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In this study, we propose an approximation for a renewal reward process that describes a stochastic control model of type (s, S) based on the first three moments of demand random variables. Various asymptotic expansions for this model exist in the literature. All these studies rely on the condition of knowing the distribution function of demand random variables and require obtaining the asymptotic expansion of the renewal function produced by them. However, obtaining a renewal function can be challenging for certain distribution families, and in some cases, the mathematical structure of the renewal function is difficult to apply. Therefore, in this study, simple and compact approximations are presented for the stochastic control model of type (s, S). The findings of this study rely on Kambo's method, through which we obtain approximations for the ergodic distribution, and the nth order ergodic moments of this process. To conclude the study, the accuracy of the proposed approximate formulas are examined through a specialized illustrative example. Moreover, it has been noted that the proposed approximation is more accurate than the approximations existing in the literature. [ABSTRACT FROM AUTHOR]

Consider a finite undirected graph and place an urn with balls of two colours at each vertex. At every discrete time step, for each urn, a fixed number of balls are drawn from that same urn with probability p and from a randomly chosen neighbour of that urn with probability 1 - p . Based on what is drawn, the urns then reinforce themselves or their neighbours. For every ball of a given colour in the sample, in case of Pólya-type reinforcement, a constant multiple of balls of that colour is added while in case of Friedman-type reinforcement, balls of the other colour are reinforced. These different choices for reinforcement give rise to multiple models. In this paper, we study the convergence of the fraction of balls of either colour across urns for all of these models. We show that in most cases the urns synchronize, that is, the fraction of balls of either colour in each urn converges to the same limit almost surely. A different kind of asymptotic behaviour is observed on bipartite graphs. We also prove similar results for the case of finite directed graphs. [ABSTRACT FROM AUTHOR]

Consider a generalized time-dependent Pólya urn process defined as follows. Let d ∈ N be the number of urns/colors. At each time n, we distribute σ n balls randomly to the d urns, proportionally to f, where f is a valid reinforcement function. We consider a general class of positive reinforcement functions R assuming some monotonicity and growth condition. The class R includes convex functions and the classical case f (x) = x α , α > 1 . The novelty of the paper lies in extending stochastic approximation techniques to the d-dimensional case and proving that eventually the process will fixate at some random urn and the other urns will not receive any balls anymore. [ABSTRACT FROM AUTHOR]

This paper considers optimization problems where the objective is the sum of a function given by an expectation and a closed convex function, and proposes stochastic composite proximal bundle (SCPB) methods for solving it. Complexity guarantees are established for them without requiring knowledge of parameters associated with the problem instance. Moreover, it is shown that they have optimal complexity when these problem parameters are known. To the best of our knowledge, this is the first proximal bundle method for stochastic programming able to deal with continuous distributions. Finally, we present computational results showing that SCPB substantially outperforms the robust stochastic approximation method in all instances considered. [ABSTRACT FROM AUTHOR]

We investigate statistical properties of the optimal value of the Sample Average Approximation of stochastic programs, continuing the study (Krätschmer in Nonasymptotic upper estimates for errors of the sample average approximation method to solve risk averse stochastic programs, 2023. Forthcoming in SIAM J. Optim.). Central Limit Theorem type results are derived for the optimal value. As a crucial point the investigations are based on a new type of conditions from the theory of empirical processes which do not rely on pathwise analytical properties of the goal functions. In particular, continuity or convexity in the parameter is not imposed in advance as usual in the literature on the Sample Average Approximation method. It is also shown that the new condition is satisfied if the paths of the goal functions are Hölder continuous so that the main results carry over in this case. Moreover, the main results are applied to goal functions whose paths are piecewise Hölder continuous as e.g. in two stage mixed-integer programs. The main results are shown for classical risk neutral stochastic programs, but we also demonstrate how to apply them to the Sample Average Approximation of risk averse stochastic programs. In this respect we consider stochastic programs expressed in terms of absolute semideviations and divergence risk measures. [ABSTRACT FROM AUTHOR]

Stochastic approximation (SA) type methods have been well studied for solving single-stage stochastic variational inequalities (SVIs). This paper proposes a dynamic stochastic projection method (DSPM) for solving multistage SVIs. In particular, we investigate an inexact single-stage SVI and present an inexact stochastic projection method (ISPM) for solving it. Then we give the DSPM to a three-stage SVI by applying the ISPM to each stage. We show that the DSPM can achieve an O (1 ϵ 2) convergence rate regarding to the total number of required scenarios for the three-stage SVI. We also extend the DSPM to the multistage SVI when the number of stages is larger than three. The numerical experiments illustrate the effectiveness and efficiency of the DSPM. [ABSTRACT FROM AUTHOR]

