Gradient Ascent Method Research Articles

Adjoint-based optimisation of time- and span-periodic flow fields with Space–Time Spectral Method: Application to non-linear instabilities in compressible boundary layer flows

We aim at computing time- and span-periodic flow fields in span-invariant configurations. The streamwise and cross-stream derivatives are discretised with finite volumes while time and the span-direction are handled with pseudo-spectral Fourier-collocation methods. Doing so, we extend the classical Time Spectral Method (TSM) to a Space–Time Spectral Method (S-TSM), by considering non-linear interactions of a finite number of time and span harmonics. For optimisation, we introduce an adjoint-based framework that allows efficient computation of the gradient of any cost functional with respect to a large-dimensional control parameter. Both theoretical and numerical aspects of the methodology are described: evaluation of matrix–vector products with S-TSM Jacobian (or its transpose) by algorithmic differentiation, solution of fixed-points with quasi-Newton method and de-aliasing in time and space, solution of direct and adjoint linear systems by iterative algorithms with a block-circulant preconditioner, performance assessment in CPU time and memory. We illustrate the methodology on the case of 3D instabilities (first Mack mode) triggered within a developing adiabatic boundary layer at M = 4.5. A gradient-ascent method allows to identify a finite-amplitude 3D forcing that triggers a non-linear response exhibiting the strongest time- and span-averaged drag on the flat-plate. In view of flow control, a gradient-descent method finally determines a finite amplitude 2D wall-heat flux that minimises the averaged drag of the plate in presence of the previously determined non-linear optimal forcing.

A 0.061-pJ/b/dB 28-Gb/s Gradient-Based Maximum Eye Tracking CDR With 2-Tap DFE Adaptation in 28-nm CMOS

This brief presents a gradient-based maximum eye tracking (GMET) scheme employed in the forwarded-clock receiver, including baud-rate clock and data recovery (CDR) and 2-tap adaptive decision feedback equalization (DFE). By optimizing the widely used gradient ascent method for robust operation, GMET achieves low computational power and high stability. Also, simultaneous adaptation using the unified algorithm enables low power consumption and low design complexity. Compared with the previous baud-rate CDR, superior performance is demonstrated under high-loss conditions. The prototype receiver is fabricated in 28-nm CMOS and occupies an active area of 0.106 mm2. At the data rate of 28 Gb/s, the receiver consumes 47 mW, corresponding to an energy efficiency of 1.68 pJ/b. Furthermore, with a channel loss of 27.7 dB at the Nyquist frequency, joint operation of the CDR and the DFE adaptation offers measured results with a margin of 0.17 unit interval (UI) at a BER lower than 10-12.

Cooperative RIS and STAR-RIS Assisted mMIMO Communication: Analysis and Optimization

Reconfigurable intelligent surface (RIS) has emerged as a cost-effective and promising solution to extend the wireless signal coverage and improve the performance via passive signal reflection. Different from existing works which do not account for the cooperation between RISs or do not provide full space coverage, we propose the marriage of cooperative double-RIS with simultaneously transmitting and reflecting RIS (STAR-RIS) technologies denoted as RIS/STAR-RIS under correlated Rayleigh fading conditions to assist the communication in a massive multiple-input multiple-output (mMIMO) setup. The proposed architecture is superior since it enjoys the benefits of the individual designs. We introduce a channel estimation approach of the cascaded channels with reduced overhead. Also, we obtain the deterministic equivalent (DE) of the downlink achievable sum spectral efficiency (SE) in closed form based on large-scale statistics. Notably, relied on statistical channel state information (CSI), we optimise both surfaces by means of the projected gradient ascent method (PGAM), and obtain the gradients in closed form. The proposed optimization achieves to maximise the sum SE of such a complex system, and has low complexity and low overhead since it can be performed at every several coherence intervals. Numerical results show the benefit of the proposed architecture and verify the analytical framework. In particular, we show that the RIS/STAR-RIS architecture outperforms the conventional double-RIS or its single-RIS counterparts.

Quantum adversarial metric learning model based on triplet loss function

Metric learning plays an essential role in image analysis and classification, and it has attracted more and more attention. In this paper, we propose a quantum adversarial metric learning (QAML) model based on the triplet loss function, where samples are embedded into the high-dimensional Hilbert space and the optimal metric is obtained by minimizing the triplet loss function. The QAML model employs entanglement and interference to build superposition states for triplet samples so that only one parameterized quantum circuit is needed to calculate sample distances, which reduces the demand for quantum resources. Considering the QAML model is fragile to adversarial attacks, an adversarial sample generation strategy is designed based on the quantum gradient ascent method, effectively improving the robustness against the functional adversarial attack. Simulation results show that the QAML model can effectively distinguish samples of MNIST and Iris datasets and has higher ϵ-robustness accuracy over the general quantum metric learning. The QAML model is a fundamental research problem of machine learning. As a subroutine of classification and clustering tasks, the QAML model opens an avenue for exploring quantum advantages in machine learning.

