We investigate safe multi-agent reinforcement learning, where agents seek to collectively maximize an aggregate sum of local objectives while satisfying their own safety constraints. The objective and constraints are described by general utilities, i.e., nonlinear functions of the long-term state-action occupancy measure, which encompass broader decision-making goals such as risk, exploration, or imitations. The exponential growth of the state-action space size with the number of agents presents challenges for global observability, further exacerbated by the global coupling arising from agents' safety constraints. To tackle this issue, we propose a primal-dual method utilizing shadow reward and κ-hop neighbor truncation under a form of correlation decay property, where κ is the communication radius.

A.1 Multimodal Large Language Models Building on the foundational capabilities of groundbreaking Large Language Models (LLMs) such as GPT [3], PALM [6], Mistral [49], and LLama [108], which excel in language understanding and reasoning, recent innovations have integrated these models with other modalities (especially vision), leading to the development of Multimodal Large Language Models (MLLMs). These advanced MLLMs combine and process visual and textual data, demonstrating enhanced versatility in addressing both traditional vision tasks [21, 40, 42, 133] and complex multimodal challenges [34, 70, 136]. Among all MLLMs, proprietary models consistently perform well. OpenAI's GPT-4-Vision [82] pioneered this space by adeptly handling both text and image content. Anthropic's Claude 3 series [7] integrates advanced vision capabilities and multilingual support, enhancing its application across diverse cognitive and real-time tasks.

Interpreting time series models is uniquely challenging because it requires identifying both the location of time series signals that drive model predictions and their matching to an interpretable temporal pattern. While explainers from other modalities can be applied to time series, their inductive biases do not transfer well to the inherently challenging interpretation of time series.

Periodic graphs are graphs consisting of repetitive local structures, such as crystal nets and polygon mesh. Their generative modeling has great potential in real-world applications such as material design and graphics synthesis. Classical models either rely on domain-specific predefined generation principles (e.g., in crystal net design), or follow geometry-based prescribed rules. Recently, deep generative models have shown great promise in automatically generating general graphs. However, their advancement into periodic graphs has not been well explored due to several key challenges in 1) maintaining graph periodicity; 2) disentangling local and global patterns; and 3) efficiency in learning repetitive patterns. To address them, this paper proposes Periodical-Graph Disentangled Variational Auto-encoder (PGD-VAE), a new deep generative model for periodic graphs that can automatically learn, disentangle, and generate local and global graph patterns.