arXiv subjects

Xun Li

Publications and source records attributed to Xun Li.

At least 55 records · Page 3Linked to original sources

arXiv2025

Optimal Consumption-Investment for General Utility with a Drawdown Constraint over a Finite-Time Horizon

We study an optimal investment and consumption problem over a finite-time horizon, in which an individual invests in a risk-free asset and a risky asset, and evaluate utility using a general utility function that exhibits loss aversion with respect to the historical maximum of consumption. Motivated by behavioral finance and habit formation theory, we model the agent's preference for maintaining a standard of living by imposing constraints on declines from the peak consumption level. To solve the resulting Hamilton-Jacobi-Bellman (HJB) variational inequality, which is fully nonlinear, we apply a dual transformation, transforming the original problem into a linear singular control problem with a constraint. By differentiating the value function further, we reduce the constrained linear singular control problem to a linear obstacle problem. We prove the existence of a solution to the obstacle problem under standard constraints. It allows us to characterize the optimal consumption and investment strategies through piecewise analytical feedback forms derived from the dual formulation. Our analysis contributes to the literature on habit formation, drawdown constraints, and stochastic control by explicitly characterizing the time-dependent free boundaries and the associated optimal feedback strategies.

math.OC↗

arXiv2025

Open-loop and closed-loop solvabilities for zero-sum stochastic linear quadratic differential games of Markovian regime switching system

This paper investigates zero-sum stochastic linear quadratic (SLQ) differential games with Markovian jumps. Open-loop and closed-loop solvabilities are studied by employing a new ``decomposition method", which decomposes the open-loop and closed-loop solvability problems of zero-sum SLQ differential games into two coupled SLQ control problems. Under the uniform convexity-concavity condition, we construct the open-loop saddle point along with its closed-loop representation based on the solution to a system of constrained coupled differential Riccati equations (CDREs), whose solvability is also established by employing the dimension extension technique and the continuation method. Finally, we provide a concrete example and present its closed-form saddle point based on the theoretical results obtained.

math.OC↗

arXiv2025

Discrete-Time LQ Stochastic Two-Person Nonzero-Sum Difference Games with Random Coefficients:~Open-Loop Nash Equilibrium

This paper presents a pioneering investigation into discrete-time two-person non-zero-sum linear quadratic (LQ) stochastic games with random coefficients. We derive necessary and sufficient conditions for the existence of open-loop Nash equilibria using convex variational calculus. To obtain explicit expressions for the Nash equilibria, we introduce fully coupled forward-backward stochastic difference equations (FBS$Δ$E, for short), which provide a dual characterization of these Nash equilibria. Additionally, we develop non-symmetric stochastic Riccati equations that decouple the stochastic Hamiltonian system for each player, enabling the derivation of closed-loop feedback forms for open-loop Nash equilibrium strategies. A notable aspect of this research is the complete randomness of the coefficients, which results in the corresponding Riccati equations becoming fully nonlinear higher-order backward stochastic difference equations. It distinguishes our non-zero-sum difference game from the deterministic case, where the Riccati equations reduce to algebraic forms.

math.OC↗

arXiv2025

Infinite Horizon Fully Coupled Nonlinear Forward-Backward Stochastic Difference Equations and Their Application to LQ Optimal Control Problems

This paper focuses on the study of infinite horizon fully coupled nonlinear forward-backward stochastic difference equations (FBS$\bigtriangleup$Es). Firstly, we establish a pair of priori estimates for the solutions to forward stochastic difference equations (S$\bigtriangleup$Es) and backward stochastic difference equations (BS$\bigtriangleup$Es), respectively. Then, to achieve broader applicability, we utilize a set of domination-monotonicity conditions that are more lenient than standard assumptions. Using these conditions, we apply continuation methods to prove the unique solvability of infinite horizon fully coupled FBS$\bigtriangleup$Es and derive a set of solution estimates. Furthermore, our results have considerable implications for a variety of related linear quadratic (LQ) problems, especially when the stochastic Hamiltonian system is consistent with FBS$\bigtriangleup$Es satisfying the introduced domination-monotonicity conditions. Thus, by solving the associated stochastic Hamiltonian system, we explicitly characterize the unique optimal control. This is the first work establishing solvability of fully coupled nonlinear FBS$\bigtriangleup$Es under domination-monotonicity conditions in infinite horizon discrete-time setting.