Jointly optimized resource allocation for SDN control and forwarding planes in edge-cloud SDN-based networks

Today’s resource allocation strategies for edge-cloud network based on Software-Defined Network (SDN) and Network Function Virtualization (NFV) architectures often make a decision of placing resource based on network locations, i.e. edge or core cloud. Unfortunately, these strategies are not optimally tailored for a growing class of Internet-of-Things (IoT) services whose traffic is designated to go through a Virtual Network Functions (VNF) service chain. Without considering the communication between SDN control plane and forwarding plane, inappropriate SDN controllers could be selected for switches, which may result in a significant setup delay of the whole service chain. In addition, the fluctuate demand of IoT services requires the entire system, that is composed of controllers, forwarding elements, i.e. switches, and physical machines, being stable during service provisioning. In this paper, we jointly address two issues, i.e. SDN controller-switch assignment and VNF placement, both are high-complexity problems. We formulate the joint optimization problem of dynamically provisioning resource for SDN controllers and VNFs in a long run. We then apply the Lyapunov optimization framework to transform a long-term optimization problem into a series of real-time problems and employ exponentiated gradient ascent (EGA) method to find a near-optimal solution. Extensive simulation and experiments show that our approach helps to optimize the system cost up to 11 ∼ 40% depending on service demand and network size.

Optimal Beacon Deployment for Positioning in Cluttered Indoor Environments

Accurate indoor positioning is vital for many indoor autonomous systems. This article focuses on the influence of beacon placement on overall positioning quality in cluttered indoor environments. We first propose a metric based on the Fisher information matrix (FIM) to evaluate the performance of the positioning service provided by a specific beacon layout. After analyzing the characteristics of the FIM, we introduce an additional penalty term in the performance metric to handle singular cases. We then investigate the optimal beacon placement with respect to overall positioning quality. We derive the gradient of the optimization objective and propose an efficient optimization method called the quotient-space gradient-based particle swarm optimization (QGPSO), which combines the quotient-space PSO with the gradient ascent method, enabling the particle swarm to obtain more accurate optimization results locally while retaining the original global exploration capability. Numerical results validate our analysis and the superiority of the proposed optimization method over other baselines.

Outage probability minimization for vehicular networks via joint clustering, UAV trajectory optimization and power allocation

In this paper, we consider the vehicular uplink communication scenario where vehicles in the same lane travel in a direction within the coverage of the base station. Due to the long communication distance and poor signal quality at the cell edge, an unmanned aerial vehicle (UAV) is used as a mobile relay to improve the communication quality. Our goal is to minimize the communication outage probability by jointing vehicle clustering with UAV trajectory optimization and power allocation of each node. Since the cluster head position, UAV position and power of each node are coupled, the primary complex problem is divided into three sub-problems namely vehicle clustering, trajectory optimization and power allocation. Firstly, the improved K-means clustering algorithm is used for vehicle clustering by addressing the minimum–maximum distance criterion. In order to adapt to the changing network topology, the cluster head vehicle is determined dynamically. Then the joint Lagrangian gradient ascent method is used to determine the UAV position and the power of each vehicle through alternate iterations. The simulation results show that the proposed joint optimization scheme (J-CTOPA) is better than the equal power scheme with fixed relay position (FR-EP) and the power allocation scheme with cruise relay trajectories (CT-PA). The results also show that faster convergence and stronger stability can be achieved while the outage probability is reduced.

Proximal policy optimization guidance algorithm for intercepting near-space maneuvering targets

This paper studies a novel guidance framework of the vehicle against a high-speed and maneuvering target based on deep reinforcement learning (DRL) considering the energy consumption, autopilot lag dynamics, and input saturation, which can effectively cope with the high flight-path angle error flight phase and various uncertainties. The guidance framework proposes an end-to-end mapping transformation between the guidance command and observation states consisting of line-of-sight (LOS) angle, relative distance, and their rate measured by the seeker. At the same time, the observability of the LOS angle and relative distance is included in constructing the reward function. Besides, the relative engagement kinematic model of the interceptor-target is established and combined with the PPO guidance algorithm, jointly described as a Markov decision process (MDP). Notably, the guidance framework is optimized using the improved proximal policy optimization (PPO) algorithm and demonstrated in a simulated terminal phase in the near-space. Specifically, the PPO guidance algorithm is structured by the policy (actor) neural network and the critic neural network, and both are standard fully-connected neural networks. Subsequently, observation states and rewards are fully collected and applied by introducing the experience replay method. Also, the exponential decay learning rate method, mini-batch stochastic gradient ascent (SGA) method, zero-score standardization, and Adam optimizer are proposed to train the reinforcement learning algorithm more efficiently. Moreover, the proposed guidance framework has an excellent generalization capability and guarantees the implementation of fixed and stochastic engagement scenarios, which means that the interceptor can realize the unlearned practical combat scenarios. The robust capacity is indicated and validated using Monte Carlo simulation under various uncertainties. Moreover, the DRL guidance framework can satisfy the onboard application requirement.

