Stochastic Algorithm Research Articles

Polyak’s Method Based on the Stochastic Lyapunov Function for Justifying the Consistency of Estimates Produced by a Stochastic Approximation Search Algorithm under an Unknown-But-Bounded Noise

In 1976–1977, Polyak published in the journal Avtomatica i Telemekhanika (Automation and Remote Control) two remarkable papers on how to study the properties of estimates of iterative pseudogradient algorithms. The first paper published in 1976 considered the general case based on the stochastic Lyapunov function, and the second one considered the linear case. The assumptions formulated in these papers and the estimates obtained in them can still be considered the state-of-the art. In the current paper, Polyak’s approach is applied to the study of the properties of estimates of a (randomized) stochastic approximation search algorithm for the case of unknown-but-bounded noise in observations. The obtained asymptotic estimates were already known earlier, and exact estimates for a finite number of observations are published for the first time.

Accelerated multi-kernel sparse stochastic optimization classifier algorithm for explainable prediction

Accelerated multi-kernel sparse stochastic optimization classifier algorithm for explainable prediction

Comparative study of deterministic and stochastic optimization algorithms applied to the absorption of CO2 by alkanolamine solution

Abstract A model based on simulated annealing approach is used with e-UNIQUAC model as well as two other algorithms to study the absorption of carbon dioxide by monoethanolamine solutions. In this work, we propose to compare the performance (through the knowledge of RMSD values) of two stochastic methods, namely the GA (genetic algorithm) and SA (simulated annealing) methods and a deterministic method that is the simplex method. These methods were applied to the absorption of carbon dioxide by an alkanolamine solution using a chemical equilibrium model and a thermodynamic equilibrium model. The latter is based on the use of the modified-UNIQUAC (UNIQUAC-electrolyte) model instead of e-NRTL model for the liquid phase and a fugacity model for the vapor phase. The chemical equilibrium in this work represents the absorption of CO2 by monoethanolamine solution at different temperatures. Solving the coupled system of material and charge balances gives us the carbon dioxide pressure while taking into account the non-ideality of the system. The three-optimization methods show good agreement with the experimental data with a better performance of the simulated annealing method..

Fast standard error estimation for joint models of longitudinal and time-to-event data based on stochastic EM algorithms.

Maximum likelihood inference can often become computationally intensive when performing joint modeling of longitudinal and time-to-event data, due to the intractable integrals in the joint likelihood function. The computational challenges escalate further when modeling HIV-1 viral load data, owing to the nonlinear trajectories and the presence of left-censored data resulting from the assay's lower limit of quantification. In this paper, for a joint model comprising a nonlinear mixed-effect model and a Cox Proportional Hazards model, we develop a computationally efficient Stochastic EM (StEM) algorithm for parameter estimation. Furthermore, we propose a novel technique for fast standard error estimation, which directly estimates standard errors from the results of StEM iterations and is broadly applicable to various joint modeling settings, such as those containing generalized linear mixed-effect models, parametric survival models, or joint models with more than two submodels. We evaluate the performance of the proposed methods through simulation studies and apply them to HIV-1 viral load data from six AIDS Clinical Trials Group studies to characterize viral rebound trajectories following the interruption of antiretroviral therapy (ART), accounting for the informative duration of off-ART periods.

Enhanced Subspace Iteration Technique for Probabilistic Modal Analysis of Statically Indeterminate Structures

In structural stochastic dynamic analysis, the consideration of the randomness in the physical parameters of the structure necessitates the establishment of numerous stochastic finite element models and the subsequent computation of their corresponding vibration modes. When the complete analysis is applied to calculate the vibration modes for each sample of the stochastic finite element model, a substantial computational expense is incurred. To enhance computational efficiency, this work presents an extended subspace iteration method aimed at rapidly determining the vibration modal parameters of statically indeterminate structures. The essence of this proposed method revolves around efficiently constructing reduced basis vectors during the subspace iteration process, utilizing flexibility disassembly perturbation and the Krylov subspace. This extended subspace iteration method proves particularly advantageous for the modal analysis of finite element models that incorporate a multitude of random variables. The proposed modal random analysis method has been validated using both a truss structure and a beam structure. The results demonstrate that the proposed method achieves substantial savings in computational time. Specifically, for the truss structure, the calculation time of the proposed method is approximately 1.2% and 65% of that required by the comprehensive analysis method and the combined approximation method, respectively. For the beam structure, on average, the computational time of the proposed method is roughly 2.1% of a full analysis and approximately 48.2% of the Ritz vector method’s time requirement. Compared to existing stochastic modal analysis algorithms, the proposed method offers improved computational accuracy and efficiency, particularly in scenarios involving high-discreteness random analyses.