Celebrities can significantly influence the public towards any desired outcome. In a bid to tackle an infectious disease, a leader (government) exploits such influence towards motivating a fraction of public to get vaccinated, sufficient enough to ensure eradication. The leader also aims to minimize the vaccinated fraction of public (that ensures eradication) and use minimal incentives to motivate the influencers; it also controls vaccine supply rates. Towards this, we consider a three-layered Stackelberg game, with the leader at the top. A set of influencers at the middle layer are involved in a stochastic vaccination game driven by incentives. The public at the bottom layer is involved in an evolutionary game with respect to vaccine responses. We prove the disease can always be eradicated once the public is sufficiently sensitive towards the vaccination choices of the influencers—with a minimal fraction of public vaccinated. This minimal fraction depends only on the disease characteristics and not on other aspects. Interestingly, there are many configurations to achieve eradication, each configuration is specified by a dynamic vaccine supply rate and a number—this number represents the count of the influencers that needs to be vaccinated to achieve the desired influence. Incentive schemes are optimal when this number equals all or just one; the former curbs free-riding among influencers, while the latter minimizes the dependency on influencers. [ABSTRACT FROM AUTHOR]

Aims: To develop a non‐linear mixed‐effects population pharmacokinetic and pharmacodynamic (PK‐PD) model describing the change in the concentration of methotrexate polyglutamates in erythrocytes (ery‐MTX‐PGn with "n" number of glutamate, representing PK component) and how this relates to modified 28‐joint Disease Activity Score incorporating erythrocyte sedimentation rate (DAS‐28‐3) for rheumatoid arthritis (RA), representing PD component. Methods: An existing PK model was fitted to data from a study consisting of 117 RA patients. The estimation of population PK‐PD parameters was performed using stochastic approximation expectation maximisation algorithm in Monolix 2021R2. The model was used to perform Monte Carlo simulations of a loading dose regimen (50mg subcutaneous methotrexate as loading doses, then 20mg weekly oral methotrexate) compared to a standard dosing regimen (10mg weekly oral methotrexate for 2 weeks, then 20mg weekly oral methotrexate). Results: Every 40 nmol/L increase in ery‐MTX‐PG3‐5 total concentration correlated with 1‐unit reduction in DAS‐28‐3. Significant covariate effects on the therapeutic response of methotrexate included the use of prednisolone in the first 4 weeks (positive use correlated with 25% reduction in DAS‐28‐3 when other variables were constant) and patient age (every 10‐year increase in age correlated with 3.4% increase in DAS‐28‐3 when other variables were constant). 4 methotrexate loading doses led to a higher percentage of patients achieving a good/moderate response compared to the standard regimen (Week 4: 87.6% vs. 39.8%; Week 10: 64.7% vs. 57.0%). Conclusions: A loading dose regimen was more likely to achieve higher ery‐MTX‐PG concentration and better therapeutic response after 4 weeks of methotrexate treatment. [ABSTRACT FROM AUTHOR]

In this article, we derive the convergence rate for the Wong–Zakai equation of some approximation of stochastic evolution equations with multiplicative noise. To be more precise, the diffusion coefficient in front of the noise is the multiplication operator, and, is therefore not bounded, a situation not treated in the literature. Since our motivation comes from problems in numerical ling, we consider a finite, high-dimensional problem approximating a stochastic evolution equation on a random time grid. By imposing suitable stability conditions on the drift term and the time grid, we achieve a convergence rate in the mean square of order $ \min \{1-\delta,2-2\gamma \} $ min { 1 − δ , 2 − 2 γ } , for some $ 0 \lt \delta \lt 1 $ 0 < δ < 1 and $ 0 \lt \gamma \lt 1/2 $ 0 < γ < 1 / 2. [ABSTRACT FROM AUTHOR]

Spatial variability and uncertainty associated with soil volumetric moisture content (SVMC) is crucial in moisture prediction accuracy, this paper sets out to address this point of SVMC by developing data-driven model. Grid samples of SVMC covered approximately a 3-ha field during the jointing growth stage of winter wheat, and SVMC were measured by Time Domain Reflectometry (TDR), located in North China Plain, China. Bayesian inference was performed to explore spatial heterogeneity, robustness, transparency, interpretability and uncertainty related to SVMC using python-based PyMC3 combined with Integrated Nested Laplace Approximation with the Stochastic Partial Differential Equation (INLA-SPDE) model. The results showed that the prediction surface of SVMC, the lower and upper limits of 95% credible intervals quantified uncertainty associated with SVMC, cauchy prior of the flexibility and adaptability to obtain state-of-the-art predictive performance is more robust than gaussian prior for SVMC prediction, the transparency and interpretability of SVMC prediction model were revealed by MCMC (Markov-Chain Monte-Carlo) trace plots, KDE (Kernel density estimates), and rank plots. The uncertainty associated with SVMC can explicitly be described using the highest-posterior density interval, the prediction lower and upper limits. [ABSTRACT FROM AUTHOR]

In the context of flight test planning, numerous uncertainties exist, encompassing aircraft status, number of flights, and weather conditions, among others. These uncertainties ultimately manifest significantly in the actual number of flight sorties executed, rendering high significance to engineering problems related to the execution of flight test missions. However, there is a dearth of research in this specific aspect. To address this gap, this paper proposes an opportunity-constrained integer programming model tailored to the unique characteristics of the problem. To handle the uncertainties, Sample Average Approximation (SAA) is employed to perform oversampling of the uncertain parameters, followed by the Adaptive Large Neighborhood Search (ALNS) algorithm to solve for the optimal solution and objective function value. Results from numerical experiments conducted at varying scales and validated with diverse sampling distributions demonstrate the effectiveness and robustness of the proposed methodology. By decoding the generated execution sequences, comprehensive mission planning schemes can be derived. This approach yields sequences that exhibit commendable feasibility and robustness for the flight test planning problem with sorties uncertainty (FTPPSU), offering valuable support for the efficient execution of future flight test missions. [ABSTRACT FROM AUTHOR]

