We propose a family of First Hitting Diffusion Models (FHDM), deep generative models that generate data with a diffusion process that terminates at a random first hitting time. This yields an extension of the standard fixed-time diffusion models that terminate at a pre-specified deterministic time. Although standard diffusion models are designed for continuous unconstrained data, FHDM is naturally designed to learn distributions on continuous as well as a range of discrete and structure domains. Moreover, FHDM enables instance-dependent terminate time and accelerates the diffusion process to sample higher quality data with fewer diffusion steps. Technically, we train FHDM by maximum likelihood estimation on diffusion trajectories augmented from observed data with conditional first hitting processes (i.e., bridge) derived based on Doob's $h$-transform, deviating from the commonly used time-reversal mechanism. We apply FHDM to generate data in various domains such as point cloud (general continuous distribution), climate and geographical events on earth (continuous distribution on the sphere), unweighted graphs (distribution of binary matrices), and segmentation maps of 2D images (high-dimensional categorical distribution). We observe considerable improvement compared with the state-of-the-art approaches in both quality and speed.

Achieving consensus among noncooperative agents remains challenging in decentralized multi-agent systems, where agents often have conflicting preferences. Existing coordination methods enable agents to reach consensus without a centralized coordinator, but do not provide formal guarantees on system-level objectives such as efficiency or fairness. To address this limitation, we propose an iterative negotiation and oversight framework that augments a decentralized negotiation mechanism with taxation-like oversight. The framework builds upon the trading auction for consensus, enabling noncooperative agents with conflicting preferences to negotiate through asset trading while preserving valuation privacy. We introduce an oversight mechanism, which implements a taxation-like intervention that guides decentralized negotiation toward system-efficient and equitable outcomes while also regulating how fast the framework converges. We establish theoretical guarantees of finite-time termination and derive bounds linking system efficiency and convergence rate to the level of central intervention. A case study based on the collaborative trajectory options program, a rerouting initiative in U.S. air traffic management, demonstrates that the framework can reliably achieve consensus among noncooperative airspace sector managers, and reveals how the level of intervention regulates the relationship between system efficiency and convergence speed. Taken together, the theoretical and experimental results indicate that the proposed framework provides a general mechanism for decentralized coordination in noncooperative multi-agent systems while safeguarding system-level objectives.

Multi-armed bandit is a useful tool to model the process of incrementally collecting data for multiple objects in a decision space.

Many abstract problems fit into this general framework, including sequential hypothesis testing, e.g.,

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In machine learning, many fundamental quantities we care to optimize such as entropy, graph cuts, diversity, coverage, diffusion, and clustering are submodular functions.

The problem instance size may be large.

Building systems that autonomously create temporal abstractions from data is a key challenge in scaling learning and planning in reinforcement learning.