预测道路用户的未来行为是自主驾驶中最具挑战性和最重要的问题之一。应用深度学习对此问题需要以丰富的感知信号和地图信息的形式融合异构世界状态，并在可能的期货上推断出高度多模态分布。在本文中，我们呈现MultiPath ++，这是一个未来的预测模型，实现了在流行的基准上实现最先进的性能。 MultiPath ++通过重新访问许多设计选择来改善多径架构。第一关键设计差异是偏离基于图像的基于输入世界状态的偏离，有利于异构场景元素的稀疏编码：多径++消耗紧凑且有效的折线，直接描述道路特征和原始代理状态信息（例如，位置，速度，加速）。我们提出了一种背景感知这些元素的融合，并开发可重用的多上下文选通融合组件。其次，我们重新考虑了预定义，静态锚点的选择，并开发了一种学习模型端到端的潜在锚嵌入的方法。最后，我们在其他ML域中探索合奏和输出聚合技术 - 常见的常见域 - 并为我们的概率多模式输出表示找到有效的变体。我们对这些设计选择进行了广泛的消融，并表明我们所提出的模型在协会运动预测竞争和Waymo开放数据集运动预测挑战上实现了最先进的性能。

This work builds on the models and concepts presented in part 1 to learn approximate dictionary representations of Koopman operators from data. Part I of this paper presented a methodology for arguing the subspace invariance of a Koopman dictionary. This methodology was demonstrated on the state-inclusive logistic lifting (SILL) basis. This is an affine basis augmented with conjunctive logistic functions. The SILL dictionary's nonlinear functions are homogeneous, a norm in data-driven dictionary learning of Koopman operators. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm. We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves the same accuracy and dimensional scaling as deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.

Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary. In a widely used algorithm, Extended Dynamic Mode Decomposition, the dictionary functions are drawn from a fixed class of functions. Recently, deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Our results provide a hypothesis to explain the success of deep neural networks in learning numerical approximations to Koopman operators. Part 2 of this paper will extend this explanation by demonstrating the subspace invariant of heterogeneous dictionaries and presenting a head-to-head numerical comparison of deepDMD and low-parameter heterogeneous dictionary learning.

We study the task of training regression models with the guarantee of label differential privacy (DP). Based on a global prior distribution on label values, which could be obtained privately, we derive a label DP randomization mechanism that is optimal under a given regression loss function. We prove that the optimal mechanism takes the form of a ``randomized response on bins'', and propose an efficient algorithm for finding the optimal bin values. We carry out a thorough experimental evaluation on several datasets demonstrating the efficacy of our algorithm.

Cloud computing holds the promise of reduced costs through economies of scale. To realize this promise, cloud computing vendors typically solve sequential resource allocation problems, where customer workloads are packed on shared hardware. Virtual machines (VM) form the foundation of modern cloud computing as they help logically abstract user compute from shared physical infrastructure. Traditionally, VM packing problems are solved by predicting demand, followed by a Model Predictive Control (MPC) optimization over a future horizon. We introduce an approximate formulation of an industrial VM packing problem as an MILP with soft-constraints parameterized by the predictions. Recently, predict-and-optimize (PnO) was proposed for end-to-end training of prediction models by back-propagating the cost of decisions through the optimization problem. But, PnO is unable to scale to the large prediction horizons prevalent in cloud computing. To tackle this issue, we propose the Predict-and-Critic (PnC) framework that outperforms PnO with just a two-step horizon by leveraging reinforcement learning. PnC jointly trains a prediction model and a terminal Q function that approximates cost-to-go over a long horizon, by back-propagating the cost of decisions through the optimization problem \emph{and from the future}. The terminal Q function allows us to solve a much smaller two-step horizon optimization problem than the multi-step horizon necessary in PnO. We evaluate PnO and the PnC framework on two datasets, three workloads, and with disturbances not modeled in the optimization problem. We find that PnC significantly improves decision quality over PnO, even when the optimization problem is not a perfect representation of reality. We also find that hardening the soft constraints of the MILP and back-propagating through the constraints improves decision quality for both PnO and PnC.

