Efficient gradient computation for optimization of hyperparameters

We are interested in learning the hyperparameters in a convex objective function in a supervised setting. The complex relationship between the input data to the convex problem and the desirable hyperparameters can be modeled by a neural network; the hyperparameters and the data then drive the convex minimization problem, whose solution is then compared to training labels. In our previous work [1], we evaluated a prototype of this learning strategy in an optimization-based sinogram smoothing plus FBP reconstruction framework. A question arising in this setting is how to efficiently compute (backpropagate) the gradient from the solution of the optimization problem, to the hyperparameters to enable end-to-end training. In this work, we first develop general formulas for gradient backpropagation for a subset of convex problems, namely the proximal mapping. To illustrate the value of the general formulas and to demonstrate how to use them, we consider the specific instance of 1-D quadratic smoothing (denoising) whose solution admits a dynamic programming (DP) algorithm. The general formulas lead to another DP algorithm for exact computation of the gradient of the hyperparameters. Our numerical studies demonstrate a 55%- 65% computation time savings by providing a custom gradient instead of relying on automatic differentiation in deep learning libraries. While our discussion focuses on 1-D quadratic smoothing, our initial results (not presented) support the statement that the general formulas and the computational strategy apply equally well to TV or Huber smoothing problems on simple graphs whose solutions can be computed exactly via DP.

Joint 3-D Positioning and Power Allocation for UAV Relay Aided by Geographic Information

<div>In this paper, we study to employ geographic information to address the blockage problem of air-to-ground links between UAV and terrestrial nodes. In particular, a UAV relay is deployed to establish communication links from a ground base station to multiple ground users. To improve communication capacity, we fifirst model the blockage effect caused by buildings according to the three-dimensional (3-D) geographic information. Then, an optimization problem is formulated to maximize the minimum capacity among users by jointly optimizing the 3-D position and power allocation of the UAV relay, under the constraints of link capacity, maximum transmit power, and blockage. To solve this complex non-convex problem, a two-loop optimization framework is developed based on Lagrangian relaxation. The outer-loop aims to obtain proper Lagrangian multipliers to ensure the solution of the Lagrangian problem converge to the tightest upper bound on the original problem. The inner-loop solves the Lagrangian problem by applying the block coordinate descent (BCD) and successive convex approximation (SCA) techniques, where UAV 3-D positioning and power allocation are alternately optimized in each iteration. Simulation results confifirm that the proposed solution signifificantly outperforms two benchmark schemes and achieves a performance close to the upper bound on the UAV relay system.</div>

Rapid and safe wire tension distribution scheme for redundant cable-driven parallel manipulators

A non-iterative analytical approach is investigated to plan the safe wire tension distribution along with the cables in the redundant cable-driven parallel robots. The proposed algorithm considers not only tracking the desired trajectory but also protecting the system against possible failures. This method is used to optimize the non-negative wire tensions through the cables which are constrained based on the workspace conditions. It also maintains both actuators’ torque and cables’ tensile strength boundary limits. The pseudo-inverse problem solution leads to an n-dimensional convex problem, which is related to the robot degrees of redundancy. In this paper, a comprehensive solution is presented for a 1–3 degree(s) of redundancy in wire-actuated robots. To evaluate the effectiveness of this method, it is verified through an experimental study on the RoboCab cable robot in the infinity trajectory tracking task. As a matter of comparison, some standard methods like Active-set and sequential quadratic programming are also presented and the average elapsed time for each method is compared to the proposed algorithm.

Throughput Fairness in Cognitive Backscatter Networks With Residual Hardware Impairments and a Nonlinear EH Model

This paper is to design a throughput fairness-aware resource allocation scheme for a cognitive backscatter network (CBN), where multiple backscatter devices (BDs) take turns to modulate information on the primary signals and backscatter the modulated signals to a cooperative receiver (C-Rx), while harvesting energy to sustain their operations. The nonlinear energy harvesting (EH) circuits at the BDs and the residual hardware impairments (HWIs) at the transceivers are considered to better reflect the properties of the practical energy harvesters and transceivers, respectively. To ensure the throughput fairness among BDs, we formulate an optimization problem to maximize the minimum throughput of BDs by jointly optimizing the transmit power of the primary transmitter, the backscattering time and reflection coefficient for each BD, subject to the primary user&rsquo;s quality of service (QoS) and BDs&rsquo; energy-causality constraints. We introduce the variable slack and decoupling methods to transform the formulated non-convex problem, and propose an iterative algorithm based on block coordinate descent (BCD) technique to solve the transformation problem. We also investigate a special CBN with a single BD and derive the optimal solution in the closed form to maximize the BD&#39;s throughput. Numerical results validate the quick convergence of the proposed iterative algorithm and that the proposed scheme ensures much fairness than the existing schemes.

