We introduce an original minimax framework for finite-time performance analysis in queueing control and propose a surprisingly simple Lyapunov-based scheduling policy with superior finite-time performance. The framework quantitatively characterizes how the expected total queue length scales with key system parameters, including the capacity of the scheduling set and the variability of arrivals and departures across queues. To our knowledge, this provides the first firm foundation for evaluating and comparing scheduling policies in the finite-time regime, including nonstationary settings, and shows that the proposed policy can provably and empirically outperform classical MaxWeight in finite time. Within this framework, we establish three main sets of results. First, we derive minimax lower bounds on the expected total queue length for parallel-queue scheduling via a novel Brownian coupling argument. Second, we propose a new policy, LyapOpt, which minimizes the full quadratic Lyapunov drift-capturing both first- and second-order terms-and achieves optimal finite-time performance in heavy traffic while retaining classical stability guarantees. Third, we identify a key limitation of the classical MaxWeight policy, which optimizes only the first-order drift: its finite-time performance depends suboptimally on system parameters, leading to substantially larger backlogs in explicitly characterized settings. Together, these results delineate the scope and limitations of classical drift-based scheduling and motivate new queueing-control methods with rigorous finite-time guarantees.

The strength of a word's relation to another word at a certain location is measured as the function value at that location. With FIRE, compositionality is represented via functional addi-tivity, whereas polysemy is represented via the set of points and the function's

In the era of rapid advancements in vehicle safety technologies, driving risk assessment has become a focal point of attention. Technologies such as collision warning systems, advanced driver assistance systems (ADAS), and autonomous driving require driving risks to be evaluated proactively and in real time. To be effective, driving risk assessment metrics must not only accurately identify potential collisions but also exhibit human-like reasoning to enable safe and seamless interactions between vehicles. Existing safety potential field models assess driving risks by considering both objective and subjective safety factors. However, their practical applicability in real-world risk assessment tasks is limited. These models are often challenging to calibrate due to the arbitrary nature of their structures, and calibration can be inefficient because of the scarcity of accident statistics. Additionally, they struggle to generalize across both longitudinal and lateral risks. To address these challenges, we propose a composite safety potential field framework, namely C-SPF, involving a subjective field to capture drivers' risk perception about spatial proximity and an objective field to quantify the imminent collision probability, to comprehensively evaluate driving risks. The C-SPF is calibrated using abundant two-dimensional spacing data from trajectory datasets, enabling it to effectively capture drivers' proximity risk perception and provide a more realistic explanation of driving behaviors. Analysis of a naturalistic driving dataset demonstrates that the C-SPF can capture both longitudinal and lateral risks that trigger drivers' safety maneuvers. Further case studies highlight the C-SPF's ability to explain lateral driver behaviors, such as abandoning lane changes or adjusting lateral position relative to adjacent vehicles, which are capabilities that existing models fail to achieve.

Riemannian convex optimization and minimax optimization have recently drawn considerable attention. Their appeal lies in their capacity to adeptly manage the non-convexity of the objective function as well as constraints inherent in the feasible set in the Euclidean sense. In this work, we delve into monotone Riemannian Variational Inequality Problems (RVIPs), which encompass both Riemannian convex optimization and minimax optimization as particular cases. In the context of Euclidean space, it is established that the last-iterates of both the extragradient (EG) and past extragradient (PEG) methods converge to the solution of monotone variational inequality problems at a rate of $O\left(\frac{1}{\sqrt{T}}\right)$ (Cai et al., 2022). However, analogous behavior on Riemannian manifolds remains an open question. To bridge this gap, we introduce the Riemannian extragradient (REG) and Riemannian past extragradient (RPEG) methods. We demonstrate that both exhibit $O\left(\frac{1}{\sqrt{T}}\right)$ last-iterate convergence. Additionally, we show that the average-iterate convergence of both REG and RPEG is $O\left(\frac{1}{{T}}\right)$, aligning with observations in the Euclidean case (Mokhtari et al., 2020). These results are enabled by judiciously addressing the holonomy effect so that additional complications in Riemannian cases can be reduced and the Euclidean proof inspired by the performance estimation problem (PEP) technique or the sum-of-squares (SOS) technique can be applied again.

Real-world problems are often not fully characterized by a single optimal solution, as they frequently involve multiple competing objectives; it is therefore important to identify the so-called Pareto frontier, which captures solution trade-offs. We propose a fully polynomial-time approximation scheme based on Dynamic Programming (DP) for computing a polynomially succinct curve that approximates the Pareto frontier to within an arbitrarily small epsilon > 0 on tree-structured networks. Given a set of objectives, our approximation scheme runs in time polynomial in the size of the instance and 1/epsilon. We also propose a Mixed Integer Programming (MIP) scheme to approximate the Pareto frontier. The DP and MIP Pareto frontier approaches have complementary strengths and are surprisingly effective. We provide empirical results showing that our methods outperform other approaches in efficiency and accuracy. Our work is motivated by a problem in computational sustainability concerning the proliferation of hydropower dams throughout the Amazon basin. Our goal is to support decision-makers in evaluating impacted ecosystem services on the full scale of the Amazon basin. Our work is general and can be applied to approximate the Pareto frontier of a variety of multiobjective problems on tree-structured networks.