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In this paper, we investigate a fully discrete approximation of stochastic diffusion-wave equation driven by additive tempered fractional Gaussian noise. This additive noise exhibits semi-long range dependence. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative and a tempered fractional Brownian motion. The space discretization is achieved via the spectral Galerkin method. The Caputo fractional derivative of order α ∈ (1 , 2) is approximated by using the Grünwald–Letnikov formula. Combining Mittag-Leffler function, Laplace transform and z -transform, we establish the error estimates of the full discretization in the sense of mean-squared L 2 -norm. Numerical experiments are presented to confirm the strong convergence rates. [ABSTRACT FROM AUTHOR]

In this paper, we devise a stochastic extragradient-like algorithm incorporated with inertial terms, which requires a single projection onto our feasible set and employs a stochastic approximation version of an Armijo-type line search scheme along a feasible direction, for solving pseudomonotone stochastic variational inequalities. In the algorithm, two different stepsize strategies are employed to update steplength sequences without using the prior knowledge of the Lipschitz constant of involved operators. In the process of the stochastic approximation, we iteratively reduce the variance of stochastic errors. The almost sure convergence, the complexity analysis, and rates are provided in a dimensional space under reasonable conditions. Finally, some numerical experiments with graphical illustrations are reported to demonstrate the applicability and the efficiency of our algorithm in comparison with some projection type methods in the literature. [ABSTRACT FROM AUTHOR]

We propose a new class of weak approximation schemes for stochastic differential equations with coefficients of suplinearly growth. Both the modified weak Euler schemes and the drift-implicit weak Euler scheme are studied. Under certain non-globally Lipschitz conditions, the proposed schemes are proved to have first-order convergence in the weak sense. Numerical experiments are included to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

We investigate existence, uniqueness and approximation of solutions to stochastic delay differential equations (SDDEs) under Carathéodory-type drift coefficients. Moreover, we also assume that both drift f = f (t , x , z) and diffusion g = g (t , x , z) coefficient are Lipschitz continuous with respect to the space variable x , but only Hölder continuous with respect to the delay variable z. We provide a construction of randomized Euler scheme for approximation of solutions of Carathéodory SDDEs, and investigate its upper error bound. Finally, we report results of numerical experiments that confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

This work is dedicated to the leaderless/leader-following stochastic scaled consensus issue of second-order stochastic multi-agent systems (SMASs) in a noisy environment. Scaled consensus represents that the ratios among agents asymptotically tend to designated constants rather than the common convergence value. To lessen the influence of communication noise, some stochastic approximation protocols with time-varying gain are designed for our underlying system, where the time-varying gain remove the restriction of nonnegative value. Compared with the existing consensus results with communication noise, the major challenge is that the introduction of time-varying gain results in the inapplicability of Lyapunov-based technique. To cope with it, a state decomposition method is utilized, and a series of sufficient necessary conditions are set up for interacting agents with constant velocity and zero velocity if the topology includes a spanning tree. Furthermore, it is conducted that the consensus and bipartite consensus can be seen as two special cases of our work. Finally, the validity of our results is demonstrated by a simulation example. • The derived theoretical results are capable for leaderless and leader-following scaled consensus of second-order SMASs, despite the presence of communication noise. • A time-varying gain is utilized to reduce the negative impact of communication noise, and the time-varying gain removes the restriction of positive time-varying gain. • Moreover, we consider the scaled consensus models without or with a negative velocity feedback. We find that the negative velocity feedback does not affect the convergence of the velocity. [ABSTRACT FROM AUTHOR]

We introduce a variant of the multiplicative Sewing Lemma in [Gerasimovičs, Hocquet, Nilssen; J. Funct. Anal. 281 (2021)] which yields arbitrary high order weak approximations to stochastic differential equations, extending the cubature approximation on Wiener space introduced by Lyons and Victoir. Our analysis allows to derive stability estimates and explicit weak convergence rates. As a particular example, a cubature approximation for stochastic differential equations driven by continuous Gaussian martingales is given. [ABSTRACT FROM AUTHOR]

• The irreversible order-based encoding used in cancelable biometric templates is reversible using IPSA-M. • IPSA-M can exploit the vulnerability of cancelable systems built on different modalities. • Countermeasures using non-uniform quantization can alleviate the effect of the IPSA-M. • Attack efficacy comparison shows that IPSA-M is efficient and practical compared to other methods. Researchers have been proposing different matching frameworks for cancelable template design to improve the matching performance and security of biometric authentication systems. Despite the advantages provided by these systems, they are often vulnerable to different attacks due to their templates' invertible nature. This study utilized an iterative perturbation stochastic approximation procedure to analyze the irreversible order-based encoding approach used in cancelable biometric template transformation. The strategy begins by exploiting the scores corresponding to the encoded words, then a mixed variable-based iterative perturbation is used to generate independent random elements and consequently the corresponding template from the scores. The strategy exploits the vulnerability of three different cancelable systems it has tested, demonstrating that other techniques of similar nature fall short of the security standard for attack mitigation that cancelable biometric systems require. After analyzing the reasons that exploit the system's vulnerability, we use a parameterized thresholding non-uniform quantization as a countermeasure to boost the system's robustness while maintaining a balanced performance-security trade-off. As a result, the system can evade attacks without significantly hindering its matching performance. Finally, generality and computational complexity evaluations on different modalities and strategies validate the attack's efficacy and realism, respectively. [ABSTRACT FROM AUTHOR]