math.OC↗

arXiv2025

Infinite horizon discounted LQ optimal control problems for mean-field switching diffusions

This paper investigates an infinite horizon discounted linear-quadratic (LQ) optimal control problem for stochastic differential equations (SDEs) incorporating regime switching and mean-field interactions. The regime switching is modeled by a finite-state Markov chain acting as common noise, while the mean-field interactions are characterized by the conditional expectation of the state process given the history of the Markov chain. To address system stability in the infinite horizon setting, a discounted factor is introduced. Within this framework, the well-posedness of the state equation and adjoint equation -- formulated as infinite horizon mean-field forward and backward SDEs with Markov chains, respectively -- is established, along with the asymptotic behavior of their solutions as time approaches infinity. A candidate optimal feedback control law is formally derived based on two algebraic Riccati equations (AREs), which are introduced for the first time in this context. The solvability of these AREs is proven through an approximation scheme involving a sequence of Lyapunov equations, and the optimality of the proposed feedback control law is rigorously verified using the completion of squares method. Finally, numerical experiments are conducted to validate the theoretical findings, including solutions to the AREs, the optimal control process, and the corresponding optimal (conditional) state trajectory. This work provides a comprehensive framework for solving infinite horizon discounted LQ optimal control problems in the presence of regime switching and mean-field interactions, offering both theoretical insights and practical computational tools.

math.OC↗

arXiv2025

Federated Learning Assisted Edge Caching Scheme Based on Lightweight Architecture DDPM

Edge caching is an emerging technology that empowers caching units at edge nodes, allowing users to fetch contents of interest that have been pre-cached at the edge nodes. The key to pre-caching is to maximize the cache hit percentage for cached content without compromising users' privacy. In this letter, we propose a federated learning (FL) assisted edge caching scheme based on lightweight architecture denoising diffusion probabilistic model (LDPM). Our simulation results verify that our proposed scheme achieves a higher cache hit percentage compared to existing FL-based methods and baseline methods.

cs.NI↗

arXiv2025

Design and Implementation of ARA Wireless Living Lab for Rural Broadband and Applications

Addressing the broadband gap between rural and urban regions requires rural-focused wireless research and innovation. In the meantime, rural regions provide rich, diverse use cases of advanced wireless, and they offer unique real-world settings for piloting applications that advance the frontiers of wireless systems (e.g., teleoperation of ground and aerial vehicles). To fill the broadband gap and to leverage the unique opportunities that rural regions provide for piloting advanced wireless applications, we design and implement the ARA wireless living lab for research and innovation in rural wireless systems and their applications in precision agriculture, community services, and so on. ARA focuses on the unique community, application, and economic context of rural regions, and it features the first-of-its-kind, real-world deployment of long-distance, high-capacity terrestrial wireless x-haul and access platforms as well as low-earth-orbit (LEO) satellite communications platforms across a rural area of diameter over 30 km. With both software-defined radios and programmable COTS systems, and through effective orchestration of these wireless resources with fiber as well as compute resources embedded end-to-end across user equipment (UE), base stations (BS), edge, and cloud, including support for Bring Your Own Device (BYOD), ARA offers programmability, performance, robustness, and heterogeneity at the same time, thus enabling rural-focused co-evolution of wireless and applications while helping advance the frontiers of wireless systems in domains such as Open RAN, NextG, and agriculture applications.

cs.NI↗

arXiv2025

NeuroLoc: Encoding Navigation Cells for 6-DOF Camera Localization

Recently, camera localization has been widely adopted in autonomous robotic navigation due to its efficiency and convenience. However, autonomous navigation in unknown environments often suffers from scene ambiguity, environmental disturbances, and dynamic object transformation in camera localization. To address this problem, inspired by the biological brain navigation mechanism (such as grid cells, place cells, and head direction cells), we propose a novel neurobiological camera location method, namely NeuroLoc. Firstly, we designed a Hebbian learning module driven by place cells to save and replay historical information, aiming to restore the details of historical representations and solve the issue of scene fuzziness. Secondly, we utilized the head direction cell-inspired internal direction learning as multi-head attention embedding to help restore the true orientation in similar scenes. Finally, we added a 3D grid center prediction in the pose regression module to reduce the final wrong prediction. We evaluate the proposed NeuroLoc on commonly used benchmark indoor and outdoor datasets. The experimental results show that our NeuroLoc can enhance the robustness in complex environments and improve the performance of pose regression by using only a single image.