Forex Investment Optimization Using Instantaneous Stochastic Gradient Ascent—Formulation of an Adaptive Machine Learning Approach

In the current complex financial world, paper currencies are vulnerable and unsustainable due to many factors such as current account deficit, gold reserves, dollar reserves, political stability, security, the presence of war in the region, etc. The vulnerabilities not limited to the above, result in fluctuation and instability in the currency values. Considering the devaluation of some Asian countries such as Pakistan, Sri Lanka, Türkiye, and Ukraine, there is a current tendency of some countries to look beyond the SWIFT system. It is not feasible to have reserves in only one currency, and thus, forex markets are likely to have significant growth in their volumes. In this research, we consider this challenge to work on having sustainable forex reserves in multiple world currencies. This research is aimed to overcome their vulnerabilities and, instead, exploit their volatile nature to attain sustainability in forex reserves. In this regard, we work to formulate this problem and propose a forex investment strategy inspired by gradient ascent optimization, a robust iterative optimization algorithm. The dynamic nature of the forex market led us to the formulation and development of the instantaneous stochastic gradient ascent method. Contrary to the conventional gradient ascent optimization, which considers the whole population or its sample, the proposed instantaneous stochastic gradient ascent (ISGA) optimization considers only the next time instance to update the investment strategy. We employed the proposed forex investment strategy on forex data containing one-year multiple currencies’ values, and the results are quite profitable as compared to the conventional investment strategies.

Time-varying dual accelerated gradient ascent: A fast network optimization algorithm

We propose a time-varying dual accelerated gradient method for minimizing the average of n strongly convex and smooth functions over a time-varying network with n nodes. We prove that the time-varying dual accelerated gradient ascent method converges at an R-linear rate with the time to reach an ϵ-neighborhood of the solution being of O(1ln⁡(1/c)ln⁡Mϵ), where c is a constant depending on the graph and objective function parameters and M is a constant depending on the initial values. We test the proposed method on two classes of problems: L2-regularized least squares and logistic classification problems. For each class, we generate 1000 problems and use the Dolan-Moré performance profiles to compare our obtained results with the ones obtained by several state-of-the-art algorithms to illustrate the efficiency of our method.

A Second-Order Generalized Integrator Frequency Locked Loop With Damping Ratio Adaptation

The complex and ever-changing harmonics in grid voltage will cause performance deterioration of the frequency-locked loops (FLLs). Although various measurements had been adopted to attenuate the deterioration, they had to make the tradeoff between the dynamic and steady-state characteristics generally. Consequently, a novel single-phase FLL that can adaptively adjust the dynamic and steady-state performance was proposed in this article. The proposed FLL regards the damping ratio of second-order generalized integrator-FLL (SOGI-FLL) as a time-varying parameter rather than a constant, and adjusts the damping ratio adaptively, so the proposed FLL was named SOGI-FLL with damping ratio adaptation (DASOGI-FLL). The adaptive mechanism is to decrease the damping ratio as frequency estimation error decreases and vice versa. To realize the mechanism, a novel variable was constructed to indirectly correlate the damping ratio with frequency estimation error. An objective function containing the constructed variable for damping ratio adaptation was designed, and the adaptive algorithm was derived by using the gradient ascent method. Then, the convergence analysis, parameter design, and digital implementation of the algorithm were elaborated. Finally, the results of simulation and experiment reveal that, benefits from the damping ratio adaptation, DASOGI-FLL can achieve rapid convergence, strong filtering capability, and high estimation accuracy simultaneously.

A Deterministic Algorithm for the Capacity of Finite-State Channels

We propose two modified versions of the classical gradient ascent method to compute the capacity of finite-state channels with Markovian inputs. For the case that the channel mutual information rate is strongly concave in a parameter taking values in a compact convex subset of some Euclidean space, our first algorithm proves to achieve polynomial accuracy in polynomial time and, moreover, for some special families of finite-state channels our algorithm can achieve exponential accuracy in polynomial time under some technical conditions. For the case that the channel mutual information rate may not be strongly concave, our second algorithm proves to be at least locally convergent.