We consider two interacting random walks on Z such that the transition probability of one walk in one direction decreases exponentially with the number of transitions of the other walk in that direction. The joint process may thus be seen as two random walks reinforced to repel each other. The strength of the repulsion is further modulated in our model by a parameter β ≥ 0. When β = 0 both processes are independent symmetric random walks on Z , and hence recurrent. We show that both random walks are further recurrent if β ∈ (0 , 1 ]. We also show that these processes are transient and diverge in opposite directions if β > 2. The case β ∈ (1 , 2 ] remains widely open. Our results are obtained by considering the dynamical system approach to stochastic approximations. [ABSTRACT FROM AUTHOR]

In this paper, the bipartite consensus problem for second-order multi-agent systems with no leader, one leader and multiple leaders are investigated, where the information exchange is disturbed by measurement noise and antagonistic information. In order to attenuate the effect of communication noise, a time-varying gain c (t) is utilized and the stochastic approximation bipartite control protocol is proposed. It is given that the underlying protocol can solve the bipartite consensus problem for MASs with no leader/one leader/multiple leaders if the communication topology is strongly connected/has a spanning tree/has a spanning forest and the c (t) satisfies some mild condition. Meanwhile, for system with these three cases, a series of sufficient and necessary conditions are given. Especially, for the case with no leader, we obtain that the final state of agent is related with the initial position and initial velocity of each agent. For the case with one leader, we can get that the followers in one group can follow up the state of one leader, and the followers in another group tend to the opposite value. Additionally, for the case with multiple leaders, the containment control can be achieved where followers' states in one group can converge to the quai-convex hull of leaders' state and the ones in another group converge to the opposite convex hull. Finally, some numerical examples are given to support our new results. [ABSTRACT FROM AUTHOR]

This paper establishes the strong convergence of the tamed Euler–Maruyama (EM) approximation for McKean–Vlasov stochastic differential equations (SDEs) with super-linear drift and Hölder diffusion coefficients. By the Yamada-Watanable technique, this paper deals with the Hölder diffusion coefficient. To obtain the desired approximation, this paper also proves the existence and uniqueness of strong solution for this class of McKean-Vlasov SDEs. When one-sided local Lipschitz condition is replaced by the global condition, the convergence rate can be obtained. Finally, two examples are presented to illustrate our results. [ABSTRACT FROM AUTHOR]

Bayesian response adaptive clinical trials are currently evaluating experimental therapies for several diseases. Adaptive decisions, such as pre-planned variations of the randomization probabilities, attempt to accelerate the development of new treatments. The design of response adaptive trials, in most cases, requires time consuming simulation studies to describe operating characteristics, such as type I/II error rates, across plausible scenarios. We investigate large sample approximations of pivotal operating characteristics in Bayesian Uncertainty directed trial Designs (BUDs). A BUD trial utilizes an explicit metric u to quantify the information accrued during the study on parameters of interest, for example the treatment effects. The randomization probabilities vary during time to minimize the uncertainty summary u at completion of the study. We provide an asymptotic analysis (i) of the allocation of patients to treatment arms and (ii) of the randomization probabilities. For BUDs with outcome distributions belonging to the natural exponential family with quadratic variance function, we illustrate the asymptotic normality of the number of patients assigned to each arm and of the randomization probabilities. We use these results to approximate relevant operating characteristics such as the power of the BUD. We evaluate the accuracy of the approximations through simulations under several scenarios for binary, time-to-event and continuous outcome models. [ABSTRACT FROM AUTHOR]

This paper studies a Gaussian process approximation for a class of stochastic traffic flow models. It can be used to efficiently and accurately evaluate the joint (in the spatial and temporal sense) distribution of vehicle-density distributions in road traffic networks of arbitrary topology. The Gaussian approximation follows, via a scaling-limit argument, from a Markovian model that is consistent with discrete-space kinematic wave models. We describe in detail how this formal result can be converted into a computational procedure. The performance of our approach is demonstrated through a series of experiments that feature various realistic scenarios. Moreover, we discuss the computational complexity of our approach by assessing how computation times depend on the network size. We also argue that the (debatable) assumption that the vehicles' headways are exponentially distributed does not negatively impact the accuracy of our approximation. • A Gaussian method to evaluate the joint distribution of vehicles in traffic networks. • Detailed implementation guidelines. • Numerical examples demonstrating the use of the methodology in realistic scenarios. • A demonstration of the methodology's low computational complexity. • Relaxation of assumptions underlying the theory to include more realistic dynamics. [ABSTRACT FROM AUTHOR]

We introduce a class of Markov chains that includes models of stochastic approximation by averaging and non-averaging. Using a martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions of such a chain, with different moment conditions on some dominating random variables of martingale differences. Finally, we apply these inequalities to stochastic approximation by averaging and empirical risk minimization. [ABSTRACT FROM AUTHOR]