cs.RO↗

arXiv2025

Weak Closed-loop Solvability for Discrete-time Stochastic Linear-Quadratic Optimal Control

In this paper, the solvability of discrete-time stochastic linear-quadratic (LQ) optimal control problem in finite horizon is considered. Firstly, it shows that the closed-loop solvability for the LQ control problem is optimal if and only if the generalized Riccati equation admits a regular solution by solving the forward and backward difference equations iteratively. To this ends, it finds that the open-loop solvability is strictly weaker than closed-loop solvability, that is, the LQ control problem is always open-loop optimal solvable if it is closed-loop optimal solvable but not vice versa. Secondly, by the perturbation method, it proves that the weak-closed loop strategy which is a feedback form of a state feedback representation is equivalent to the open-loop solvability of the LQ control problem. Finally, an example sheds light on the theoretical results established.

math.OC↗

arXiv2025

Interpreting core forms of urban morphology linked to urban functions with explainable graph neural network

Understanding the high-order relationship between urban form and function is essential for modeling the underlying mechanisms of sustainable urban systems. Nevertheless, it is challenging to establish an accurate data representation for complex urban forms that are readily explicable in human terms. This study proposed the concept of core urban morphology representation and developed an explainable deep learning framework for explicably symbolizing complex urban forms into the novel representation, which we call CoMo. By interpretating the well-trained deep learning model with a stable weighted F1-score of 89.14%, CoMo presents a promising approach for revealing links between urban function and urban form in terms of core urban morphology representation. Using Boston as a study area, we analyzed the core urban forms at the individual-building, block, and neighborhood level that are important to corresponding urban functions. The residential core forms follow a gradual morphological pattern along the urban spine, which is consistent with a center-urban-suburban transition. Furthermore, we prove that urban morphology directly affects land use efficiency, which has a significantly strong correlation with the location (R2=0.721, p<0.001). Overall, CoMo can explicably symbolize urban forms, provide evidence for the classic urban location theory, and offer mechanistic insights for digital twins.

cs.CE↗

arXiv2025

Understanding infection risks of COVID-19 in the city: an investigation of infected neighborhoods in Wuhan

During the COVID-19 pandemic, built environments in dense urban settings become major sources of infection. This study tests the difference of demographics and surrounding built environments across high-, medium- and low-infection neighborhoods, to inform the high-risk areas in the city. We found that high-infection neighborhoods own a higher ratio of aged population than other neighborhoods on average. However, it shows no statistical difference in terms of population density. Additionally, high-infection neighborhoods are closer to high-risk built environments than the others. In a walking distance, they also can access more of the high-risk built environments except for the wholesale markets and shopping malls. These findings advise policy-makers to deploy social distancing measures in precision, regulating the access of high-risk facilities to mitigate the impacts of COVID-19.

physics.soc-ph↗

arXiv2025

Weak Closed-loop Solvability for Discrete-time Linear-Quadratic Optimal Control

In this paper, the open-loop, closed-loop, and weak closed-loop solvability for discrete-time linear-quadratic (LQ) control problem is considered due to the fact that it is always open-loop optimal solvable if the LQ control problem is closed-loop optimal solvable but not vice versa. The contributions are two-fold. On the one hand, the equivalent relationship between the closed-loop optimal solvability and the solution of the generalized Riccati equation is given. On the other hand, when the system is merely open-loop solvable, we have found the equivalent existence form of the optimal solution by perturbation method, which is said to be a weak closed-loop solution. Moreover, it obtains that there is an open-loop optimal control with a linear feedback form of the state. The essential technique is to solve the forward and backward difference equations by iteration. An example sheds light on the theoretical results established.