The researchers believe that the number of epidemic diseases will increase in the twenty-first century. The recent virus histories, Sars-CoV, H1N1/09, MERS-CoV, Zika, Sars-CoV-2, point to this new reality. We need to be prepared to give a fast and precise response to the new epidemic diseases. We need to improve the responses because the current measures are so expensive in all aspects. To help with this new demand, we propose an epidemic model developed with a focus on control applications. The proposed model describes epidemic diseases split into unlimited compartments defined by classes (biological aspects) and groups (populational aspects) that are independent. It divides the population into clusters of individuals with homogeneous behavior. The high flexibility of the proposed model gives it the versatility needed in control applications. Moreover, the proposed model is an epidemic model with a deterministic behavior that presents an approximation for stochastic effects, contemplates the individuals' contact network effects, and its structure is ready for the big-data age. In this work, we analyzed, showed the mathematical properties, and simulated the proposed compartmental epidemic disease model to detail for the reader how the model works and how to use it. [ABSTRACT FROM AUTHOR]

In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints. We investigate the convergence of the method, which is based on a stochastic approximation approach with random stopping combined with an iterative procedure for updating Lagrange multipliers. The algorithm is applied to a multi-shape optimization problem with geometric constraints and demonstrated numerically. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate the Wong–Zakai approximation results for two dimensional stochastic Cahn–Hilliard–Navier–Stokes model. The model consists of a Navier–Stokes system coupled with convective Cahn–Hilliard equations. It describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids under the influence of multiplicative noise. Our main result describes the support of the distribution of solutions. As in [2], both inclusions are proved by means of a general Wong–Zakai type result of convergence in probability for nonlinear stochastic PDEs driven by a Hilbert‐valued Brownian motion and some adapted finite‐dimensional approximation of this process. Note that the coupling between the Navier–Stokes system and the Cahn–Hilliard equations makes the analysis more involved. [ABSTRACT FROM AUTHOR]

The established relationships between the size, shape, and terminal velocity of raindrops, along with the spheroidal shape approximation (SSA), are commonly employed for calculating radar observables in rain. This study, however, reveals the SSA's limitations in accurately simulating spectral and integrated backscattering polarimetric variables in rain at the W-band. Improving existing models is a complex task that demands high-precision data from both laboratory settings and natural rain, enhanced stochastic shape approximation techniques, and comprehensive scattering simulations. To circumvent these challenges, this study introduces a simpler and more straightforward approach – the empirical scattering model (ESM). The ESM is derived from an analysis of high-quality, low-turbulence Doppler spectra, which were selected from measurements taken with a 94 GHz radar at three different locations between 2021 and 2024. The ESM's primary advantages over the SSA include superior accuracy and the direct incorporation of microphysical effects observed in natural rain. This study demonstrates that the ESM can potentially clarify issues in existing retrieval and calibration methods that use polarimetric observations at the W-band. The findings of this study are not only valuable for experts in cloud radar polarimetry but also for scattering modelers and laboratory experimenters since explaining the presented observations necessitates a more profound understanding of the microphysical properties and processes in rain. [ABSTRACT FROM AUTHOR]

In this paper, we study the Wong-Zakai approximations of stochastic evolution equations driven by a multiplicative white noise and their related dynamical behavior, where the Wong-Zakai approximations are given by a stationary process via the Wiener shift. Firstly, we show that the solutions of these stochastic evolution equations can be approximated almost surely with a polynomial rate. Next, we explore the Wong-Zakai approximations on the center manifolds of these stochastic evolution equations under an exponential trichotomy condition. Finally, we prove that these approximate center manifolds converge almost surely, with a polynomial rate. [ABSTRACT FROM AUTHOR]

Many systems in the manufacturing industry have spatial distribution characteristics, which correlate with both time and space. Such systems are known as distributed parameter systems (DPSs). Due to the spatiotemporal coupling characteristics, the modeling of such systems is quite complex. The paper presents a new approach for three-dimensional fuzzy modeling using Simultaneous Perturbation Stochastic Approximation (SPSA) for nonlinear DPSs. The Affinity Propagation clustering approach is utilized to determine the optimal number of fuzzy rules and construct a collection of preceding components for three-dimensional fuzzy models. Fourier space base functions are used in the resulting components of three-dimensional fuzzy models, and their parameters are learned by the SPSA algorithm. The proposed three-dimensional fuzzy modeling technique was utilized on a conventional DPS within the semiconductor manufacturing industry, with the simulation experiments confirming its efficacy. [ABSTRACT FROM AUTHOR]

Copyright of Canadian Journal of Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we propose a modified RFedSVRG method by incorporating the Barzilai–Borwein (BB) method to approximate second-order information on the manifold for Federated Learning (FL). Moreover, we use the BB strategy to obtain self-adjustment of step size. We show the convergence of our methods under some assumptions. The numerical experiments on both synthetic and real datasets demonstrate that the proposed methods outperform some used methods in FL in some test problems. [ABSTRACT FROM AUTHOR]

