我们介绍了基于目标观点的线性和二次近似值的非线性控制算法的实现。我们提出了一种梯度下降，一种高斯 - 纽顿方法，一种牛顿方法，具有线性二次或二次近似值的差分动态编程方法，各种线路搜索策略以及这些算法的正则变体。我们在可区分的编程框架中得出所有算法的计算复杂性，并提出足够的最佳条件。我们比较了几个基准的算法，例如使用汽车的自行车模型进行自动驾驶。该算法用公开可用的软件包中的可区分编程语言进行编码。

我们研究在线交互式强盗设置中的非模块化功能。我们是受到某些元素之间自然互补性的应用程序的动机：这仅使用只能代表元素之间竞争力的下函数来表达这一点。我们通过两种方式扩展了纯粹的下二次方法。首先，我们假设该物镜可以分解为单调下模量和超模块函数的总和，称为BP物镜。在这里，互补性自然是由超模型成分建模的。我们开发了UCB风格的算法，在每一轮比赛中，在采取行动以平衡对未知目标（探索）和选择似乎有希望的行动（剥削）的行动之间揭示的嘈杂收益。根据全知识的贪婪基线来定义遗憾和超模块化曲率，我们表明该算法最多可以在$ o（\ sqrt {t}）$ hore $ t $ t $ t $ the $ t $ t $ the $ t $ t $ the $ the。其次，对于那些不承认BP结构的功能，我们提供了类似的遗憾保证，从其表现比率角度来看。这适用于几乎但不完全是子模型的功能。我们在数值上研究了Movielens数据集上电影推荐的任务，并选择用于分类的培训子集。通过这些示例，我们证明了该算法的性能以及将这些问题视为单次生管的缺点。

学习问题通常表现出一个有趣的反馈机制，其中人口数据对竞争决策者的行为作出反应。本文为这种现象制定了一种新的游戏理论框架，称为多人执行预测。我们专注于两个不同的解决方案概念，即（i）表现稳定稳定的均衡和（ii）纳什均衡的比赛。后者均衡可以说是更具信息性的，但只有在游戏是单调时才有效地发现。我们表明，在温和的假设下，可以通过各种算法有效地发现所需稳定的均衡，包括重复再培训和重复（随机）梯度播放。然后，我们为游戏的强大单调性建立透明的充分条件，并使用它们开发用于查找纳什均衡的算法。我们研究了衍生免费方法和自适应梯度算法，其中每个玩家在学习其分发和梯度步骤的学习的分配和梯度步骤之间交替。合成和半合成数值实验说明了结果。

连续DR-unmodular函数是一类通常的非凸/非凹形功能，满足递减的回报（DR）属性，这意味着它们沿着非负方向凹入。现有的工作已经研究了单调连续的DR-unmodular最大化，经过凸起约束，提供了有效的算法，具有近似保证。在许多应用中，例如计算图的稳定性数，单调DR-unmodular物镜函数具有沿非负方向强烈凹入的额外性质（即，强烈的DR-SUBSOCULAL）。在本文中，我们考虑了一个US $-$-Smotone DR-unmodular函数的子类，它强烈博弈潜水函数并具有有界曲率，我们展示了如何利用这种额外的结构来获得更快的算法，以获得更高的保证对最大化的保证更快问题。我们提出了一种新的算法，该算法仅在仅$ \ lceil \ frac {l} {\ mu} \ rceil $迭代之后匹配可怕的最佳$ 1- \ frac {c} {e} $近似比。[0， 1] $和$ \ mu \ geq 0 $是曲率和强大的DR-subsodularity参数。此外，我们研究了这个问题的投影梯度上升（PGA）方法，并通过改进的$ \ FRAC {1} {1 + C} $近似比（与$ \ FRAC {1}相比提供了对算法的精细分析{2} $在现有作品中）和线性收敛速度。实验结果说明了我们所提出的算法的效率和有效性。

这项工作考虑了最佳手臂识别的选择性采样问题。给定一组潜在选项$ \ mathcal {z} \ subset \ mathbb {r} ^ d $，学习者旨在计算概率大于1- \ delta $，$ \ arg \ max_ {z \ mathcal { z}} z ^ {\ top} \ theta _ {\ ast} $ where $ \ theta _ {\ art} $未知。在每个时间步骤中，潜在的测量$ x_t \ in \ mathcal {x} \ subset \ mathbb {r} ^ d $被绘制的iid，学习者可以选择采取测量，在这种情况下，他们观察到嘈杂的测量$ x ^ {\ top} \ theta _ {\ ast} $，或弃权采取测量并等待可能更多的信息点到达流。因此，学习者在他们采取的标签样本数量之间面临的基本折衷，并且当他们收集足够的证据来宣布最好的手臂并停止抽样时。这项工作的主要结果精确地表征了标记的样本和停止时间之间的这种权衡，并提供了一种算法，几乎最佳地实现了给出所需停止时间的最小标签复杂性。此外，我们表明最佳决策规则具有基于决定点是否处于椭圆形的简单几何形式。最后，我们的框架足以捕获先前作品的二进制分类。