A Convex Data-Driven Approach for Nonlinear Control Synthesis

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is built on the density-function-based stability certificate that is the dual to the Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently using the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory can be understood through the lens of Perron–Frobenius and Koopman operators. This allows us to use data-driven methods to approximate these operators and combine them with the SOS techniques to establish a convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.

Age-Aware Utility Maximization in Relay-Assisted Wireless Powered Communication Networks

This article investigates a relay-assisted wireless powered communication network (WPCN), where the access point (AP) inspires the auxiliary nodes to participate together in charging the sensor, and then the sensor uses its harvested energy to send status update packets to the AP. An incentive mechanism is designed to overcome the selfishness of the auxiliary node. In order to further improve the system performance, we establish a Stackelberg game to model the efficient cooperation between the AP–sensor pair and auxiliary node. Specifically, we formulate two utility functions for the AP–sensor pair and the auxiliary node, and then formulate two maximization problems respectively. As the former problem is non-convex, we transform it into a convex problem by introducing an extra slack variable, and then by using the Lagrangian method, we obtain the optimal solution with closed-form expressions. Numerical experiments show that the larger the transmit power of the AP, the smaller the age of information (AoI) of the AP–sensor pair and the less the influence of the location of the auxiliary node on AoI. In addition, when the distance between the AP and the sensor node exceeds a certain threshold, employing the relay can achieve better AoI performance than non-relaying systems.

Topology optimization for fail-safe designs using moving morphable components as a representation of damage

Designs obtained with topology optimization (TO) are usually not safe against damage. In this paper, density-based TO is combined with a moving morphable component (MMC) representation of structural damage in an optimization problem for fail-safe designs. Damage is inflicted on the structure by an MMC which removes material, and the goal of the design problem is to minimize the compliance for the worst possible damage. The worst damage is sought by optimizing the position of the MMC to maximize the compliance for a given design. This non-convex problem is treated using a gradient-based solver by initializing the MMC at multiple locations and taking the maximum of the compliances obtained. The use of MMCs to model damage gives a finite element-mesh-independent method, and by allowing the components to move rather than remain at fixed locations, more robust structures are obtained. Numerical examples show that the proposed method can produce fail-safe designs with reasonable computational cost.

S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem

The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the 2 → 2 scattering matrix S2→2 such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boundary interesting theories can be found, many times at vertices of the space. Here we consider 3 + 1 dimensional theories and focus on the equivalent dual convex minimization problem that provides strict upper bounds for the regularized primal problem and has interesting practical and physical advantages over the primal problem. Its variables are dual partial waves kℓ(s) that are free variables, namely they do not have to obey any crossing, unitarity or other constraints. Nevertheless they are directly related to the partial waves fℓ(s), for which all crossing, unitarity and symmetry properties result from the minimization. Numerically, it requires only a few dual partial waves, much as one wants to possibly match experimental results. We consider the case of scalar fields which is related to pion physics.

Physical layer security transmission scheme based on artificial noise in cooperative SWIPT NOMA system

Aiming at high energy consumption and information security problem in the simultaneous wireless information and power transfer (SWIPT) multi-user wiretap network, we propose a user-aided cooperative non-orthogonal multiple access (NOMA) physical layer security transmission scheme to minimize base station (BS) transmitted power in this paper. In this scheme, the user near from BS is adopted as a friendly relay to improve performance of user far from BS. An energy harvesting (EH) technology-based SWIPT is employed at the near user to collect energy which can be used at cooperative stage. Since eavesdropper in the downlink of NOMA system may use successive interference cancellation (SIC) technology to obtain the secrecy information of receiver, to tackle this problem, artificial noise (AN) is used at the BS to enhance security performance of secrecy information. Moreover, semidefinite relaxation (SDR) method and successive convex approximation (SCA) technique are combined to solve the above non-convex problem. Simulation results show that in comparison with other methods, our method can effectively reduce the transmitted power of the BS on the constraints of a certain level of the secrecy rates of two users.