This paper is motivated by the paper [2]. The main aim of this paper is to extend the stability result from [16], related to the θ-Euler- Maruyama method (θ ∈ (1/2, 1)) for a class of neutral stochastic differential equations with time-dependent delay. The theta method is defined such that, in general case, it is implicit in both drift coefficient and neutral term. Sufficient conditions of the a.s. exponential stability of the θ-Euler-Maruyama method, including the linear growth condition on the drift coe_cient of the equation, are revealed. The stability result is established for larger class of neutral terms than that considered in the second cited paper. An example is provided to support the main results of the paper. [ABSTRACT FROM AUTHOR]

Computing cross-partial derivatives using fewer model runs is relevant in modeling, such as stochastic approximation, derivative-based ANOVA, exploring complex models, and active subspaces. This paper introduces surrogates of all the cross-partial derivatives of functions by evaluating such functions at N randomized points and using a set of L constraints. Randomized points rely on independent, central, and symmetric variables. The associated estimators, based on N L model runs, reach the optimal rates of convergence (i.e., O (N − 1) ), and the biases of our approximations do not suffer from the curse of dimensionality for a wide class of functions. Such results are used for (i) computing the main and upper bounds of sensitivity indices, and (ii) deriving emulators of simulators or surrogates of functions thanks to the derivative-based ANOVA. Simulations are presented to show the accuracy of our emulators and estimators of sensitivity indices. The plug-in estimates of indices using the U-statistics of one sample are numerically much stable. [ABSTRACT FROM AUTHOR]

This paper focuses on approximating stochastic delay differential equations with delayed impulses using Euler-Maruyama-type approximations. One key difference from previous literature is that the impulsive perturbations considered in this paper are past-dependent. Additionally, both the time delays in the stochastic delay differential equations and in the impulsive functions are functions of time. We establish the mean square convergence of the Euler-Maruyama approximations under a local Lipschitz condition and a linear growth condition. Furthermore, we determine the order of convergence under a global Lipschitz condition and provide an illustrative example. [ABSTRACT FROM AUTHOR]

Slow kinetic processes in molecular systems can be analyzed by computing the dominant eigenpairs of the Koopman operator or its generator. In this context, the Variational Approach to Markov Processes (VAMP) provides a rigorous way of discerning the quality of different approximate models. Kernel methods have been shown to provide accurate and robust estimates for slow kinetic processes, but they are sensitive to hyper-parameter selection and require the solution of large-scale generalized eigenvalue problems, which can easily become computationally demanding for large data sizes. In this contribution, we employ a stochastic approximation of the kernel based on random Fourier features (RFFs) to derive a small-scale dual eigenvalue problem that can be easily solved. We provide an interpretation of this procedure in terms of a finite, randomly generated basis set. By combining the RFF approach and model selection by means of the VAMP score, we show that kernel parameters can be efficiently tuned and accurate estimates of slow molecular kinetics can be obtained for several benchmarking systems, such as deca alanine and the NTL9 protein. [ABSTRACT FROM AUTHOR]

Classical optimizers play a crucial role in determining the accuracy and convergence of variational quantum algorithms; leading algorithms use a near-term quantum computer to solve the ground state properties of molecules, simulate dynamics of different quantum systems, and so on. In the literature, many optimizers, each having its own architecture, have been employed expediently for different applications. In this work, we consider a few popular and efficacious optimizers and assess their performance in variational quantum algorithms for applications in quantum chemistry in a realistic noisy setting. We benchmark the optimizers with critical analysis based on quantum simulations of simple molecules, such as hydrogen, lithium hydride, beryllium hydride, water, and hydrogen fluoride. The errors in the ground state energy, dissociation energy, and dipole moment are the parameters used as yardsticks. All the simulations were carried out with an ideal quantum circuit simulator, a noisy quantum circuit simulator, and finally a noisy simulator with noise embedded from the IBM Cairo quantum device to understand the performance of the classical optimizers in ideal and realistic quantum environments. We used the standard unitary coupled cluster ansatz for simulations, and the number of qubits varied from two starting from the hydrogen molecule to ten qubits in hydrogen fluoride. Based on the performance of these optimizers in the ideal quantum circuits, the conjugate gradient, limited-memory Broyden—Fletcher—Goldfarb—Shanno bound, and sequential least squares programming optimizers are found to be the best-performing gradient-based optimizers. While constrained optimization by linear approximation (COBYLA) and Powell's conjugate direction algorithm for unconstrained optimization (POWELL) perform most efficiently among the gradient-free methods, in noisy quantum circuit conditions, simultaneous perturbation stochastic approximation, POWELL, and COBYLA are among the best-performing optimizers. [ABSTRACT FROM AUTHOR]