This paper develops a two-stage stochastic model to investigate the evolution of random fields on the unit sphere S 2 in R 3. The model is defined by a time-fractional stochastic diffusion equation on S 2 governed by a diffusion operator with a time-fractional derivative defined in the Riemann–Liouville sense. In the first stage, the model is characterized by a homogeneous problem with an isotropic Gaussian random field on S 2 as an initial condition. In the second stage, the model becomes an inhomogeneous problem driven by a time-delayed Brownian motion on S 2. The solution to the model is given in the form of an expansion in terms of complex spherical harmonics. An approximation to the solution is given by truncating the expansion of the solution at degree L ≥ 1. The rate of convergence of the truncation errors as a function of L and the mean square errors as a function of time are also derived. It is shown that the convergence rates depend not only on the decay of the angular power spectrum of the driving noise and the initial condition, but also on the order of the fractional derivative. We study sample properties of the stochastic solution and show that the solution is an isotropic Hölder continuous random field. Numerical examples and simulations inspired by the cosmic microwave background (CMB) are given to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

Coupled multi-physics simulations play a crucial role in the design and operation of nuclear reactors, particularly in assessing the behavior of used nuclear fuel. This study focuses on exploring the efficacy of coupled calculations for used nuclear fuel through the integration of neutron transport and thermal-hydraulics codes. Neutronics calculations were conducted using the Monte Carlo code Serpent, while thermal-hydraulic calculations utilized the Computational Fluid Dynamics (CFD) software OpenFOAM. The investigation was focused on a VVER-440 fuel pin situated in a hexagonal coolant flow area. Three computational grids were generated, containing 0.15 million, 0.39 million, and 1.1 million computational cells, along with three variants of axial material refinement featuring 42, 21, and 10 material layers. The purpose was to analyze the impact of spatial refinement on key parameters such as multiplication factor, power flux, and temperature fields. Several relaxation factors in Picard iterations were systematically compared to enhance the convergence speed of the coupling procedure. Notably, simulations without relaxation (α = 1) resulted in oscillations in predicted results, while a low value of α led to slow convergence. The investigation revealed that employing a stochastic approximation with a varying relaxation factor coupled with a varying number of simulated particles demonstrated superior performance compared to cases with a constant relaxation factor α or a stochastic approximation with a constant number of simulated particles. Furthermore, it was observed that the resolution of axial fuel segmentation significantly influenced predicted multiplication factor k i n f and temperature profiles. Interestingly, the spatial resolution of the computational grid exhibited minimal impact on the predicted results. • CFD code OpenFOAM and Monte Carlo neutron transport code Serpent were coupled. • Relaxation of power flux improved the simulation convergence. • The stochastic approximation converged faster than the fixed number of neutrons case. • Axial segmentation of material input had a significant effect on predicted results. [ABSTRACT FROM AUTHOR]

This article investigates an event-triggered strategy to deal with the bipartite consensus issue for stochastic multiagent systems (SMASs) in a communication noisy environment. The communication network can be modeled by a random signed graph and the communication noise is compound noises (additive noise and multiplicative noise). The stochastic event-triggered bipartite consensus control protocol for SMASs with compound noises is presented by the stochastic approximation (SA) method. Due to the control gain is time-varying and agent-dependent, the implementation of event-triggered control protocol may cause out-sync of the control gain. Meanwhile, the coexistence of stochastic antagonistic information and compound noises causes it hard to turn the noises term into an error equation, which leads to the fact that the traditional error transition method is invalid for our underlying system. To deal with these challenges, the state's boundedness for each agent is first constructed by the Lyapunov method, and then the event-triggered bipartite consensus can be demonstrated via a new semi-decomposition technique. Finally, the effectiveness of the proposed SA controller is verified by two examples. [ABSTRACT FROM AUTHOR]

Consensus of networked nonlinear nonparametric time-varying systems is studied, and the nonlinearity at input may possess arbitrary growth rate. In addition, the communication noise is also under consideration. The purely distributed control algorithm is designed on the basis of distributed stochastic approximation algorithm with expanding truncations (DSAAWET). The truncation mechanism neutralizes the divergent tendency caused by unknown nonlinearities and noises, which makes the algorithm well tackle more general nonlinearities with high growth rate and more complicated structure noises. We first prove the average consensus over fixed digraph, and then extend the results to averagely connected time-varying digraphs. Finally, the validity of the algorithm is justified by numerical simulations. [ABSTRACT FROM AUTHOR]

We consider the situation where multiple transportation service providers cooperate to offer an integrated multi-modal platform to enhance the convenience to the passengers through ease in multi-modal journey planning, payment, and first and last mile connectivity. This market structure allows the multi-modal platform to coordinate profits across modes and also provide incentives to the passengers. Accordingly, in this paper, we use cooperative game theory coupled with the hyperpath-based stochastic user equilibrium framework to study such a market. We assume that the platform sets incentives (price discount or excess charge on passengers) along every edge in the transportation network. We derive the continuity and monotonicity properties of the equilibrium flow with respect to the incentives along every edge. The optimal incentives that maximize the profit of the platform are obtained through a two time-scale stochastic approximation algorithm. We use the asymmetric Nash bargaining solution to design a fair profit sharing scheme among the service providers. We show that the profit for each service provider increases after cooperation on such a platform. Finally, we complement the theoretical results through two numerical simulations. [ABSTRACT FROM AUTHOR]

