remarkable property of graphs which is the latent hierarchical grouping of nodes, where each node manifests its membership to a specific group based on the context composed by its neighboring nodes. When modeling the neighborhood structure for graph representation learning, most prior works ignore such latent groups and nodes' membership to different groups, not to mention the hierarchy. Thus, they fall short of delivering a comprehensive understanding of the nodes under different contexts in a graph. In this paper, we propose a novel hierarchical attentive membership model for graph embedding, where the latent memberships for each node are dynamically discovered based on its neighboring context. Both group-level and individual-level attentions are performed when aggregating neighboring states to generate node embeddings. We introduce structural constraints to explicitly regularize the inferred memberships of each node, such that a well-defined hierarchical grouping structure is captured. The proposed model outperformed a set of state-of-the-art graph embedding solutions on node classification and link prediction tasks in a variety of graphs including citation networks and social networks. Qualitative evaluations visualize the learned node embeddings along with the inferred memberships, which proved the concept of membership hierarchy and enables explainable embedding learning in graphs.