In this paper we study the nonconvex constrained composition optimization, in which the objective contains a composition of two expected-value functions whose accurate information is normally expensive to calculate. We propose a STochastic nEsted Primal-dual (STEP) method for such problems. In each iteration, with an auxiliary variable introduced to track the inner layer function values we compute stochastic gradients of the nested function using a subsampling strategy. To alleviate difficulties caused by possibly nonconvex constraints, we construct a stochastic approximation to the linearized augmented Lagrangian function to update the primal variable, which further motivates to update the dual variable in a weighted-average way. Moreover, to better understand the asymptotic dynamics of the update schemes we consider a deterministic continuous-time system from the perspective of ordinary differential equation (ODE). We analyze the Karush-Kuhn-Tucker measure at the output by the STEP method with constant parameters and establish its iteration and sample complexities to find an \epsilon-stationary point, ensuring that expected stationarity, feasibility as well as complementary slackness are below accuracy \epsilon. To leverage the benefit of the (near) initial feasibility in the STEP method, we propose a two-stage framework incorporating a feasibility-seeking phase, aiming to locate a nearly feasible initial point. Moreover, to enhance the adaptivity of the STEP algorithm, we propose an adaptive variant by adaptively adjusting its parameters, along with a complexity analysis. Numerical results on a risk-averse portfolio optimization problem and an orthogonal nonnegative matrix decomposition reveal the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Turning is one of the most important material removal processes in manufacturing, where the proper understanding of the process is crucial for the quality of the final product. In this study, the stochastic cutting force is utilized to enhance the existing 1-degree-of-freedom turning model. A stochastic model is adopted to address the stochastic resonance phenomenon occurring near stability boundaries. Additionally, a novel simplified stochastic model is introduced with additive noise only. The comparison of the two models reveals that, with the recommended noise intensity of 0.1 to 1%, there is no significant difference in the stability charts and mean square characteristics between the two models. As a result, the time-consuming numerical methods can be bypassed, as the simplified model offers a computationally more efficient analytical approach to compute variance based on power spectral density (PSD). By combining techniques such as D-separation to determine stability boundaries and the PSD-based variance calculation, it only takes a minute instead of hours to construct a heatmap using the introduced simplified stochastic turning model that clearly outlines dangerous stochastic resonance regions inside the stable domain. [ABSTRACT FROM AUTHOR]

Through the Bayesian lens of four-dimensional variational (4D-Var) data assimilation, uncertainty in model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive forward models, posterior covariance knowledge must be relaxed to deterministic or stochastic approximations. In the carbon flux inversion literature, proposed a stochastic method capable of approximating posterior variances of linear functionals of the model parameters that is particularly well suited for large-scale Earth-system 4D-Var data assimilation tasks. This note formalizes this algorithm and clarifies its properties. We provide a formal statement of the algorithm, demonstrate why it converges to the desired posterior variance quantity of interest, and provide additional uncertainty quantification allowing incorporation of the Monte Carlo sampling uncertainty into the method's Bayesian credible intervals. The methodology is demonstrated using toy simulations and a realistic carbon flux inversion observing system simulation experiment. [ABSTRACT FROM AUTHOR]

In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the deterministic case and have never been studied from a stochastic approximation viewpoint despite the recent advances in stochastic methods for single-level, bilevel, and multi-objective optimization. To solve bilevel problems with a multi-objective lower level, different approaches can be considered depending on the interpretation of the lower-level optimality. An optimistic formulation that was previously introduced for the deterministic case consists of minimizing the upper-level function over all non-dominated lower-level solutions. In this paper, we develop new risk-neutral and risk-averse formulations, address their main computational challenges, and develop the corresponding deterministic and stochastic gradient-based algorithms. [ABSTRACT FROM AUTHOR]

We analyse the $\Gamma$ -convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient. The limit is a local free-discontinuity functional, where the bulk term can be completely characterized in terms of an asymptotic cell formula. From that, we can deduce an homogenisation result in the stochastic setting. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the global approximation of solutions of stochastic differential equations (SDEs) driven by countably dimensional Wiener process. Under certain regularity conditions imposed on the coefficients, we show lower bounds for exact asymptotic error behaviour. For that reason, we analyse separately two classes of admissible algorithms: based on equidistant, and possibly not equidistant meshes. Our results indicate that in both cases, decrease of any method error requires significant increase of the cost term, which is illustrated by the product of cost and error diverging to infinity. This is, however, not visible in the finite-dimensional case. In addition, we propose an implementable, path-independent Euler algorithm with adaptive step-size control, which is asymptotically optimal among algorithms using specified truncation levels of the underlying Wiener process. Our theoretical findings are supported by numerical simulation in Python language. [ABSTRACT FROM AUTHOR]

The ability to accurately predict others' behavior is central to the safety and efficiency of robotic systems in interactive settings, such as human–robot interaction and multi-robot teaming tasks. Unfortunately, robots often lack access to key information on which these predictions may hinge, such as other agents' goals, attention, and willingness to cooperate. Dual control theory addresses this challenge by treating unknown parameters of a predictive model as stochastic hidden states and inferring their values at runtime using information gathered during system operation. While able to optimally and automatically trade off exploration and exploitation, dual control is computationally intractable for general interactive motion planning, mainly due to the fundamental coupling between the robot's trajectory plan and its prediction of other agents' intent. In this paper, we present a novel algorithmic approach to enable active uncertainty reduction for interactive motion planning based on the implicit dual control paradigm. Our approach relies on sampling-based approximation of stochastic dynamic programming, leading to a model predictive control problem that can be readily solved by real-time gradient-based optimization methods. The resulting policy is shown to preserve the dual control effect for a broad class of predictive models with both continuous and categorical uncertainty. To ensure the safe operation of the interacting agents, we use a runtime safety filter (also referred to as a "shielding" scheme), which overrides the robot's dual control policy with a safety fallback strategy when a safety-critical event is imminent. We then augment the dual control framework with an improved variant of the recently proposed shielding-aware robust planning scheme, which proactively balances the nominal planning performance with the risk of high-cost emergency maneuvers triggered by low-probability agent behaviors. We demonstrate the efficacy of our approach with both simulated driving studies and hardware experiments using 1/10 scale autonomous vehicles. [ABSTRACT FROM AUTHOR]