Post-Training Attribute Unlearning in Recommender Systems

With the growing privacy concerns in recommender systems, recommendation unlearning is getting increasing attention. Existing studies predominantly use training data, i.e., model inputs, as unlearning target. However, attackers can extract private information from the model even if it has not been explicitly encountered during training. We name this unseen information as attribute and treat it as unlearning target. To protect the sensitive attribute of users, Attribute Unlearning (AU) aims to make target attributes indistinguishable. In this paper, we focus on a strict but practical setting of AU, namely Post-Training Attribute Unlearning (PoT-AU), where unlearning can only be performed after the training of the recommendation model is completed. To address the PoT-AU problem in recommender systems, we propose a two-component loss function. The first component is distinguishability loss, where we design a distribution-based measurement to make attribute labels indistinguishable from attackers. We further extend this measurement to handle multi-class attribute cases with efficient computational overhead. The second component is regularization loss, where we explore a function-space measurement that effectively maintains recommendation performance compared to parameter-space regularization. We use stochastic gradient descent algorithm to optimize our proposed loss. Extensive experiments on four real-world datasets demonstrate the effectiveness of our proposed methods.

A stochastic algorithm for quantile regression models with fixed effects

In this paper, we present a stochastic algorithm for parameter estimation based on panel quantile regression model. We propose an easy-to-implement estimator based on the proposed algorithm. We profile the quantile-specific fixed effects as functions of the parameters of interest based on the Gaussian mixture representation of the asymmetric Laplace (AL) likelihood and eliminate the fixed effects through a data transformation. Parameters of interest can be estimated via quantile regression. Under a set of sufficient conditions, the proposed estimator is consistent and asymptotically normal when n and T both go to infinity. The proposed estimator is illustrated via both simulations and real data examples.

Stochastic golden ratio algorithm to non-convex stochastic mixed variational inequality problem

Stochastic golden ratio algorithm to non-convex stochastic mixed variational inequality problem

Development and Application of a Tornado Database for the Chinese Mainland

This study develops a preliminary tornado database for the Chinese mainland using information provided by the Yearbook of Meteorological Disasters in China (YMDC) from 2003 to 2019 and other public media report data. This database includes tornado occurrence time, geographical location, intensity, and damage descriptions. A modified Enhanced Fujita (EF) scale criterion adapted to the description of the damage indicator (DI) and degree of damage (DOD) in the YMDC and media reports is presented to better estimate the tornado intensity. The spatial and temporal distribution characteristics of tornadoes in Chinese mainland are examined. A stochastic simulation algorithm is proposed to perform a risk assessment of tornado hazards. The occurrence of tornadoes is randomly sampled using negative binomial distribution. The kernel density estimation (KDE) method based on the Gaussian kernel is applied to estimate the probability density of geographically dependent tornado occurrence before randomly generating tornado occurrence locations. The probability and conditional probability of tornado occurrence with different intensity levels are calculated for different counties in Jiangsu and Guangdong Provinces using Bayes’ theorem. The database provides a forward step toward rational assessment of tornado-induced disasters in Chinese mainland. The database can be accessed at https://doi.org/10.4121/19801633.v1 (Zhang et al., 2022).