Active Disturbance Rejection Control (ADRC) emerges as a promising control method that can effectively handle uncertainties and disturbances. However, many model-based ADRC tuning methods turn laborious to achieve satisfactory control performance, when the critical process parameters are difficult to accurately obtain, especially the time delay information. To this end, this paper aims to propose a data-driven iterative tuning method for time-delayed ADRC (TD-ADRC). Based on parameter scaling technique, the quantitative correlation among control performance, robustness and normalized controller parameters are investigated. It is then used to design robust nominal controller. Then, based on the TD-ADRC inner-loop equivalent structure, an iterative feedback tuning (IFT) method is proposed to optimally obtain the nominal first order plus time delay (FOPTD) process model. Its unbiasedness and convergence are also described. With the empirical relations and the IFT stochastic approximation algorithm, a data-driven iterative tuning method for TA-ADRC is proposed, which allows a reasonable trade-off between system performance and robustness. Simulation results validate the efficacy of the proposed method, and a water-tank control experiment depicts a promising prospect in control practice. • A data-driven iterative tuning method for time-delayed ADRC is proposed considering both control performance and robustness. • An unbiased gradient estimate with respect to the model parameters under noise conditions is derived. • Control parameters are tuned iteratively through a data-driven method: iterative feedback tuning method. [ABSTRACT FROM AUTHOR]

We describe a model for m vertex reinforced interacting random walks on complete graphs with d ≥ 2 vertices. The transition probability of a random walk to a given vertex depends exponentially on the proportion of visits made by all walks to that vertex. The individual proportion of visits is modulated by a strength parameter that can be set equal to any real number. This model covers a large variety of interactions including different vertex repulsion and attraction strengths between any two random walks as well as self-reinforced interactions. We show that the process of empirical vertex occupation measures defined by the interacting random walks converges (a.s.) to the limit set of the flow induced by a smooth vector field. Further, if the set of equilibria of the field is formed by isolated points, then the vertex occupation measures converge (a.s.) to an equilibrium of the field. These facts are shown by means of the construction of a strict Lyapunov function. We show that if the absolute value of the interaction strength parameters are smaller than a certain upper bound, then, for any number of random walks (m ≥ 2) on any graph (d ≥ 2), the vertex occupation measures converge towards a unique equilibrium. We provide two additional examples of repelling random walks for the cases m = d = 2 and m ∈ { 3 , 4 , 5 } with d = 2. The latter is used to study some properties of three, four and five exponentially repelling random walks on Z. [ABSTRACT FROM AUTHOR]

The location verification of the vehicles interacting during the process of communication needs to be cooperatively determined under Non Line Of Sight (NLOS) situations for facilitating risk free environment with the least degree of congestion. The vehicular nodes in NLOS conditions possess the possibility of introducing channel congestion and broadcast storm into the network either intentionally or unintentionally during the event of emergency message dissemination in the vehicular network. Thus, the NLOS vehicular nodes of the network need to be detected through direct interaction and neighbourhood collaboration such that the rate of emergency message dissemination is sustained to the maximum degree. In this paper, a Rank Criteria Improved Confidence-based Centroid Scheme (RCICCS) is proposed for potential localization of NLOS nodes. This proposed RCICCS scheme uses an integrated cost, computed using the primitive cost and penalty cost in order to increase the effectiveness in localizing NLOS nodes. Thus effective location of NLOS nodes is determined based on rank criterion-based neighbor confidence measure that are iteratively enhanced during the process of perturbation using the method of gradients. The experimental analysis of the proposed RCICCS scheme confirmed a remarkable enhancement rate of emergency message delivery and neighbourhood awareness under NLOS conditions. [ABSTRACT FROM AUTHOR]

We perform a stochastic model reduction of the Kuramoto–Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant order parameter, finite-size networks exhibit persistent temporal fluctuations of the order parameter. These fluctuations are caused by the interaction of the synchronised oscillators with the non-entrained oscillators. We present numerical results suggesting that the collective effect of the non-entrained oscillators on the synchronised cluster can be approximated by a Gaussian process. This allows for an effective closed evolution equation for the synchronised oscillators driven by a Gaussian process which we approximate by a two-dimensional Ornstein–Uhlenbeck process. Our reduction reproduces the stochastic fluctuations of the order parameter and leads to a simple stochastic differential equation for the order parameter. • We reduce the deterministic dynamics of coupled oscillators to a self-consistent stochastic model for the synchronised oscillators. • The effect of the non-entrained rogue oscillators is modelled by an effective Gaussian process. • Fluctuations of the order parameter are described by coloured noise rather than Brownian motion. [ABSTRACT FROM AUTHOR]