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these estimators as the sample size goes to infinity. This area of study has a long tradition in stochastic programming. However, the literature is lacking consistency analysis for problems in which the decision variables are taken from an infinite-dimensional space, which arise in optimal control, scientific machine learning, and statistical estimation. By exploiting the typical problem structures found in these applications that give rise to hidden norm compactness properties for solution sets, we prove consistency results for nonconvex risk-averse stochastic optimization problems formulated in infinite-dimensional space. The proof is based on several crucial results from the theory of variational convergence. The theoretical results are demonstrated for several important problem classes arising in the literature. [ABSTRACT FROM AUTHOR]

The stochastic food chain model is an important model within the field of ecological research. Since existing models are difficult to describe the influence of cross-diffusion and random factors on the evolution of species populations, this work is concerned with a stochastic cross-diffusion three-species food chain model with prey-taxis, in which the direction of predators' movement is opposite to the gradient of prey, i.e., a higher density of prey. The existence and uniqueness of martingale solutions are established in a Hilbert space by using the stochastic Galerkin approximation method, the tightness criterion, Jakubowski's generalization of the Skorokhod theorem, and the Vitali convergence theorem. Furthermore, asymptotic behaviors around the steady states of the stochastic cross-diffusion three-species food chain model in the time mean sense are investigated. Finally, numerical simulations are carried out to illustrate the results of our analysis. [ABSTRACT FROM AUTHOR]

Summary: Since the dawn of quantum computing (QC), theoretical developments like Shor's algorithm proved the conceptual superiority of QC over traditional computing. However, such quantum supremacy claims are difficult to achieve in practice because of the technical challenges of realizing noiseless qubits. In the near future, QC applications will need to rely on noisy quantum devices that offload part of their work to classical devices. One way to achieve this is by using parameterized quantum circuits in optimization or even in machine learning tasks. The energy requirements of quantum algorithms have not yet been studied extensively. In this article, we explore several optimization algorithms using both theoretical insights and numerical experiments to understand their impact on energy consumption. Specifically, we highlight why and how algorithms like quantum natural gradient descent, simultaneous perturbation stochastic approximations or circuit learning methods, are at least 2×$$ 2\times $$ to 4×$$ 4\times $$ more energy efficient than their classical counterparts; why feedback‐based quantum optimization is energy‐inefficient; and how techniques like Rosalin can improve the energy efficiency of other algorithms by a factor of ≥$$ \ge $$20×$$ \times $$. Finally, we use the NchooseK high‐level programming model to run optimization problems on both gate‐based quantum computers and quantum annealers. Empirical data indicate that these optimization problems run faster, have better success rates, and consume less energy on quantum annealers than on their gate‐based counterparts. [ABSTRACT FROM AUTHOR]

Motivated by important applications to the analysis of complex noise-induced phenomena, we consider a problem of the constructive description of randomly forced equilibria for nonlinear systems with multiplicative noise. Using the apparatus of the first approximation systems, we construct an approximation of mean square deviations that explicitly takes into account the presence of multiplicative noises, depending on the current system state. A spectral criterion of existence and exponential stability of the stationary second moments for the solution of the first approximation system is presented. For mean square deviation, we derive an expansion in powers of the small parameter of noise intensity. Based on this theory, we derive a new, more accurate approximation of mean square deviations in a general nonlinear system with multiplicative noises. This approximation is compared with the widely used approximation based on the stochastic sensitivity technique. The general mathematical results are illustrated with examples of the model of climate dynamics and the van der Pol oscillator with hard excitement. [ABSTRACT FROM AUTHOR]