Statistical Inference with Local Optima

We study the statistical properties of an estimator derived by applying a gradient ascent method with multiple initializations to a multi-modal likelihood function. We derive the population quantity that is the target of this estimator and study the properties of confidence intervals (CIs) constructed from asymptotic normality and the bootstrap approach. In particular, we analyze the coverage deficiency due to finite number of random initializations. We also investigate the CIs by inverting the likelihood ratio test, the score test, and the Wald test, and we show that the resulting CIs may be very different. We propose a two-sample test procedure even when the maximum likelihood estimator is intractable. In addition, we analyze the performance of the EM algorithm under random initializations and derive the coverage of a CI with a finite number of initializations. Supplementary materials for this article are available online.

On a Variation of Two-Part Tariff Pricing of Services: A Data-Driven Approach

Problem definition: We present a data-driven pricing problem motivated from our collaboration with a satellite service provider. In particular, we study a variant of the two-part tariff pricing scheme. The firm offers a set of data plans consisting of a bundle of data at a fixed price plus additional data at a variable price. Most literature on two-part tariff problems focuses on models that assume full information. However, little attention has been devoted to this problem from a data-driven perspective without full information. One of the main challenges when working with data comes from missing data. Methodology/results: First, we develop a new method to address the missing data problem, which comes from different sources: (i) the number of unobserved customers, (ii) customers’ willingness to pay (WTP), and (iii) demand from unobserved customers. We introduce an iteration procedure to maximize the likelihood by combining the expectation maximization algorithm with a gradient ascent method. We also formulate the pricing optimization problem as a dynamic program (DP) using a discretized set of prices. From applying Sample Average Approximation, the DP obtains a solution within 3.8% of the optimal solution of the sampled instances, on average, and within 18% with 95% confidence from the optimal solution of the exact problem. By extending the DP formulation, we show that it is better to optimize on prices rather than bundles, obtaining revenues close to optimizing jointly on both. Managerial implications: The sensitivity analysis of the problem parameters is key for decision makers to understand the risks of their pricing decisions. Indeed, assuming a higher variability of customers’ WTP induces higher revenue risks. In addition, revenues are barely (highly) sensitive to the customers’ assumed WTP variability when considering a high (low) number of unobserved customers. Finally, we extend the model to incorporate price-dependent consumption.

Optimal Accuracy-Privacy Trade-Off of Inference as Service

In this paper, we propose a general framework to provide a desirable trade-off between inference accuracy and privacy protection in the inference as service scenario (IAS). Instead of sending data directly to the server, the user will preprocess the data through a privacy-preserving mapping, which will increase privacy protection but reduce inference accuracy. To properly address the trade-off between privacy protection and inference accuracy, we formulate an optimization problem to find the privacy-preserving mapping. Even though the problem is non-convex in general, we characterize nice structures of the problem and develop an iterative algorithm to find the desired privacy-preserving mapping, with convergence analysis provided under certain assumptions. From numerical examples, we observe that the proposed method has better performance than gradient ascent method in the convergence speed, solution quality and algorithm stability.

Design of an Intelligent Reflecting Surface Aided mmWave Massive MIMO Using X-Precoding

In this paper, we consider an intelligent reflecting surface (IRS) aided millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) system using hybrid beamforming/combining. To enhance error performance, we adopt X-code (or X-precoder), a low-complexity precoding technique for traditional MIMO channels, to encode information symbols. We first derive an upper bound on word error rate (WER), based on which we design jointly IRS phase shifts and X-code (or X-precoder) to minimize WER. Specifically, we propose two algorithms for IRS design exploiting alternating optimization and gradient ascent optimization methods. Then we devise X-code and X-precoder, respectively, by minimizing average WER over all channel realizations and WER for each channel realization. We also provide their diversity analysis. Further, we present the procedure of decoupling fully digital beamformer/combiner at transceiver into the optimal hybrid one. Finally, simulation results show that both IRS optimization algorithms have similar WERs whereas gradient ascent approach has a lower computational complexity. Simulations demonstrate that the designed X-code (or X-precoder) provides a significant performance gain.