This paper studies the decentralized stochastic optimization problem over an undirected network, where each agent owns its local private functions made up of two non-smooth functions and an expectation-valued function. A decentralized stochastic primal–dual algorithm is proposed, by combining the variance-reduced method and the stochastic approximation method. The local gradients are estimated by using the mean of a variable number of sample gradients and the stochastic error decreases with the number of samples in the stochastic approximation process. The highlight of this paper is the extension of the primal–dual algorithm to the stochastic optimization problems. The effectiveness of the proposed algorithm and the correctness of the theory are verified by numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we study the numerical approximation to stochastic differential equations with positive solutions. Inspired by the logarithmic truncated Euler–Maruyama method developed by Yi et al. (2021) and Lei et al. (2023), we construct a novel numerical method, called the positivity preserving logarithmic transformed truncated Milstein method, for the efficient solution of the underlying equation. Under certain assumptions, we prove the exponential integrability of the numerical solutions. On this basis, we further obtain the strong convergence and strong convergence rate of order 1 for the presented method under additional conditions. Especially, this method is applied to the stochastic tumor model with Allee effect. Several numerical experiments are performed to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we investigate explicit numerical approximations for stochastic differential delay equations (SDDEs) under a local Lipschitz condition by employing the adaptive Euler-Maruyama (EM) method. Working in both finite and infinite horizons, we achieve strong convergence results of the adaptive EM solution. We also obtain the order of convergence in finite horizon. In addition, we show almost sure exponential stability of the adaptive approximate solution for both SDEs and SDDEs. [ABSTRACT FROM AUTHOR]

In this paper, we consider low-rank approximations for the solutions to the stochastic Helmholtz equation with random coefficients. A Stochastic Galerkin finite element method is used for the discretization of the Helmholtz problem. Existence theory for the low-rank approximation is established when the system matrix is indefinite. The low-rank algorithm does not require the construction of a large system matrix which results in an advantage in terms of CPU time and storage. Numerical results show that, when the operations in a low-rank method are performed efficiently, it is possible to obtain an advantage in terms of storage and CPU time compared to computations in full rank. We also propose a general approach to implement a preconditioner using the low-rank format efficiently. [ABSTRACT FROM AUTHOR]

Full utilization of the potential regulation ability of flexible loads in an integrated energy system (IES) and expanding its structure for more flexibility via integrating auxiliary devices is the key to realizing its high-efficiency operation and high-proportion renewable consumption. The present paper builds the flexible regulation models of thermal and electrical loads and introduces them to the structure expansion planning of IES. A two-stage stochastic probability optimization method integrating the uncertain operation of introducing flexible loads is then proposed to balance the additional costs of device integration and the benefits of performance promotion. Herein, an enhanced sample average approximation based on a stochastic hierarchy scenario generation method is developed to solve the optimization. The regulation mechanisms of flexible loads and their influence on expansion planning are then analyzed by comparing the optimized results. The results show that the path to decreasing the cost via introducing flexible thermal and electrical loads into optimization is increasing renewable consumption and coordinating an increment in renewable consumption and average electrical efficiency, respectively. The regulation between them has synergism on cost reduction and saturation on increasing renewable consumption. The synergism can reduce the cost by 0.62 %. Besides, there is a synergism between electric boiler integration and flexible loads, which further reduces the total cost of the expanded IES by 24.86 %. [Display omitted] [ABSTRACT FROM AUTHOR]

Sample efficiency is a limiting factor for existing distributed multi-agent reinforcement learning (MARL) algorithms over networked multi-agent systems. In this paper, the sample efficiency problem is tackled by formally incorporating the entropy regularization into the distributed MARL algorithm design. Firstly, a new entropy-regularized MARL problem is formulated under the model of networked multi-agent Markov decision processes with observation-based policies and homogeneous agents, where the policy parameter sharing among the agents provably preserves the optimality. Secondly, an on-policy distributed actor–critic algorithm is proposed, where each agent shares its parameters of both the critic and actor for consensus update. Then, the convergence analysis of the proposed algorithm is provided based on the stochastic approximation theory under the assumption of linear function approximation of the critic. Furthermore, a practical off-policy version of the proposed algorithm is developed which possesses scalability, data efficiency and learning stability. Finally, the proposed distributed algorithm is compared against the solid baselines including two classic centralized training algorithms in the multi-agent particle environment, whose learning performance is empirically demonstrated through extensive simulation experiments. [ABSTRACT FROM AUTHOR]

This paper studies the behavior of solitons in the Korteweg–de Vries equation under the influence of multiplicative noise. We introduce stochastic processes that track the amplitude and position of solitons based on a rescaled frame formulation and stability properties of the soliton family. We furthermore construct tractable approximations to the stochastic soliton amplitude and position which reveal their leading-order drift. We find that the statistical properties predicted by our method agree well with numerical evidence. [ABSTRACT FROM AUTHOR]