The stochastic approximation (SA) method stands as the foundational mathematical tool for modern large-scale optimization and machine learning. Therefore, gaining a theoretical understanding of SA algorithms is of fundamental interest. In their paper titled "A Lyapunov Theory for Finite-Sample Guarantees of Markovian Stochastic Approximation," Chen et al. present a unified Lyapunov framework for the finite-sample analysis of a Markovian SA algorithm under a contractive operator with respect to an arbitrary norm. The key novelty lies in the construction of a smooth Lyapunov function called the generalized Moreau envelope. The authors demonstrate the effectiveness of their SA results in the context of reinforcement learning (RL), specifically through popular algorithms such as variants of temporal difference (TD) learning and Q-learning. As byproducts, the results provide theoretical insights into the efficiency of bootstrapping in TD learning with eligibility traces and the bias-variance tradeoff in off-policy learning. This paper develops a unified Lyapunov framework for finite-sample analysis of a Markovian stochastic approximation (SA) algorithm under a contraction operator with respect to an arbitrary norm. The main novelty lies in the construction of a valid Lyapunov function called the generalized Moreau envelope. The smoothness and an approximation property of the generalized Moreau envelope enable us to derive a one-step Lyapunov drift inequality, which is the key to establishing the finite-sample bounds. Our SA result has wide applications, especially in the context of reinforcement learning (RL). Specifically, we show that a large class of value-based RL algorithms can be modeled in the exact form of our Markovian SA algorithm. Therefore, our SA results immediately imply finite-sample guarantees for popular RL algorithms such as n-step temporal difference (TD) learning, TD (λ) , off-policy V-trace, and Q-learning. As byproducts, by analyzing the convergence bounds of n-step TD and TD (λ) , we provide theoretical insight into the problem about the efficiency of bootstrapping. Moreover, our finite-sample bounds of off-policy V-trace explicitly capture the tradeoff between the variance of the stochastic iterates and the bias in the limit. Funding: This work was supported by RTX, the National Science Foundation [Grants 2019844, 2107037, 211247, 2112533, 2144316, and 2240982], and the Machine Learning Laboratory at University of Texas at Austin. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0249. [ABSTRACT FROM AUTHOR]

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Estimating free energy differences, an important problem in computational drug discovery and in a wide range of other application areas, commonly involves a computationally intensive process of sampling a family of high-dimensional probability distributions and a procedure for computing estimates based on those samples. The variance of the free energy estimate of interest typically depends strongly on how the total computational resources available for sampling are divided among the distributions, but determining an efficient allocation is difficult without sampling the distributions. Here we introduce the Times Square sampling algorithm, a novel on-the-fly estimation method that dynamically allocates resources in such a way as to significantly accelerate the estimation of free energies and other observables, while providing rigorous convergence guarantees for the estimators. We also show that it is possible, surprisingly, for on-the-fly free energy estimation to achieve lower asymptotic variance than the maximum-likelihood estimator MBAR, raising the prospect that on-the-fly estimation could reduce variance in a variety of other statistical applications. for this article are available online. [ABSTRACT FROM AUTHOR]

In this work, we obtain weak order-2 conditions of Runge–Kutta method for the optimal control of stochastic differential equations which occurs in many areas of economics and finance and recently in cognitive sciences and neuroscience. We get the order conditions that a stochastic Runge–Kutta technique must meet to have weak order two by comparing the stochastic expansion of the approximation with the associated Taylor scheme. Moreover, we present numerical examples which verify the theoretical results. We conclude our paper by a summary and an outlook to future research and application. [ABSTRACT FROM AUTHOR]

For numerical approximations to stochastic differential equations using the Euler-- Maruyama scheme, we propose incorporating approximate random variables computed using low precisions, such as single and half precision. We propose and justify a model for the rounding error incurred, and produce an average case error bound for two and four way differences, appropriate for regular and nested multilevel Monte Carlo estimations. Our rounding error model recovers and extends the statistical model by Arciniega and Allen [Stoch. Anal. Appl., 21 (2003), pp. 281-- 300], while bounding the size that systematic and biased rounding errors are permitted to be. By considering the variance structure of multilevel Monte Carlo correction terms in various precisions with and without a Kahan compensated summation, we compute the potential speed ups offered from the various precisions. We find single precision offers the potential for approximate speed improvements by a factor of 7 across a wide span of discretization levels. Half precision offers comparable improvements for several levels of coarse simulations, and even offers improvements by a factor of 10--12 for the very coarsest few levels, which are likely to dominate higher order methods such as the Milstein scheme. [ABSTRACT FROM AUTHOR]

We revisit the Stochastic Score Classification (SSC) problem introduced by Gkenosis et al. (ESA 2018): We are given n tests. Each test j can be conducted at cost cj, and it succeeds independently with probability pj. Further, a partition of the (integer) interval { 0,. . ., n} into B smaller intervals is known. The goal is to conduct tests so as to determine that interval from the partition in which the number of successful tests lies while minimizing the expected cost. Ghuge, Gupta, and Nagarajan (IPCO 2022) recently showed that a polynomial-time constant-factor approximation algorithm exists. We show that interweaving the two strategies that order tests increasingly by their cj/pj and cj/(1 - pj) ratios, respectively--as already proposed by Gkensosis et al. for a special case--yields a small approximation ratio. We also show that the approximation ratio can be slightly decreased from 6 to 3 + 2√2 ≈ 5.828 by adding in a third strategy that simply orders tests increasingly by their costs. The similar analyses for both algorithms are nontrivial but arguably clean. Finally, we complement the implied upper bound of 3 + 2√2 on the adaptivity gap with a lower bound of 3/2. Since the lower-bound instance is a so-called unit-cost k-of-n instance, we settle the adaptivity gap in this case. [ABSTRACT FROM AUTHOR]

In this paper, we consider the well-posedness for the anticipated backward stochastic Schrödinger equation in a bounded domain or the whole space $ \mathbb {R}^d $ R d , which is associated to a stochastic control problem of nonlinear Schrödinger equations with time delay effect. The approach to establish the existence and uniqueness of adapted solutions are mainly based on the complex Itô's formula, the Galerkin's approximation method and the martingale representation theorem. [ABSTRACT FROM AUTHOR]

