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George Yin

Publications and source records attributed to George Yin.

At least 19 recordsLinked to original sources
arXiv2026

Maximum Principles for Partially Observed Controls of Forward SPDEs and Backward SDEs with Jumps

This work establishes two versions of the Pontryagin-type maximum principles for partially observed optimal control of coupled forward stochastic partial differential equations (FSPDEs) and backward stochastic differential equations (BSDEs) with jumps in convex control domains. The FSPDE-BSDE system is driven by cylindrical Wiener processes, finite-dimensional Brownian motions, and compensated Poisson random measures. For systems with deterministic coefficients, a direct method is employed and particular attention is focused on establishing the well-posedness of a singular backward SPDE with jumps. For systems with random coefficients, a Malliavin calculus approach is developed. The main novelty here is the establishment of the well-posedness of an operator-valued SPDE with jumps, which provides a new stochastic flow representation for linear SPDEs with jumps.

math.OC↗
arXiv2025

Optimal Control of Stochastic Partial Differential Equations with Partial Observations: Stochastic Maximum Principles and Numerical Approximation

This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a cylindrical Wiener process and finitely many Brownian motions, while observations are in an Euclidean space having correlated noise. For convex control domain and diffusion coefficients in the state being control-independent, numerical algorithms are developed to solve the partially observed optimal control problems using stochastic gradient descent algorithm combined with finite element approximations and the branching filtering algorithm. Numerical experiments are conducted for demonstration.

math.OC↗
arXiv2024

A hybrid deep learning method for finite-horizon mean-field game problems

This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep learning algorithm. Under the framework of finite-horizon mean-field games, the induced measure and Monte-Carlo algorithm are adopted to establish the iterative mean-field interaction in Markov chain approximation method and deep learning, respectively. The Markov chain approximation method plays a key role in constructing the iterative algorithm and estimating an initial value of a neural network, whereas stochastic approximation is used to find accurate parameters in a bounded region. The convergence of the hybrid algorithm is proved; two numerical examples are provided to illustrate the results.

math.OC↗
arXiv2024

Second-Order Fast-Slow Stochastic Systems

This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and stochastic acceleration in a random environment. Our effort is to carry out asymptotic analysis to establish large deviations principles. Our focus is on obtaining the desired results for systems under weaker conditions. When the fast-varying process is a diffusion, neither Lipschitz continuity nor linear growth needs to be assumed. Our approach is based on combinations of the intuition from Smoluchowski-Kramers approximation, and the methods initiated in [34] relying on the concepts of relatively large deviations compactness and the identification of rate functions. When the fast-varying process is under a general setup with no specified structure, the paper establishes the large deviations principle of the underlying system under the assumption on the local large deviations principles of the corresponding first-order system.

math.PR↗
arXiv2024

Closed-loop Equilibria for Mean-Field Games in Randomly Switching Environments with General Discounting Costs

This work is devoted to finding the closed-loop equilibria for a class of mean-field games (MFGs) with infinitely many symmetric players in a common switching environment when the cost functional is under general discount in time. There are two key challenges in the application of the well-known Hamilton-Jacobi-Bellman and Fokker-Planck (HJB-FP) approach to our problems: the path-dependence due to the conditional mean-field interaction and the time-inconsistency due to the general discounting cost. To overcome the difficulties, a theory for a class of systems of path-dependent equilibrium Hamilton-Jacobi-Bellman equations (HJBs) is developed. Then closed-loop equilibrium strategies can be identified through a two-step verification procedure. It should be noted that the closed-loop equilibrium strategies obtained satisfy a new form of local optimality in the Nash sense. The theory obtained extends the HJB-FP approach for classical MFGs to more general conditional MFGs with general discounting costs.