• Propose a novel data-driven, model-free framework. • Development of a hybrid knowledge-guided improved simultaneous perturbation stochastic approximation algorithm. • Validation of the effectiveness and efficiency of the proposed method in a systematic way. Steam generator level control systems play a crucial role in ensuring safe, economical, and stable operation of nuclear power plants. However, traditional control systems exhibit limited efficiency in commissioning and are susceptible to human error. Additionally, traditional parameter tuning methods are typically experienced-based, cumbersome, and time-consuming, making it challenging to obtain optimal parameters. To address these issues, we propose a hybrid knowledge-guided improved simultaneous perturbation stochastic approximation algorithm (HK-SPSA) to optimize the control parameters of steam generator level control systems. Firstly, the algorithm utilizes iteration point adjacency information to approximate the current optimization process status and guide the adaptive adjustment of the iteration step size. Secondly, it utilizes composite gradient information generated by the estimated historical and current gradients to guide the optimization direction and the tuning of iteration step size. Simulation experiments have shown that HK-SPSA improves optimization performance and reduces the costs of optimization and adjustment compared to traditional methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a stochastic gradient algorithm for minimizing a smooth objective function that is an expectation over noisy cost samples and only the latter are observed for any given parameter. Our algorithm employs a gradient estimation scheme with random perturbations obtained from the truncated Cauchy distribution. We analyze the bias and variance of the proposed gradient estimator. Our algorithm is found to be particularly useful in the case when the objective function is non-convex and the parameter dimension is high. From an asymptotic convergence analysis, we establish that our algorithm converges almost surely to the set of stationary points of the objective function. Further, the asymptotic convergence rate of our algorithm is better than Gaussian smoothed functional (GSF) and simultaneous perturbation stochastic approximation (SPSA), which are two popular algorithms that employ random perturbations for gradient estimation. We also show that our algorithm avoids unstable equilibria and thereby converges to local minima. In addition, we establish a non-asymptotic bound for our algorithm toward finding a stationary point of the non-convex objective function. [ABSTRACT FROM AUTHOR]

We consider stochastic algorithms derived from methods for solving deterministic optimization problems, especially comparison-based algorithms derived from stochastic approximation algorithms with a constant step-size. We develop a methodology for proving geometric convergence of the parameter sequence { θ n } n ⩾ 0 of such algorithms. We employ the ordinary differential equation (ODE) method, which relates a stochastic algorithm to its mean ODE, along with a Lyapunov-like function Ψ such that the geometric convergence of Ψ (θ n) implies – in the case of an optimization algorithm – the geometric convergence of the expected distance between the optimum and the search point generated by the algorithm. We provide two sufficient conditions for Ψ (θ n) to decrease at a geometric rate: Ψ should decrease "exponentially" along the solution to the mean ODE, and the deviation between the stochastic algorithm and the ODE solution (measured by Ψ) should be bounded by Ψ (θ n) times a constant. We also provide practical conditions under which the two sufficient conditions may be verified easily without knowing the solution of the mean ODE. Our results are any-time bounds on Ψ (θ n) , so we can deduce not only the asymptotic upper bound on the convergence rate, but also the first hitting time of the algorithm. The main results are applied to a comparison-based stochastic algorithm with a constant step-size for optimization on continuous domains. [ABSTRACT FROM AUTHOR]

We are interested in finding an approximation for the solution of stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm) with Hurst parameter H > 1 2. Based on Taylor expansion we derive a numerical scheme and investigate its convergence. Under some assumptions on drift and diffusion, we show that the introduced method is convergent with strong rate of convergence Δ H , where Δ is the diameter of partition used for discretization. In addition, we explain the simulation of the proposed method and show the accuracy of our results by presenting an example. [ABSTRACT FROM AUTHOR]

We consider a design problem where experimental conditions (design points X i) are presented in the form of a sequence of i.i.d. random variables, generated with an unknown probability measure μ , and only a given proportion α ∈ (0 , 1) can be selected. The objective is to select good candidates X i on the fly and maximize a concave function Φ of the corresponding information matrix. The optimal solution corresponds to the construction of an optimal bounded design measure ξ α ∗ ≤ μ ∕ α , with the difficulty that μ is unknown and ξ α ∗ must be constructed online. The construction proposed relies on the definition of a threshold τ on the directional derivative of Φ at the current information matrix, the value of τ being fixed by a certain quantile of the distribution of this directional derivative. Combination with recursive quantile estimation yields a nonlinear two-time-scale stochastic approximation method. It can be applied to very long design sequences since only the current information matrix and estimated quantile need to be stored. Convergence to an optimum design is proved. Various illustrative examples are presented. • A two-time-scale stochastic approximation scheme is used for the on-line selection of experimental points. • Any classical design criterion (concave function of the information matrix) can be used. • The optimal solution corresponds to the construction of an optimal bounded design measure. • Arbitrarily long sequences of points can be considered, as only the current information matrix and an estimated quantile of a directional derivative need to be stored. [ABSTRACT FROM AUTHOR]