The stochastic proximal distance algorithm

The stochastic proximal distance algorithm

Artificial Optimizer Algorithm for Power System Stabilizer design problem and multidisciplinary engineering applications

The novelty of this research lies in presenting a fresh stochastic algorithm enthused via ‘Velociraptor’ social intelligence in wildlife (or nature), known as the Velociraptor Group Optimization algorithm (VROA). In this strategy, ‘Velociraptor’ co-operative natural life cycle is mathematically framed, and novel mechanisms are presented to perform search (or exploration) and hunting (or exploitation). This suggests that the proposed method reveals a noteworthy ability in both exploitation and exploration. Furthermore, it successfully stabilities exploration and exploitation, supporting the search process. In the direction of evaluating the VROA, we utilized it on 51 CEC'17, CEC'20, and CEC'22 standard benchmark suites and six multidisciplinary engineering optimization functions. Furthermore, well-known statistical methods like Wilcoxon rank-sum test and Friedman's test have been used to verify the strength of the proposed algorithm against various optimizers. The tabulated numerical and statistical solutions show that VROA performs better than recent optimizers on most standard test suites and has efficiently attained the most competent resolution while concurrently upholding adherence to the designated constraints. The results validate that VROA can offer efficient and accurate optimal solutions in evaluation with recent metaheuristics.

On the Performance of the Minimax Optimal Strategy in the Stochastic Case of Logistic Bandits

The multi-armed bandit problem is a well-established model for examining the exploration/exploitation trade-offs in sequential decision-making tasks. This study focuses on the logistic bandit, where rewards are derived from two distinct datasets of movie ratings, ranging from 1 to 5, each characterized by different variances. Previous research has shown that regret bounds for multi-armed bandit algorithms can be unstable across varying environments. However, this paper provides new insights by demonstrating the robustness of the Minimax Optimal Strategy in the Stochastic (MOSS) algorithm across environments with differing reward variances. Unlike prior studies, this research shows that MOSS maintains superior performance in both dense and sparse reward settings, consistently outperforming widely used algorithms like UCB and TS, particularly in high variance conditions and over sufficient trials. The findings indicate that MOSS achieves logarithmic expected regret for both types of environments, effectively balancing exploration and exploitation. Specifically, with K arms and T time steps, the regret R(T) of MOSS is bounded by O((KT logT )). This work highlights MOSS as a robust solution for handling diverse stochastic conditions, filling a crucial gap in the understanding of its practical adaptability across different reward distributions.

Intraspecific predator interference promotes biodiversity in ecosystems.

Explaining biodiversity is a fundamental issue in ecology. A long-standing puzzle lies in the paradox of the plankton: many species of plankton feeding on a limited variety of resources coexist, apparently flouting the competitive exclusion principle (CEP), which holds that the number of predator (consumer) species cannot exceed that of the resources at a steady state. Here, we present a mechanistic model and demonstrate that intraspecific interference among the consumers enables a plethora of consumer species to coexist at constant population densities with only one or a handful of resource species. This facilitated biodiversity is resistant to stochasticity, either with the stochastic simulation algorithm or individual-based modeling. Our model naturally explains the classical experiments that invalidate the CEP, quantitatively illustrates the universal S-shaped pattern of the rank-abundance curves across a wide range of ecological communities, and can be broadly used to resolve the mystery of biodiversity in many natural ecosystems.

Intraspecific predator interference promotes biodiversity in ecosystems

Explaining biodiversity is a fundamental issue in ecology. A long-standing puzzle lies in the paradox of the plankton: many species of plankton feeding on a limited variety of resources coexist, apparently flouting the competitive exclusion principle (CEP), which holds that the number of predator (consumer) species cannot exceed that of the resources at a steady state. Here, we present a mechanistic model and demonstrate that intraspecific interference among the consumers enables a plethora of consumer species to coexist at constant population densities with only one or a handful of resource species. This facilitated biodiversity is resistant to stochasticity, either with the stochastic simulation algorithm or individual-based modeling. Our model naturally explains the classical experiments that invalidate the CEP, quantitatively illustrates the universal S-shaped pattern of the rank-abundance curves across a wide range of ecological communities, and can be broadly used to resolve the mystery of biodiversity in many natural ecosystems.