math.OC↗
arXiv2024

Contingency Detection in Modern Power Systems: A Stochastic Hybrid System Method

This paper introduces a new stochastic hybrid system (SHS) framework for contingency detection in modern power systems (MPS). The framework uses stochastic hybrid system representations in state space models to expand and facilitate capability of contingency detection. In typical microgrids (MGs), buses may contain various synchronous generators, renewable generators, controllable loads, battery systems, regular loads, etc. For development of SHS models in power systems, this paper introduces the concept of dynamic and non-dynamic buses. By converting a physical power grid into a virtual linearized state space model and representing contingencies as random switching of system structures and parameters, this paper formulates the contingency detection problem as a joint estimation problem of discrete event and continuous states in stochastic hybrid systems. This method offers unique advantages, including using common measurement signals on voltage and current synchrophasors to detect different types and locations of contingencies, avoiding expensive local direct fault measurements and detecting certain contingencies that cannot be directly measured. The method employs a small and suitably-designed probing signal to sustain the ability of persistent contingency detection. Joint estimation algorithms are presented with their proven convergence and reliability properties. Examples that use an IEEE 5-bus system demonstrate the main ideas and derivation steps. Simulation case studies on an IEEE 33-bus system are used for detecting transmission line faults and sensor interruptions.

eess.SY↗
arXiv2024

Stochastic Hybrid System Modeling and State Estimation of Modern Power Systems under Contingency

This paper introduces a stochastic hybrid system (SHS) framework in state space model to capture sensor, communication, and system contingencies in modern power systems (MPS). Within this new framework, the paper concentrates on the development of state estimation methods and algorithms to provide reliable state estimation under randomly intermittent and noisy sensor data. MPSs employ diversified measurement devices for monitoring system operations that are subject to random measurement errors and rely on communication networks to transmit data whose channels encounter random packet loss and interruptions. The contingency and noise form two distinct and interacting stochastic processes that have a significant impact on state estimation accuracy and reliability. This paper formulates stochastic hybrid system models for MPSs, introduces coordinated observer design algorithms for state estimation, and establishes their convergence and reliability properties. A further study reveals a fundamental design tradeoff between convergence rates and steady-state error variances. Simulation studies on the IEEE 5-bus system and IEEE 33-bus system are used to illustrate the modeling methods, observer design algorithms, convergence properties, performance evaluations, and impact sensor system selections.

eess.SY↗
arXiv2024

Kitchen Food Waste Image Segmentation and Classification for Compost Nutrients Estimation

The escalating global concern over extensive food wastage necessitates innovative solutions to foster a net-zero lifestyle and reduce emissions. The LILA home composter presents a convenient means of recycling kitchen scraps and daily food waste into nutrient-rich, high-quality compost. To capture the nutritional information of the produced compost, we have created and annotated a large high-resolution image dataset of kitchen food waste with segmentation masks of 19 nutrition-rich categories. Leveraging this dataset, we benchmarked four state-of-the-art semantic segmentation models on food waste segmentation, contributing to the assessment of compost quality of Nitrogen, Phosphorus, or Potassium. The experiments demonstrate promising results of using segmentation models to discern food waste produced in our daily lives. Based on the experiments, SegFormer, utilizing MIT-B5 backbone, yields the best performance with a mean Intersection over Union (mIoU) of 67.09. Class-based results are also provided to facilitate further analysis of different food waste classes.

cs.CV↗
arXiv2022

Harvesting of a stochastic population under a mixed regular-singular control formulation

This work focuses on optimal harvesting-renewing for a stochastic population. A mixed regular-singular control formulation with a state constraint and regime-switching is introduced. The decision-makers either harvest or renew with finite or infinite harvesting/renewing rates. The payoff functions depend on the harvesting/renewing rates. Several properties of the value functions are established. The limiting value function as the white noise intensity approaches infinity is identified. The Markov chain approximation method is used to find a numerical approximation of the value function and optimal strategies.