This article aims to investigate the pathwise convergence of the higher order scheme, introduced by Jentzen (2011) [9] , for the stochastic Burgers' equation (SBE) driven by space-time white noise. In particular, first and second order derivatives of the non-linear drift term of the SBE are assumed to be defined and bounded in Sobolev spaces using the definition of distribution derivative i.e. Lemma 4.7 in Blömker and Jentzen (2013) [2] is extended. Based on this extension, temporal convergence analysis of the higher order scheme is carried out for the SBE with additive noise. As a result, minimum temporal convergence order is improved from θ (Theorem 4.1 in Blömker et al. (2013) [3]) to 2 θ , where every θ ∈ (0 , 1 2)). Numerical experiments are performed to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

In the realm of ant foraging studies, researchers commonly map the movement of ant colonies to Markov Chain Monte Carlo (MCMC) models based on the probability matching strategy, aiming to achieve optimal foraging outcomes. When faced with multiple resources, ants often exhibit remarkable flexibility by patrolling over the foraging area and maximizing resource utilization. However, the regular MCMC models face challenges when resources are multimodally distributed as they struggle to efficiently explore the state space, particularly when modes are distantly separated. Building upon the existing partial momentum refreshment model, we propose a stochastic approximation partial momentum refreshment (SAPMR) model that not only performs equally well as regular MCMC models in bimodal distributions featuring two closely located modes but also overcomes energy barriers associated with multimodal distributions characterized by distantly separated modes. The synthetic data generated using SAPMR exhibits characteristics reminiscent of ants' behavior such as Lévy-like patterns and maintaining a constant scaling function (≈ 1) when examining the relationship between the rescaled event speed and the rescaled time. • A stochastic approximation partial momentum refreshment (SAPMR) model is proposed for simulating ants' walk in patrolling multiple resources. • The convergence of SAPMR is provided. • The synthetic data created by SAPMR possesses "ant-like" characteristics. [ABSTRACT FROM AUTHOR]

Since it is difficult to implement implicit schemes on the infinite-dimensional space, we aim to develop the explicit numerical method for approximating super-linear stochastic functional differential equations (SFDEs). Precisely, borrowing the truncation idea and linear interpolation we propose an explicit truncated Euler–Maruyama (EM) scheme for SFDEs, and obtain the boundedness and convergence in L p (p ≥ 2). We also prove the convergence rate with 1 / 2 order. Different from some previous works (Mao, 2003; Zhang et al., 2018), we release the global Lipschitz restriction on the diffusion coefficient. Furthermore, we reveal that numerical solutions preserve the underlying exponential stability. Moreover, we give several examples to support our theory. [ABSTRACT FROM AUTHOR]

We consider strong convergence of numerical approximations for a stochastic strongly damped wave equation driven by a class of additive space–time noises characterized by a parameter β ∈ (− 1 , 2 ]. With the help of the Wong–Zakai (WZ) approximation to the noise, i.e., replacing the driven noise with its finite spectral expansion truncation, we obtain an approximate equation. Based on the consistency and high regularity of the approximate equation, we develop two exponential integrators for time-stepping discretization and use the spectral Galerkin method in space to develop full-discrete schemes. Performing error estimates in the strong sense, we show that the optimal strong order in time of the proposed WZ-approximation-based exponential Euler scheme is min { 1 , 1 + β / 2 − ϵ } , which is | β | / 2 order higher than the order of min { 1 , 1 + β } in the existing works when β ∈ (− 1 , 0). Moreover, we prove that the proposed WZ-approximation-based exponential trapezoidal scheme is of min { 3 / 2 , 1 + β / 2 − ϵ } -order strong convergence in time when β ∈ [ − 1 / 4 , 2 ] , so it can break the first order barrier and obtain a higher accurate numerical solution. Numerical examples are performed to verify and develop the theoretical findings. [ABSTRACT FROM AUTHOR]

The LATIN method has been developed and successfully applied to a variety of deterministic problems, but few work has been developed for nonlinear stochastic problems. This paper presents a stochastic LATIN method to solve stochastic and/or parameterized elastoplastic problems. To this end, the stochastic solution is decoupled into spatial, temporal and stochastic spaces, and approximated by the sum of a set of products of triplets of spatial functions, temporal functions and random variables. Each triplet is then calculated in a greedy way using a stochastic LATIN iteration. The high efficiency of the proposed method relies on two aspects: The nonlinearity is efficiently handled by inheriting advantages of the classical LATIN method, and the randomness and/or parameters are effectively treated by a sample-based approximation of stochastic spaces. Further, the proposed method is not sensitive to the stochastic and/or parametric dimensions of inputs due to the sample description of stochastic spaces. It can thus be applied to high-dimensional stochastic and parameterized problems. Five numerical examples demonstrate the promising performance of the proposed stochastic LATIN method. • A stochastic LATIN method is developed for stochastic elastoplastic analysis. • Random and parameterized inputs are handled using a unified probability framework. • Decoupled approximations of solutions are used in both local and global stages. • Stochastic elastoplastic constitutive models are evolved in a non-intrusive way. • High-dimensional stochastic elastoplastic problems can be solved efficiently. [ABSTRACT FROM AUTHOR]