We propose two parametric approaches to evaluate swing contracts with firm constraints. Our objective is to define approximations for the optimal control, which represents the amounts of energy purchased throughout the contract. The first approach involves approximating the optimal control by means of an explicit parametric function, where the parameters are determined using stochastic gradient descent based algorithms. The second approach builds on the first one, where we replace parameters in the first approach by the output of a neural network. Our numerical experiments demonstrate that by using Langevin based algorithms, both parameterizations provide, in a short computation time, better prices compared to state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered. With the help of stochastic approximation algorithms with expanding truncations, the authors give the recursive estimates for the parameters of both the linear system and the binary sensor. Under reasonable conditions, all constructed estimates are proved to be convergent to the true values with probability one, and the convergence rates are also established. A simulation example is provided to justify the theoretical results. [ABSTRACT FROM AUTHOR]

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis–Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi‐Random Parametric Expectation Maximization (QRPEM) for a realistic two‐compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log‐normal cases. [ABSTRACT FROM AUTHOR]

Stochastic optimization has experienced significant growth in recent decades, with the increasing prevalence of variance reduction techniques in stochastic optimization algorithms to enhance computational efficiency. In this paper, we introduce two projection-free stochastic approximation algorithms for maximizing diminishing return (DR) submodular functions over convex constraints, building upon the Stochastic Path Integrated Differential EstimatoR (SPIDER) and its variants. Firstly, we present a SPIDER Continuous Greedy (SPIDER-CG) algorithm for the monotone case that guarantees a (1 - e - 1) OPT - ε approximation after O (ε - 1) iterations and O (ε - 2) stochastic gradient computations under the mean-squared smoothness assumption. For the non-monotone case, we develop a SPIDER Frank–Wolfe (SPIDER-FW) algorithm that guarantees a 1 4 (1 - min x ∈ C ‖ x ‖ ∞) OPT - ε approximation with O (ε - 1) iterations and O (ε - 2) stochastic gradient estimates. To address the practical challenge associated with a large number of samples per iteration, we introduce a modified gradient estimator based on SPIDER, leading to a Hybrid SPIDER-FW (Hybrid SPIDER-CG) algorithm, which achieves the same approximation guarantee as SPIDER-FW (SPIDER-CG) algorithm with only O (1) samples per iteration. Numerical experiments on both simulated and real data demonstrate the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

Data sites selected from modeling high-dimensional problems often appear scattered in nonpaternalistic ways. Except for sporadic-clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These features defy any theoretical treatment that requires local or global quasi-uniformity of distribution of data sites. Incorporating a recently developed application of integral operator theory in machine learning, we propose and study in the current article a new framework to analyze kernel interpolation of high-dimensional data, which features bounding stochastic approximation error by the spectrum of the underlying kernel matrix. Both theoretical analysis and numerical simulations show that spectra of kernel matrices are reliable and stable barometers for gauging the performance of kernel-interpolation methods for high-dimensional data. [ABSTRACT FROM AUTHOR]

This paper studied the numerical approximation of the stochastic differential equations driven by non-global Lipschitz drift coefficient and multiplicative noise. An efficient data-driven method, called extended continuous latent process flow, was proposed for the underlying problem. Compared with the piecewise construction of a variational posterior process used in the classical continuous latent process flow developed by Deng et al. [13], the principle idea of our method was to derive a variational lower bound by constructing a posterior latent process conditional on all information over the whole time interval to maximize the log-likelihood generated by the observations, which reduces the computational cost and, thus, provides a convenient way to approximate the considered equation. Particularly, our new method showed a better approximation to the underlying equation than the classical drift-θ discretization scheme through numerical error comparison. Numerical experiments were finally reported to demonstrate the effectiveness and generalization performance of the proposed method. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to simultaneously and stochastically maximize autonomous flight performance of a variable wing incidence angle having an unmanned aerial vehicle (UAV) and its flight control system (FCS) design. Design/methodology/approach: A small UAV is produced in Iskenderun Technical University Drone Laboratory. Its wing incidence angle is able to change before UAV flight. FCS parameters and wing incidence angle are simultaneously and stochastically designed to maximize autonomous flight performance using an optimization method named simultaneous perturbation stochastic approximation. Obtained results are also benefitted during UAV flight simulations. Findings: Applying simultaneous and stochastic design approach for a UAV having passively morphing wing incidence angle and its flight control system, autonomous flight performance is maximized. Research limitations/implications: Permission of the Directorate General of Civil Aviation in Turkish Republic is necessary for real-time flights. Practical implications: Simultaneous stochastic variable wing incidence angle having UAV and its flight control system design approach is so useful for maximizing UAV autonomous flight performance. Social implications: Simultaneous stochastic variable wing incidence angle having UAV and its flight control system design methodology succeeds confidence, excellent autonomous performance index and practical service interests of UAV users. Originality/value: Creating an innovative method to recover autonomous flight performance of a UAV and generating an innovative procedure carrying out simultaneous stochastic variable wing incidence angle having UAV and its flight control system design idea. [ABSTRACT FROM AUTHOR]