math.OC↗
arXiv2022

On an Ergodic Two-Sided Singular Control Problem

Motivated by applications in natural resource management, risk management, and finance, this paper is focused on an ergodic two-sided singular control problem for a general one-dimensional diffusion process. The control is given by a bounded variation process. Under some mild conditions, the optimal reward value as well as an optimal control policy are derived by the vanishing discount method. Moreover, the Abelian and Cesàro limits are established. Then a direct solution approach is provided at the end of the paper.

math.OC↗
arXiv2022

Stochastic epidemic SIR models with hidden states

This paper focuses on and analyzes realistic SIR models that take stochasticity into account. The proposed systems are applicable to most incidence rates that are used in the literature including the bilinear incidence rate, the Beddington-DeAngelis incidence rate, and a Holling type II functional response. Given that many diseases can lead to asymptomatic infections, we look at a system of stochastic differential equations that also includes a class of hidden state individuals, for which the infection status is unknown. We assume that the direct observation of the percentage of hidden state individuals that are infected, $α(t)$, is not given and only a noise-corrupted observation process is available. Using the nonlinear filtering techniques in conjunction with an invasion type analysis (or analysis using Lyapunov exponents from the dynamical system point of view), this paper proves that the long-term behavior of the disease is governed by a threshold $λ\in \mathbb{R}$ that depends on the model parameters. It turns out that if $λ<0$ the number $I(t)$ of infected individuals converges to zero exponentially fast, or the extinction happens. In contrast, if $λ>0$, the infection is endemic and the system is permanent. We showcase our results by applying them in specific illuminating examples. Numerical simulations are also given to illustrate our results.

math.PR↗
arXiv2021

Stochastic Approximation with Discontinuous Dynamics, Differential Inclusions, and Applications

This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and non-smooth analysis, and stochastic differential inclusions. Under broad conditions, it is shown that a suitably scaled sequence of the iterates has a differential inclusion limit. In addition, it is shown for the first time that a centered and scaled sequence of the iterates converges weakly to a stochastic differential inclusion limit. The results are then used to treat several application examples including Markov decision process, Lasso algorithms, Pegasos algorithms, support vector machine classification, and learning. Some numerical demonstrations are also provided.

math.PR↗
arXiv2021

Stability and Stabilization of Coupled Jump Diffusions and Applications

This paper develops stability and stabilization results for systems of fully coupled jump diffusions. Such systems frequently arise in numerous applications where each subsystem (component) is operated under the influence of other subsystems (components). This paper derives sufficient conditions under which the underlying coupled jump diffusion is stable. The results are then applied to investigate the stability of linearizable jump diffusions, fast-slow coupled jump diffusions. Moreover, weak stabilization of interacting systems and consensus of leader-following systems are examined.

math.PR↗
arXiv2021

Dynamical systems with fast switching and slow diffusion: Hyperbolic equilibria and stable limit cycles

We study the long-term qualitative behavior of randomly perturbed dynamical systems. More specifically, we look at limit cycles of stochastic differential equations (SDE) with Markovian switching, in which the process switches at random times among different systems of SDEs, when the switching is fast and the diffusion (white noise) term is small. The system is modeled by $$ dX^{ε,δ}(t)=f(X^{ε,δ}(t), α^ε(t))dt+\sqrtδσ(X^{ε,δ}(t), α^ε(t))dW(t) , \ X^ε(0)=x, $$ where $α^ε(t)$ is a finite state space Markov chain with irreducible generator $Q=(q_{ij})$. The relative changing rates of the switching and the diffusion are highlighted by the two small parameters $ε$ and $δ$. We associate to the system the averaged ODE \[ d\bar X(t)=\bar f(\bar X(t))dt, \ X(0)=x, \] where $\bar f(\cdot)=\sum_{i=1}^{m_0}f(\cdot, i)ν_i$ and $(ν_1,\dots,ν_{m_0})$ is the unique invariant probability measure of the Markov chain with generator $Q$. Suppose that for each pair $(ε,δ)$ of parameters, the process has an invariant probability measure $μ^{ε,δ}$, and that the averaged ODE has a limit cycle in which there is an averaged occupation measure $μ^0$ for the averaged equation. We are able to prove that if $\bar f$ has finitely many unstable or hyperbolic fixed points, then $μ^{ε,δ}$ converges weakly to $μ^0$ as $ε\to 0$ and $δ\to 0$. Our results generalize to the setting of state-dependent switching \[ \mathbb{P}\{α^ε(t+Δ)=j~|~α^ε=i, X^{ε,δ}(s),α^ε(s), s\leq t\}=q_{ij}(X^{ε,δ}(t))Δ+o(Δ),~~ i\neq j \] as long as the generator $Q(\cdot)=(q_{ij}(\cdot))$ is bounded, Lipschitz, and irreducible for all $x\in\mathbb{R}^d$. We conclude our analysis by studying a predator-prey model.