We consider the problem of multi-agent navigation and collision avoidance when observations are limited to the local neighborhood of each agent. We propose InforMARL, a novel architecture for multi-agent reinforcement learning (MARL) which uses local information intelligently to compute paths for all the agents in a decentralized manner. Specifically, InforMARL aggregates information about the local neighborhood of agents for both the actor and the critic using a graph neural network and can be used in conjunction with any standard MARL algorithm. We show that (1) in training, InforMARL has better sample efficiency and performance than baseline approaches, despite using less information, and (2) in testing, it scales well to environments with arbitrary numbers of agents and obstacles.

Rates of missing data often depend on record-keeping policies and thus may change across times and locations, even when the underlying features are comparatively stable. In this paper, we introduce the problem of Domain Adaptation under Missingness Shift (DAMS). Here, (labeled) source data and (unlabeled) target data would be exchangeable but for different missing data mechanisms. We show that when missing data indicators are available, DAMS can reduce to covariate shift. Focusing on the setting where missing data indicators are absent, we establish the following theoretical results for underreporting completely at random: (i) covariate shift is violated (adaptation is required); (ii) the optimal source predictor can perform worse on the target domain than a constant one; (iii) the optimal target predictor can be identified, even when the missingness rates themselves are not; and (iv) for linear models, a simple analytic adjustment yields consistent estimates of the optimal target parameters. In experiments on synthetic and semi-synthetic data, we demonstrate the promise of our methods when assumptions hold. Finally, we discuss a rich family of future extensions.

数据驱动的湍流建模正在经历数据科学算法和硬件开发后的兴趣激增。我们讨论了一种使用可区分物理范式的方法，该方法将已知的物理学与机器学习结合起来，以开发汉堡湍流的闭合模型。我们将1D汉堡系统视为一种原型测试问题，用于建模以对流为主的湍流问题中未解决的术语。我们训练一系列模型，这些模型在后验损失函数上结合了不同程度的物理假设，以测试模型在一系列系统参数（包括粘度，时间和网格分辨率）上的疗效。我们发现，以部分微分方程形式的归纳偏差的约束模型包含已知物理或现有闭合方法会产生高度数据效率，准确和可推广的模型，并且表现优于最先进的基准。以物理信息形式添加结构还为模型带来了一定程度的解释性，可能为封闭建模的未来提供了垫脚石。

机器学习（ML）是指根据大量数据预测有意义的输出或对复杂系统进行分类的计算机算法。 ML应用于各个领域，包括自然科学，工程，太空探索甚至游戏开发。本文的重点是在化学和生物海洋学领域使用机器学习。在预测全球固定氮水平，部分二氧化碳压力和其他化学特性时，ML的应用是一种有前途的工具。机器学习还用于生物海洋学领域，可从各种图像（即显微镜，流车和视频记录器），光谱仪和其他信号处理技术中检测浮游形式。此外，ML使用其声学成功地对哺乳动物进行了分类，在特定的环境中检测到濒临灭绝的哺乳动物和鱼类。最重要的是，使用环境数据，ML被证明是预测缺氧条件和有害藻华事件的有效方法，这是对环境监测的重要测量。此外，机器学习被用来为各种物种构建许多对其他研究人员有用的数据库，而创建新算法将帮助海洋研究界更好地理解海洋的化学和生物学。

本文提出了秤，这是一个一般框架，将公平原则转化为基于约束马尔可夫决策过程（CMDP）的共同表示。借助因果语言，我们的框架可以在决策过程（程序公平）以及决策（结果公平）产生的结果上构成限制。具体而言，我们表明可以将众所周知的公平原理编码为实用程序组件，非毒性组件或鳞片中心中的因果分量。我们使用涉及模拟医疗方案和现实世界中Compas数据集的一组案例研究来说明量表。实验表明，我们的框架产生了公平的政策，这些政策在单步和顺序决策方案中体现了替代公平原则。