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NP-hard, because it contains vector cardinality minimization as a special case.In this paper, we show that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds with overwhelming probability, provided the codimension of the subspace is Ω(r(m + n) log mn), where m, n are the dimensions of the matrix, and r is its rank.The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this pre-existing concept and outline a dictionary relating concepts from cardinality minimization to those of rank minimization. We also discuss several algorithmic approaches to solving the norm minimization relaxations, and illustrate our results with numerical examples.

Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in an environment with obstacles is challenging and cannot be guaranteed in a finite time. We propose an algorithm in which the accuracy of the path planning is iteratively increased. The approach provides a certificate when the uncertainties on estimates of the shortest paths become small enough to guarantee the optimality of the goal assignment. To this end, we apply results from assignment sensitivity assuming upper and lower bounds on the length of the shortest paths. We then provide polynomial-time methods to find such bounds by applying sampling-based path planning. The upper bounds are given by feasible paths, the lower bounds are obtained by expanding the sample set and leveraging knowledge of the sample dispersion. We demonstrate the application of the proposed method with a multi-robot path-planning case study.

Large language models show improved downstream task performance when prompted to generate step-by-step reasoning to justify their final answers. These reasoning steps greatly improve model interpretability and verification, but objectively studying their correctness (independent of the final answer) is difficult without reliable methods for automatic evaluation. We simply do not know how often the stated reasoning steps actually support the final end task predictions. In this work, we present ROSCOE, a suite of interpretable, unsupervised automatic scores that improve and extend previous text generation evaluation metrics. To evaluate ROSCOE against baseline metrics, we design a typology of reasoning errors and collect synthetic and human evaluation scores on commonly used reasoning datasets. In contrast with existing metrics, ROSCOE can measure semantic consistency, logicality, informativeness, fluency, and factuality - among other traits - by leveraging properties of step-by-step rationales. We empirically verify the strength of our metrics on five human annotated and six programmatically perturbed diagnostics datasets - covering a diverse set of tasks that require reasoning skills and show that ROSCOE can consistently outperform baseline metrics.

Machine Learning (ML) technologies have been increasingly adopted in Medical Cyber-Physical Systems (MCPS) to enable smart healthcare. Assuring the safety and effectiveness of learning-enabled MCPS is challenging, as such systems must account for diverse patient profiles and physiological dynamics and handle operational uncertainties. In this paper, we develop a safety assurance case for ML controllers in learning-enabled MCPS, with an emphasis on establishing confidence in the ML-based predictions. We present the safety assurance case in detail for Artificial Pancreas Systems (APS) as a representative application of learning-enabled MCPS, and provide a detailed analysis by implementing a deep neural network for the prediction in APS. We check the sufficiency of the ML data and analyze the correctness of the ML-based prediction using formal verification. Finally, we outline open research problems based on our experience in this paper.

Fairness-aware mining of massive data streams is a growing and challenging concern in the contemporary domain of machine learning. Many stream learning algorithms are used to replace humans at critical decision-making points e.g., hiring staff, assessing credit risk, etc. This calls for handling massive incoming information with minimum response delay while ensuring fair and high quality decisions. Recent discrimination-aware learning methods are optimized based on overall accuracy. However, the overall accuracy is biased in favor of the majority class; therefore, state-of-the-art methods mainly diminish discrimination by partially or completely ignoring the minority class. In this context, we propose a novel adaptation of Na\"ive Bayes to mitigate discrimination embedded in the streams while maintaining high predictive performance for both the majority and minority classes. Our proposed algorithm is simple, fast, and attains multi-objective optimization goals. To handle class imbalance and concept drifts, a dynamic instance weighting module is proposed, which gives more importance to recent instances and less importance to obsolete instances based on their membership in minority or majority class. We conducted experiments on a range of streaming and static datasets and deduced that our proposed methodology outperforms existing state-of-the-art fairness-aware methods in terms of both discrimination score and balanced accuracy.