• An efficient simulation system is proposed for the urban rail networked operation. • The interaction between passenger and train is delicately depicted in simulation. • A simulation-based constrained SPSA algorithm is used to coordinate train timetables. • The improved solution reduces passenger waiting time without adding operating cost. Synchronous optimization of train timetables is to solve the problem of train service coordination among different lines in the urban rail transit network, which can reduce passenger waiting time and subsequently enhance passenger satisfaction. This paper develops an efficient simulation system to reproduce the train operation of an urban rail network. It takes into account the realistic characteristics of urban rail operations, including time-dependent demand, dynamic dwell time, and train capacity constraint. In the simulations, both the train trajectories and the passenger waiting time can be easily obtained. On this basis, a simulation-based algorithm (i.e., simultaneous perturbation stochastic approximation, SPSA) is designed to search an improved flexible-interval dispatch solution in the network. A case study of the Chengdu urban rail transit network is implemented to verify the effectiveness of the simulation system and the optimization algorithm. The simulation system is found to be time efficient since it takes less than 1 s to simulate the network with 4 h of operation and more than 200,000 passengers. The optimization algorithm is also effective as it can reduce the average passenger waiting time by 9.52 % compared to the equal-interval dispatch solution without increasing the train service frequency. It is also found that the reduction in waiting time is mainly due to the improved coordination of train services in the transfer station. [ABSTRACT FROM AUTHOR]

This paper considers a novel multi-agent linear stochastic approximation algorithm driven by Markovian noise and general consensus-type interaction, in which each agent evolves according to its local stochastic approximation process which depends on the information from its neighbors. The interconnection structure among the agents is described by a time-varying directed graph. While the convergence of consensus-based stochastic approximation algorithms when the interconnection among the agents is described by doubly stochastic matrices (at least in expectation) has been studied, less is known about the case when the interconnection matrix is simply stochastic. For any uniformly strongly connected graph sequences whose associated interaction matrices are stochastic, the paper derives finite-time bounds on the mean-square error, defined as the deviation of the output of the algorithm from the unique equilibrium point of the associated ordinary differential equation. For the case of interconnection matrices being stochastic, the equilibrium point can be any unspecified convex combination of the local equilibria of all the agents in the absence of communication. Both the cases with constant and time-varying step-sizes are considered. In the case when the convex combination is required to be a straight average and interaction between any pair of neighboring agents may be uni-directional, so that doubly stochastic matrices cannot be implemented in a distributed manner, the paper proposes a push-sum-type distributed stochastic approximation algorithm and provides its finite-time bound for the time-varying step-size case by leveraging the analysis for the consensus-type algorithm with stochastic matrices and developing novel properties of the push-sum algorithm. Distributed temporal difference learning is discussed as an illustrative application. [ABSTRACT FROM AUTHOR]

Since stochastic approximation (SA) based algorithms are easy to implement and need less memory, they are very popular in distributed stochastic optimization problems. Many works have focused on the consistency of the objective values and the iterates returned by the SA based algorithms. It is of fundamental interest to know how to quantify the uncertainty associated with SA solutions via the confidence regions of a prescribed level of significance for the true solution. In this paper, we discuss the framework of constructing the asymptotic confidence regions of the optimal solution to distributed stochastic optimization problem with a focus on the distributed stochastic gradient tracking method. To attain this goal, we first present the asymptotic normality of Polyak–Ruppert averaged distributed stochastic gradient tracking method. We then estimate the corresponding covariance matrix through online estimators. Finally, we provide a practical procedure to build the asymptotic confidence regions for the optimal solution. Numerical tests are also conducted to show the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

Motivated by the goal of improving the efficiency of a sequential design with small sample size, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modeling and nonrecursive iteration. Consistency of the Bayes estimator is established. Simulation studies show its superiority in small-sample performance to Robbins–Monro type procedures. Extension to a version of generalized multivariate quantile is presented. • A novel Bayesian stochastic approximation method to estimate the root of a regression function. • Adaptive local modeling and nonrecursive iteration. • Superiority in small-sample performance to Robbins–Monro type procedures. • Extension to a version of generalized multivariate quantile. [ABSTRACT FROM AUTHOR]

In this article we establish central limit theorems for multilevel Polyak–Ruppert averaged stochastic approximation schemes. We work under very mild technical assumptions and consider the slow regime in which typical errors decay like N − δ with δ ∈ (0 , 1 2) and the critical regime in which errors decay of order N − 1 ∕ 2 log N in the runtime N of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the distributed control problem for multi-agent systems (MASs) subject to multiplicative and additive noises over switching networks, where both cooperative and antagonistic interactions coexist. The communication topology is governed by a continuous-time Markovian chain. A stochastic approximation technique is utilized to handle stochastic bipartite consensus with communication noises. The major challenge, due to the fact that the intensity of the multiplicative noise is nonlinearly coupled with the distance between agents, is that the coexistence of antagonistic information and multiplicative noise makes the multiplicative noise term impossible to be converted into an error form. This leads to the inapplicability of the Lyapunov-based method. To cope with this, we first show the boundedness of agents' states where the second moment approach is employed. Based on it, the mean square and almost surely bipartite consensus are achieved under some mild requirements. The efficiency of the proposed method is supported by an example. [ABSTRACT FROM AUTHOR]