math.PR↗
arXiv2021

Stochastic Functional Kolmogorov Equations II: Extinction

This work, Part II, together with its companion Part I develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equations depending on the current as well as the past states. Because of the complexity of the problems, it is natural to divide our contributions into two parts to answer a long-standing question in biology and ecology. What are the minimal conditions for long-term persistence and extinction of a population? Part I of our work provides characterization of persistence, whereas in this part, extinction is the main focus. The main techniques used in this paper are combination of the newly developed functional It^o formula and a dynamical system approach. Compared to the study of stochastic Kolmogorov systems without delays, the main difficulty is that infinite dimensional systems have to be treated. The extinction is characterized after investigating random occupation measures and examining behavior of functional systems around boundaries. Our characterizations of long-term behavior of the systems reduces to that of Kolmogorov systems without delay when there is no past dependence. A number of applications are also examined.

math.PR↗
arXiv2021

Stochastic Functional Kolmogorov Equations (I): Persistence

This work (Part (I)) together with its companion (Part (II) [45]) develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equations depending on the current as well as the past states. Because of the complexity of the results, it seems to be instructive to divide our contributions to two parts. In contrast to the existing literature, our effort is to advance the knowledge by allowing delay and past dependence, yielding essential utility to a wide range of applications. A long-standing question of fundamental importance pertaining to biology and ecology is: What are the minimal necessary and sufficient conditions for long-term persistence and extinction (or for long-term coexistence of interacting species) of a population? Regardless of the particular applications encountered, persistence and extinction are properties shared by Kolmogorov systems. While there are many excellent treaties of stochastic-differential-equation-based Kolmogorov equations, the work on stochastic Kolmogorov equations with past dependence is still scarce. Our aim here is to answer the aforementioned basic question. This work, Part (I), is devoted to characterization of persistence, whereas its companion, Part (II) [45], is devoted to extinction. The main techniques used in this paper include the newly developed functional It^o formula and asymptotic coupling and Harris-like theory for infinite dimensional systems specialized to functional equations. General theorems for stochastic functional Kolmogorov equations are developed first. Then a number of applications are examined to obtain new results substantially covering, improving, and extending the existing literature. Furthermore, these conditions reduce to that of Kolmogorov systems when there is no past dependence.

math.PR↗
arXiv2021

Multi-kernel Passive Stochastic Gradient Algorithms and Transfer Learning

This paper develops a novel passive stochastic gradient algorithm. In passive stochastic approximation, the stochastic gradient algorithm does not have control over the location where noisy gradients of the cost function are evaluated. Classical passive stochastic gradient algorithms use a kernel that approximates a Dirac delta to weigh the gradients based on how far they are evaluated from the desired point. In this paper we construct a multi-kernel passive stochastic gradient algorithm. The algorithm performs substantially better in high dimensional problems and incorporates variance reduction. We analyze the weak convergence of the multi-kernel algorithm and its rate of convergence. In numerical examples, we study the multi-kernel version of the passive least mean squares (LMS) algorithm for transfer learning to compare the performance with the classical passive version.

cs.LG↗