A design strategy with the combination of neuro-regression and stochastic optimizations on the hyperelastic gasket

For numerous years, PVC and aluminum doors and windows have been integral components of buildings. The primary technical requisites for doors and windows encompass superior acoustic performance, thermal insulation, and effective sealing. Particularly, the sealing properties, crucially important, are ensured by the gaskets fitted onto the profiles. This paper aims to present a gasket design with a new methodology that includes a systematic modeling-optimization process based on multiple non-linear neuro-regression. Comprehensive research has been done by multiple non-linear neuro-regression analyses of gaskets due to deficient studies in the literature on hyperelastic materials. 17 candidate functional forms based on four basic mathematical structures (polynomial, trigonometric, logarithmic, and linear functions, and their hybrid or rational forms) have been proposed to model the FEM data of the gasket. Hybrid versions of three stochastic search algorithms, Differential Evolution, Random Search, and Simulated Annealing, are considered to solve highly non-linear, non-convex, multi-variables mixed continuous-discrete problems. The experimental results were compared with the numerical result using the finite-element analysis (FEA). Nonlinear static analyses were performed with Abaqus. Stress and logarithmic strain distributions are obtained. A good correlation was found between the experimental and the numerical results The optimum locations and numbers of the nodes have been found to obtain the minimum overflow distance and the maximum compression surface area for gaskets having the same topological structure.

A new stochastic global algorithm for critical load optimization of dome trusses

A new stochastic global algorithm for critical load optimization of dome trusses

Automated Machine Learning for Optimized Load Forecasting and Economic Impact in the Greek Wholesale Energy Market

This study investigates the use of automated machine learning to forecast the demand of electrical loads. A stochastic optimization algorithm minimizes the cost and risk of the traded asset across different markets using a generic framework for trading activities of load portfolios. Assuming an always overbought condition in the Day-Ahead as well as in the Futures Market, the excess energy returns without revenue to the market, and the results are compared with a standard contract in Greece, which stands as the lowest as far as the billing price is concerned. The analysis achieved a mean absolute percentage error (MAPE) of 12.89% as the best fitted model and without using any kind of pre-processing methods.

Telescope Alignment Method Using a Modified Stochastic Parallel Gradient Descent Algorithm

To satisfy the demands of high image quality and resolutions, telescope alignment is indispensable. In this paper, a wavefront sensorless method based on a modified stochastic parallel gradient descent algorithm (SPGD) called the adaptive moment estimation SPGD (Adam SPGD) algorithm is proposed. Simulations are carried out using a four-mirror telescope, whose aperture is 6 m and fields of view are Φ2°. Three misalignments are shown as examples. Positions of the secondary mirror and third mirror are employed to compensate aberrations. The results show that merit functions and energy distributions of corrected images match with the designed ones. The mean RMS of residual wavefront errors is smaller than λ/14 (λ = 0.5 μm), indicating that the misalignments are well compensated. The results verify the effectiveness of our method.

Statement of Retraction: Convergence in quadratic mean of averaged stochastic gradient algorithms without strong convexity nor bounded gradient

Statement of Retraction: Convergence in quadratic mean of averaged stochastic gradient algorithms without strong convexity nor bounded gradient

Optimization of Load-transfer Functions for a Large-diameter Pile in Multi-layered Geological Conditions via a Stochastic Search Algorithm

The paper presents the combination of the load transfer method (computational model) and the genetic algorithm (optimization model) for the automated inverse analysis of instrumented pile load tests. The output of this process are the input parameters governing the shape of the load-transfer functions and thus the prediction accuracy when the load-transfer method is used as a design tool for deep foundations. The optimization problem is converted into an unconstrained task by applying the static penalty approach. Two types of measurements are considered in a newly proposed objective function: the load-displacement curve monitored in a pile head and the axial force profiles along a pile derived from strain gauges. Firstly, the local sensitivity analysis via the Design of Experiments is carried out to identify the parameters of the genetic algorithm which significantly influences the rate of convergence during the optimization process. Subsequently, a fully automated inverse analysis of the loading test of the large-diameter bored pile in multilayered geological conditions is presented. The simultaneous combination of two instrumentation sources leads to a stable unique solution with a sufficient match between the prediction and measurements despite a larger number of unknown – optimized variables.