Non-convex Global Minimization and False Discovery Rate Control for the TREX

The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that it requires solving a non-convex optimization problem. This paper shows a remarkable result: despite the non-convexity of the TREX problem, there exists a polynomial-time algorithm that is guaranteed to find the global minimum. This result adds the TREX to a very short list of non-convex optimization problems that can be globally optimized (principal components analysis being a famous example). After deriving and developing this new approach, we demonstrate that (i) the ability of the preexisting TREX heuristic to reach the global minimum is strongly dependent on the difficulty of the underlying statistical problem, (ii) the new polynomial-time algorithm for TREX permits a novel variable ranking and selection scheme, (iii) this scheme can be incorporated into a rule that controls the false discovery rate (FDR) of included features in the model. To achieve this last aim, we provide an extension of the results of Barber & Candes (2015) to establish that the knockoff filter framework can be applied to the TREX. This investigation thus provides both a rare case study of a heuristic for non-convex optimization and a novel way of exploiting non-convexity for statistical inference

A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations

A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation

Collective Robot Reinforcement Learning with Distributed Asynchronous Guided Policy Search

In principle, reinforcement learning and policy search methods can enable robots to learn highly complex and general skills that may allow them to function amid the complexity and diversity of the real world. However, training a policy that generalizes well across a wide range of real-world conditions requires far greater quantity and diversity of experience than is practical to collect with a single robot. Fortunately, it is possible for multiple robots to share their experience with one another, and thereby, learn a policy collectively. In this work, we explore distributed and asynchronous policy learning as a means to achieve generalization and improved training times on challenging, real-world manipulation tasks. We propose a distributed and asynchronous version of Guided Policy Search and use it to demonstrate collective policy learning on a vision-based door opening task using four robots. We show that it achieves better generalization, utilization, and training times than the single robot alternative.Comment: Submitted to the IEEE International Conference on Robotics and Automation 201

A model-based residual approach for human-robot collaboration during manual polishing operations

A fully robotized polishing of metallic surfaces may be insufficient in case of parts with complex geometric shapes, where a manual intervention is still preferable. Within the EU SYMPLEXITY project, we are considering tasks where manual polishing operations are performed in strict physical Human-Robot Collaboration (HRC) between a robot holding the part and a human operator equipped with an abrasive tool. During the polishing task, the robot should firmly keep the workpiece in a prescribed sequence of poses, by monitoring and resisting to the external forces applied by the operator. However, the user may also wish to change the orientation of the part mounted on the robot, simply by pushing or pulling the robot body and changing thus its configuration. We propose a control algorithm that is able to distinguish the external torques acting at the robot joints in two components, one due to the polishing forces being applied at the end-effector level, the other due to the intentional physical interaction engaged by the human. The latter component is used to reconfigure the manipulator arm and, accordingly, its end-effector orientation. The workpiece position is kept instead fixed, by exploiting the intrinsic redundancy of this subtask. The controller uses a F/T sensor mounted at the robot wrist, together with our recently developed model-based technique (the residual method) that is able to estimate online the joint torques due to contact forces/torques applied at any place along the robot structure. In order to obtain a reliable residual, which is necessary to implement the control algorithm, an accurate robot dynamic model (including also friction effects at the joints and drive gains) needs to be identified first. The complete dynamic identification and the proposed control method for the human-robot collaborative polishing task are illustrated on a 6R UR10 lightweight manipulator mounting an ATI 6D sensor

Does algorithmic trading improve liquidity?

Algorithmic trading has sharply increased over the past decade. Equity market liquidity has improved as well. Are the two trends related? For a recent five-year panel of New York Stock Exchange (NYSE) stocks, we use a normalized measure of electronic message traffic (order submissions, cancellations, and executions) as a proxy for algorithmic trading, and we trace the associations between liquidity and message traffic. Based on within-stock variation, we find that algorithmic trading and liquidity are positively related. To sort out causality, we use the start of autoquoting on the NYSE as an exogenous instrument for algorithmic trading. Previously, specialists were responsible for manually disseminating the inside quote. As stocks were phased in gradually during early 2003, the manual quote was replaced by a new automated quote whenever there was a change to the NYSE limit order book. This market structure change provides quicker feedback to traders and algorithms and results in more message traffic. For large-cap stocks in particular, quoted and effective spreads narrow under autoquote and adverse selection declines, indicating that algorithmic trading does causally improve liquidity