FadeLoc: Smart Device Localization for Generalized ${\kappa {-} \mu}$ Faded IoT Environment

In this paper, we propose <i>FadeLoc</i> a novel method for localizing smart devices in an Internet of Things (IoT) environment, based on the Received Signal Strength (RSS), and a generic <inline-formula><tex-math notation="LaTeX">$\kappa \-\mu$</tex-math></inline-formula> fading model where <inline-formula><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> denote the fading parameters. The RSS-based localization is challenging because of noise, fading, and non-line-of-sight (NLOS) effects, thus necessitating an appropriate fading model to best fit the varying RSS values. The advantage of a generic fading model is that it can accommodate all existing fading distributions based on the estimate of <inline-formula><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>. Hence, the localization can be performed for any fading environment. We derive the maximum likelihood estimate of the smart device location using a generic <inline-formula><tex-math notation="LaTeX">$\kappa \-\mu$</tex-math></inline-formula> fading model considering the Large and Small approximations of modified first-order Bessel function and propose an adaptive order selection method with high localization accuracy and faster convergence. We also analyze the convergence of the gradient ascent method for the <inline-formula><tex-math notation="LaTeX">$\kappa \-\mu$</tex-math></inline-formula> fading model. The proposed method is evaluated on a simulated <inline-formula><tex-math notation="LaTeX">$\kappa \-\mu$</tex-math></inline-formula> fading environment, real outdoor environment, and a complex indoor fading environment. The average localization errors are 2.07&#x00A0;m, 3.5&#x00A0;m, and 0.5&#x00A0;m, respectively, for the three experimental settings, outperforming the state-of-the-art localization methods in the presence of fading.

A stacking weighted k-Nearest neighbour with thresholding

• Stacking of binary classifiers to consider label correlations. • Thresholding the decision boundary. • Feature weighting in order to correlation adjustment. • Dealing with imbalanced data problem by optimizing F -measure. • Using gradient ascent method. In Multi-label problems, each instance is associated with a set of predefined labels. Binary Relevance, as a common approach, uses one binary classifier for each label and ignores the probable dependencies between some labels. Stacked-Binary Relevance (SBR) was proposed to consider the label dependencies, by augmenting a second layer of binary models using the predicted labels of the first level binary models as additional features. By reusing all predicted labels, SBR implicitly assumes full dependencies between labels, which is not usually a true assumption in the real world. Moreover, SBR uses a constant threshold in decision functions of the binary models, while adjusting the threshold for each label specially for imbalanced ones can improve the performance. This paper proposes a k -Nearest Neighbor stacking method that adjusts the thresholds in decision functions of the binary classifiers and uses a feature-weighted distance measure to reduce the effect of irrelevant labels in stacking. The method can leverage positive/negative and symmetric/asymmetric label dependencies expressed as feature weights. Also, it can tackle the main shortcomings of SBR (revealed in the existence of irrelevant labels and imbalanced data). Using 22 multi-label datasets, the proposed method is assessed and outperforms state-of-the-art methods presented in the literature.

Fast Alignment Algorithm for Autocalibration in Digital Monopulse Radars

Calibration is important for digital monopulse radars since the target tracking performance would be degraded by the amplitude and phase imbalance among channels. However, the alignment between the radar to be calibrated and the test probe is a challenge, especially for antennas with high gain and narrow beamwidth. In this letter, we propose a fast alignment algorithm for the autocalibration of digital monopulse radars using the gradient ascent method based on the tentative radiation pattern gradient model. We verify the feasibility and the high efficiency of the proposed algorithm by simulations and an experiment of a W-band digital monopulse radar. The elapsed time of the proposed algorithm is 0.01 <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">%</b> of the existing method and requires lower equipment complexity compared with the scanning-based method.

Overcoming the problems caused by collinearity in mixed-effects logistic model: determining the contribution of various types of violence on depression in pregnant women

BackgroundCollinearity is a common and problematic phenomenon in studies on public health. It leads to inflation in variance of estimator and reduces test power. This phenomenon can occur in any model. In this study, a new ridge mixed-effects logistic model (RMELM) is proposed to overcome consequences of collinearity in correlated binary responses.MethodsParameters were estimated through penalized log-likelihood with combining expectation maximization (EM) algorithm, gradient ascent, and Fisher-scoring methods. A simulation study was performed to compare new model with mixed-effects logistic model(MELM). Mean square error, relative bias, empirical power, and variance of random effects were used to evaluate RMELM. Also, contribution of various types of violence, and intervention on depression among pregnant women experiencing intimate partner violence(IPV) were analyzed by new and previous models.ResultsSimulation study showed that mean square errors of fixed effects were decreased for RMELM than MELM and empirical power were increased. Inflation in variance of estimators due to collinearity was clearly shown in the MELM in data on IPV and RMELM adjusted the variances.ConclusionsAccording to simulation results and analyzing IPV data, this new estimator is appropriate to deal with collinearity problems in the modelling of correlated binary responses.