Advances in reinforcement learning have led to its successful application in complex tasks with continuous state and action spaces. Despite these advances in practice, most theoretical work pertains to finite state and action spaces. We propose building a theoretical understanding of continuous state and action spaces by employing a geometric lens. Central to our work is the idea that the transition dynamics induce a low dimensional manifold of reachable states embedded in the high-dimensional nominal state space. We prove that, under certain conditions, the dimensionality of this manifold is at most the dimensionality of the action space plus one. This is the first result of its kind, linking the geometry of the state space to the dimensionality of the action space. We empirically corroborate this upper bound for four MuJoCo environments. We further demonstrate the applicability of our result by learning a policy in this low dimensional representation. To do so we introduce an algorithm that learns a mapping to a low dimensional representation, as a narrow hidden layer of a deep neural network, in tandem with the policy using DDPG. Our experiments show that a policy learnt this way perform on par or better for four MuJoCo control suite tasks.

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances in the theoretical understanding of neural networks, we study how a randomly initialized neural network with piece-wise linear activation splits the data manifold into regions where the neural network behaves as a linear function. We derive bounds on the density of boundary of linear regions and the distance to these boundaries on the data manifold. This leads to insights into the expressivity of randomly initialized deep neural networks on non-Euclidean data sets. We empirically corroborate our theoretical results using a toy supervised learning problem. Our experiments demonstrate that number of linear regions varies across manifolds and the results hold with changing neural network architectures. We further demonstrate how the complexity of linear regions is different on the low dimensional manifold of images as compared to the Euclidean space, using the MetFaces dataset.

Dynamic movement primitives are widely used for learning skills which can be demonstrated to a robot by a skilled human or controller. While their generalization capabilities and simple formulation make them very appealing to use, they possess no strong guarantees to satisfy operational safety constraints for a task. In this paper, we present constrained dynamic movement primitives (CDMP) which can allow for constraint satisfaction in the robot workspace. We present a formulation of a non-linear optimization to perturb the DMP forcing weights regressed by locally-weighted regression to admit a Zeroing Barrier Function (ZBF), which certifies workspace constraint satisfaction. We demonstrate the proposed CDMP under different constraints on the end-effector movement such as obstacle avoidance and workspace constraints on a physical robot. A video showing the implementation of the proposed algorithm using different manipulators in different environments could be found here https://youtu.be/hJegJJkJfys.

将有用的背景知识传达给加强学习（RL）代理是加速学习的重要方法。我们介绍了Rlang，这是一种特定领域的语言（DSL），用于将域知识传达给RL代理。与RL社区提出的其他现有DSL不同，该基础是决策形式主义的单个要素（例如，奖励功能或政策功能），RLANG可以指定有关马尔可夫决策过程中每个元素的信息。我们为rlang定义了精确的语法和基础语义，并提供了解析器实施，将rlang程序基于算法 - 敏捷的部分世界模型和政策，可以由RL代理利用。我们提供一系列示例RLANG程序，并演示不同的RL方法如何利用所得的知识，包括无模型和基于模型的表格算法，分层方法和深度RL算法（包括策略梯度和基于价值的方法）。

将机器人部署在现实世界中的机器人（例如家庭和灵活的制造线路）中，要求机器人按需任务。线性时间逻辑（LTL）是一种广泛使用的规范语言，具有组成语法，自然会在任务中引起共同点。但是，大多数先前关于使用LTL规范的强化学习的研究都独立治疗了每个新公式。我们提出了LTL-Transfer，这是一种新颖的算法，通过将培训任务的政策分割为便携式过渡性的技能，能够满足各种各样的LTL LTL规范，同时尊重安全性批判性约束，从而使跨任务的子policy重复使用。我们在Minecraft启发的领域中进行的实验表明，LTL转移能够满足500个看不见的任务中90％以上的能力，同时仅培训50个任务规格，并且从不违反安全限制。我们还在家庭环境中将LTL转移部署在四倍的移动操纵器上，以显示其以零拍的方式转移到许多获取和交付任务的能力。

我们提出了一种新型的参数化技能学习算法，旨在学习可转移的参数化技能并将其合成为新的动作空间，以支持长期任务中的有效学习。我们首先提出了新颖的学习目标 - 以轨迹为中心的多样性和平稳性 - 允许代理商能够重复使用的参数化技能。我们的代理商可以使用这些学习的技能来构建时间扩展的参数化行动马尔可夫决策过程，我们为此提出了一种层次的参与者 - 批判算法，旨在通过学习技能有效地学习高级控制政策。我们从经验上证明，所提出的算法使代理能够解决复杂的长途障碍源环境。

