Inversionoflinearsystems As mentioned in Corollary(1), for the Lasso, when computing the gradient off, one can either invert an nlinear system or anm mlinear system.

Autonomous driving systems face the formidable challenge of navigating intricate and dynamic environments with uncertainty. This study presents a unified prediction and planning framework that concurrently models short-term aleatoric uncertainty (SAU), long-term aleatoric uncertainty (LAU), and epistemic uncertainty (EU) to predict and establish a robust foundation for planning in dynamic contexts. The framework uses Gaussian mixture models and deep ensemble methods, to concurrently capture and assess SAU, LAU, and EU, where traditional methods do not integrate these uncertainties simultaneously. Additionally, uncertainty-aware planning is introduced, considering various uncertainties. The study's contributions include comparisons of uncertainty estimations, risk modeling, and planning methods in comparison to existing approaches. The proposed methods were rigorously evaluated using the CommonRoad benchmark and settings with limited perception. These experiments illuminated the advantages and roles of different uncertainty factors in autonomous driving processes. In addition, comparative assessments of various uncertainty modeling strategies underscore the benefits of modeling multiple types of uncertainties, thus enhancing planning accuracy and reliability. The proposed framework facilitates the development of methods for UAP and surpasses existing uncertainty-aware risk models, particularly when considering diverse traffic scenarios. Project page: https://swb19.github.io/UAP/.

In this paper we present a model for decision making under complete ignorance. By complete ignorance it is meant that all that is known is the set of possible consequences associated to each action. Especially there is no set of states that can be enumerated in order to compare actions. We give two natural axioms for rational decision making under complete ignorance. We show that the optimality criteria satisfying these two axioms are the ones which consider only the extremal consequences of actions. We compare our axioms with related ones from the literature.