Verifying Reinforcement Learning up to Infinity

Formally verifying that reinforcement learning systems act safely is increasingly important, but existing methods only verify over finite time. This is of limited use for dynamical systems that run indefinitely. We introduce the first method for verifying the time-unbounded safety of neural networks controlling dynamical systems. We develop a novel abstract interpretation method which, by constructing adaptable template-based polyhedra using MILP and interval arithmetic, yields sound---safe and invariant---overapproximations of the reach set. This provides stronger safety guarantees than previous time-bounded methods and shows whether the agent has generalised beyond the length of its training episodes. Our method supports ReLU activation functions and systems with linear, piecewise linear and non-linear dynamics defined with polynomial and transcendental functions. We demonstrate its efficacy on a range of benchmark control problems.

PTSD in the Year Following Sexual Assault: A Meta-Analysis of Prospective Studies

Objective: Sexual assault is associated with higher rates of posttraumatic stress disorder (PTSD) than other traumas, and the course of PTSD may differ by trauma type. However, the course of PTSD after sexual assault has not been summarized. The aim of this meta-analysis was to identify the prevalence and severity of PTSD and changes to the average rate of recovery in the 12 months following sexual assault. Method: Authors searched four databases for prospective studies published before April 2020 and sought relevant unpublished data. Eligible studies assessed PTSD in at least 10 survivors of sexual assault in at least two time points, starting within 3 months postassault. Random effects linear-linear piecewise models were used to identify changes in average recovery rate and produce model-implied estimates of monthly point prevalence and mean symptom severity. Results: Meta-analysis of 22 unique samples ( N = 2,106) indicated that 74.58% (95% confidence interval [CI]: [67.21, 81.29]) and 41.49% (95% CI: [32.36, 50.92]) of individuals met diagnostic criteria for PTSD at the first and 12th month following sexual assault, respectively. PTSD symptom severity was 47.94% (95% CI: [41.27, 54.61]) and 29.91% (95% CI: [23.10, 36.73]) of scales’ maximum severity at the first and 12th month following sexual assault, respectively. Most symptom recovery occurred within the first 3 months following sexual assault, after which point the average rate of recovery slowed. Conclusions: Findings indicate that PTSD is common and severe following sexual assault, and the first 3 months postassault may be a critical period for natural recovery.

Evolutionary Robot Calibration and Nonlinear Compensation Methodology Based on GA-DNN and an Extra Compliance Error Model

This study addresses the problem of nonlinear error predictive compensation to achieve high positioning accuracy for advanced industrial applications. An improved calibration method based on the generalisation performance evaluation is proposed to enhance the stability and accuracy of robot calibration. With the development of technology, a deep neural network (DNN) optimised by a genetic algorithm (GA) is applied to predict the nonlinear error of the calibrated robot. To address the change of external payload, an extra compliance error model is established with a linear piecewise method. A global compensation method combining the GA-DNN nonlinear regression prediction model and the compliance error model is then proposed to achieve the robot’s high-precision positioning performance under any external payload. Experimental results obtained on a Staubli RX160L robot with a FARO laser tracker are introduced to demonstrate the effectiveness and benefits of our proposed methodology. The enhanced positioning accuracy can reach 0.22 mm with 98% probability (i.e., the maximum positioning error in all test data).

Analysis of load mismatch effect compensation in Doherty power amplifier

This paper presents a theoretical and experimental analysis of the capabilities of the dual-input Doherty power amplifier (DPA) architecture to mitigate efficiency and output power degradations when used in a mismatched load environment. Following a simplified linear piecewise approach, an analytical demonstration is proposed to derive optimal radio frequency drives applied to the Auxiliary path of the DPA to restore power performances while avoiding large signal voltage clipping of active cells. The proposed analytical study is corroborated with harmonic balance simulated results of a C-band, 20-W GaN DPA prototype. The fabricated dual-input DPA prototype has been measured under 1.5-VSWR mismatch configurations to validate the proposed analysis.

Assigning orders to suppliers with linear piecewise concave costs

Purpose: Once a set of suppliers has been determined, according to criteria of quality, price and reliability, among others, there remains the problem of assigning orders to the selected suppliers, in order to cover the needs at the lowest cost. We consider the case in which the needs of a component for a set of plants should be covered by suppliers with linear piecewise concave cost functions, a lower bound on the order size for the non-zero deliveries and a capacity constraint. The purpose is to design procedures for solving this problem.Design/methodology/approach: With the aim of providing practical tools to solve the problem of assigning orders to suppliers with linear piecewise concave costs, two mixed integer linear programs are proposed.Findings: The two MILP models are compared through an extensive computational experiment. This shows that both models, with a slight advantage for one of them, can be solved within a very short time, even when the dimensions of the instance largely exceed those that can occur in real cases.Originality/value: The paper proposes novel models that can be used to solve the problem to optimality in reasonable times and with standard optimization software.

Research of Periodic Orbits and Chaos Produced in 1-D Liner Piecewise-Smooth Maps with Single Discontinuity, Positive and Negative Slopes

Last four decades have seen a major development in the theory of piece-wise smooth discontinuous maps for the analysis of typical bifurcation phenomena for systems that can be modelled as such. The major focus of this paper is the analysis of 1-D linear piecewise smooth maps with a discontinuity, one positive and another negative slope. Interestingly, this type of map analysis has been carried out by various authors and the results have been reported in literature. For example, the existence of period adding cascade in particular parameter regions specified by the parameters ‘a’ and ‘b’ was proven. The new range of parameters this work presents are a ϵ (0,1), b ϵ (-1, 0) and a ϵ (0,1), b ϵ (- , -1). Elementary algebraic and geometric tools have been used to analyze the periodicities in the 1-D linear piecewise smooth discontinuous map with respect to parameters a, b, µ and l. Various examples have been illustrated along with the plotted bifurcation curves. The analysis of the behaviour of the system with varied parameter ranges indicates that non-trivial cases are present for negative values of one or more parameters. A sample basin of attraction plot is illustrated as well. Further, an analytic proof for the existence of LnR orbits for the region a ϵ (0,1), b ϵ (-1, 0) was successfully produced, which is unpublished till date. The research concentrates on the theoretical results.