Lagrangian Decomposition for Classical Planning (Extended Abstract)

Optimal cost partitioning of classical planning heuristics has been shown to lead to excellent heuristic values but is often prohibitively expensive to compute. We analyze the application of Lagrangian decomposition, a classical tool in mathematical programming, to cost partitioning of operator-counting heuristics. This allows us to view the computation as an iterative process that can be seeded with any cost partitioning and that improves over time. In the case of non-negative cost partitioning of abstraction heuristics the computation reduces to independent shortest path problems and does not require an LP solver

Randomized Polar Codes for Anytime Distributed Machine Learning

We present a novel distributed computing framework that is robust to slow compute nodes, and is capable of both approximate and exact computation of linear operations. The proposed mechanism integrates the concepts of randomized sketching and polar codes in the context of coded computation. We propose a sequential decoding algorithm designed to handle real valued data while maintaining low computational complexity for recovery. Additionally, we provide an anytime estimator that can generate provably accurate estimates even when the set of available node outputs is not decodable. We demonstrate the potential applications of this framework in various contexts, such as large-scale matrix multiplication and black-box optimization. We present the implementation of these methods on a serverless cloud computing system and provide numerical results to demonstrate their scalability in practice, including ImageNet scale computations

BP-RRT: Barrier Pair Synthesis for Temporal Logic Motion Planning

For a nonlinear system (e.g. a robot) with its continuous state space trajectories constrained by a linear temporal logic specification, the synthesis of a low-level controller for mission execution often results in a non-convex optimization problem. We devise a new algorithm to solve this type of non-convex problems by formulating a rapidly-exploring random tree of barrier pairs, with each barrier pair composed of a quadratic barrier function and a full state feedback controller. The proposed method employs a rapid-exploring random tree to deal with the non-convex constraints and uses barrier pairs to fulfill the local convex constraints. As such, the method solves control problems fulfilling the required transitions of an automaton in order to satisfy given linear temporal logic constraints. At the same time it synthesizes locally optimal controllers in order to transition between the regions corresponding to the alphabet of the automaton. We demonstrate this new algorithm on a simulation of a two linkage manipulator robot.Comment: 6 pages, 5 figures. Accepted for publication in IEEE Conference on Decision and Control (CDC) copyright 2020 IEE

Dynamic whole-body motion generation under rigid contacts and other unilateral constraints

The most widely used technique for generating wholebody motions on a humanoid robot accounting for various tasks and constraints is inverse kinematics. Based on the task-function approach, this class of methods enables the coordination of robot movements to execute several tasks in parallel and account for the sensor feedback in real time, thanks to the low computation cost. To some extent, it also enables us to deal with some of the robot constraints (e.g., joint limits or visibility) and manage the quasi-static balance of the robot. In order to fully use the whole range of possible motions, this paper proposes extending the task-function approach to handle the full dynamics of the robot multibody along with any constraint written as equality or inequality of the state and control variables. The definition of multiple objectives is made possible by ordering them inside a strict hierarchy. Several models of contact with the environment can be implemented in the framework. We propose a reduced formulation of the multiple rigid planar contact that keeps a low computation cost. The efficiency of this approach is illustrated by presenting several multicontact dynamic motions in simulation and on the real HRP-2 robot

Theory and Applications of Robust Optimization

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.Comment: 50 page

Off-line computing for experimental high-energy physics

The needs of experimental high-energy physics for large-scale computing and data handling are explained in terms of the complexity of individual collisions and the need for high statistics to study quantum mechanical processes. The prevalence of university-dominated collaborations adds a requirement for high-performance wide-area networks. The data handling and computational needs of the different types of large experiment, now running or under construction, are evaluated. Software for experimental high-energy physics is reviewed briefly with particular attention to the success of packages written within the discipline. It is argued that workstations and graphics are important in ensuring that analysis codes are correct, and the worldwide networks which support the involvement of remote physicists are described. Computing and data handling are reviewed showing how workstations and RISC processors are rising in importance but have not supplanted traditional mainframe processing. Examples of computing systems constructed within high-energy physics are examined and evaluated