反向运动 - 发现，达到给定的笛卡尔空间末端执行器的姿态共同的姿势 - 是机器人共同操作，因为目标和航点在笛卡尔空间通常定义，但机器人必须在关节间隙来控制。然而，现有的逆运动学解算器返回一个单一的解决方案的姿势，其中，具有多于6个自由度支持无穷多个这样的解决方案，其可以是在限制的存在是有用的系统，姿势偏好或障碍。我们介绍了使用深层神经网络学习生成这样的运动链的解空间不同组样本的方法。得到的样品能够迅速地生成（在10ms的下2000和解决方案），并精确地（至10毫米之内且2度的精确的溶液）并在必要时能够迅速地通过经典方法精制。

Existing automated techniques for software documentation typically attempt to reason between two main sources of information: code and natural language. However, this reasoning process is often complicated by the lexical gap between more abstract natural language and more structured programming languages. One potential bridge for this gap is the Graphical User Interface (GUI), as GUIs inherently encode salient information about underlying program functionality into rich, pixel-based data representations. This paper offers one of the first comprehensive empirical investigations into the connection between GUIs and functional, natural language descriptions of software. First, we collect, analyze, and open source a large dataset of functional GUI descriptions consisting of 45,998 descriptions for 10,204 screenshots from popular Android applications. The descriptions were obtained from human labelers and underwent several quality control mechanisms. To gain insight into the representational potential of GUIs, we investigate the ability of four Neural Image Captioning models to predict natural language descriptions of varying granularity when provided a screenshot as input. We evaluate these models quantitatively, using common machine translation metrics, and qualitatively through a large-scale user study. Finally, we offer learned lessons and a discussion of the potential shown by multimodal models to enhance future techniques for automated software documentation.

View-dependent effects such as reflections pose a substantial challenge for image-based and neural rendering algorithms. Above all, curved reflectors are particularly hard, as they lead to highly non-linear reflection flows as the camera moves. We introduce a new point-based representation to compute Neural Point Catacaustics allowing novel-view synthesis of scenes with curved reflectors, from a set of casually-captured input photos. At the core of our method is a neural warp field that models catacaustic trajectories of reflections, so complex specular effects can be rendered using efficient point splatting in conjunction with a neural renderer. One of our key contributions is the explicit representation of reflections with a reflection point cloud which is displaced by the neural warp field, and a primary point cloud which is optimized to represent the rest of the scene. After a short manual annotation step, our approach allows interactive high-quality renderings of novel views with accurate reflection flow. Additionally, the explicit representation of reflection flow supports several forms of scene manipulation in captured scenes, such as reflection editing, cloning of specular objects, reflection tracking across views, and comfortable stereo viewing. We provide the source code and other supplemental material on https://repo-sam.inria.fr/ fungraph/neural_catacaustics/

In large-scale machine learning, recent works have studied the effects of compressing gradients in stochastic optimization in order to alleviate the communication bottleneck. These works have collectively revealed that stochastic gradient descent (SGD) is robust to structured perturbations such as quantization, sparsification, and delays. Perhaps surprisingly, despite the surge of interest in large-scale, multi-agent reinforcement learning, almost nothing is known about the analogous question: Are common reinforcement learning (RL) algorithms also robust to similar perturbations? In this paper, we investigate this question by studying a variant of the classical temporal difference (TD) learning algorithm with a perturbed update direction, where a general compression operator is used to model the perturbation. Our main technical contribution is to show that compressed TD algorithms, coupled with an error-feedback mechanism used widely in optimization, exhibit the same non-asymptotic theoretical guarantees as their SGD counterparts. We then extend our results significantly to nonlinear stochastic approximation algorithms and multi-agent settings. In particular, we prove that for multi-agent TD learning, one can achieve linear convergence speedups in the number of agents while communicating just $\tilde{O}(1)$ bits per agent at each time step. Our work is the first to provide finite-time results in RL that account for general compression operators and error-feedback in tandem with linear function approximation and Markovian sampling. Our analysis hinges on studying the drift of a novel Lyapunov function that captures the dynamics of a memory variable introduced by error feedback.