math.OC↗

arXiv2025

Beyond surveys: A High-Precision Wealth Inequality Mapping of China's Rural Households Derived from Satellite and Street View Imageries

Wide coverage and high-precision rural household wealth data is an important support for the effective connection between the national macro rural revitalization policy and micro rural entities, which helps to achieve precise allocation of national resources. However, due to the large number and wide distribution of rural areas, wealth data is difficult to collect and scarce in quantity. Therefore, this article attempts to integrate "sky" remote sensing images with "ground" village street view imageries to construct a fine-grained "computable" technical route for rural household wealth. With the intelligent interpretation of rural houses as the core, the relevant wealth elements of image data were extracted and identified, and regressed with the household wealth indicators of the benchmark questionnaire to form a high-precision township scale wealth prediction model (r=0.85); Furthermore, a national and township scale map of rural household wealth in China was promoted and drawn. Based on this, this article finds that there is a "bimodal" pattern in the distribution of wealth among rural households in China, which is reflected in a polarization feature of "high in the south and low in the north, and high in the east and low in the west" in space. This technological route may provide alternative solutions with wider spatial coverage and higher accuracy for high-cost manual surveys, promote the identification of shortcomings in rural construction, and promote the precise implementation of rural policies.

econ.GN↗

arXiv2024

Stochastic linear quadratic optimal control problems with regime-switching jumps in infinite horizon

This paper investigates a stochastic linear-quadratic (SLQ, for short) control problem regulated by a time-invariant Markov chain in infinite horizon. Under the $L^2$-stability framework, we study a class of linear backward stochastic differential equations (BSDE, for short) in infinite horizon and discuss the open-loop and closed-loop solvabilities of the SLQ problem. The open-loop solvability is characterized by the solvability of a system of coupled forward-backward stochastic differential equations (FBSDEs, for short) in infinite horizon and the convexity of the cost functional, and the closed-loop solvability is shown to be equivalent to the open-loop solvability, which in turn is equivalent to the existence of a static stabilizing solution to the associated constrained coupled algebra Riccati equations (CAREs, for short). Under the uniform convexity assumption, we obtain the unique solvability of associated CAREs and construct the corresponding closed-loop optimal strategy. Finally, we also solve a class of discounted SLQ problems and give two concrete examples to illustrate the results developed in the earlier sections.

math.OC↗

arXiv2024

Facial Expression Recognition with Controlled Privacy Preservation and Feature Compensation

Facial expression recognition (FER) systems raise significant privacy concerns due to the potential exposure of sensitive identity information. This paper presents a study on removing identity information while preserving FER capabilities. Drawing on the observation that low-frequency components predominantly contain identity information and high-frequency components capture expression, we propose a novel two-stream framework that applies privacy enhancement to each component separately. We introduce a controlled privacy enhancement mechanism to optimize performance and a feature compensator to enhance task-relevant features without compromising privacy. Furthermore, we propose a novel privacy-utility trade-off, providing a quantifiable measure of privacy preservation efficacy in closed-set FER tasks. Extensive experiments on the benchmark CREMA-D dataset demonstrate that our framework achieves 78.84% recognition accuracy with a privacy (facial identity) leakage ratio of only 2.01%, highlighting its potential for secure and reliable video-based FER applications.

cs.CV↗

arXiv2024

Policy Iteration Reinforcement Learning Method for Continuous-Time Linear-Quadratic Mean-Field Control Problems

This paper employs a policy iteration reinforcement learning (RL) method to study continuous-time linear-quadratic mean-field control problems in infinite horizon. The drift and diffusion terms in the dynamics involve the states, the controls, and their conditional expectations. We investigate the stabilizability and convergence of the RL algorithm using a Lyapunov Recursion. Instead of solving a pair of coupled Riccati equations, the RL technique focuses on strengthening an auxiliary function and the cost functional as the objective functions and updating the new policy to compute the optimal control via state trajectories. A numerical example sheds light on the established theoretical results.

math.OC↗

arXiv2024

Optimal consumption under a drawdown constraint over a finite horizon

This paper studies a finite horizon utility maximization problem on excessive consumption under a drawdown constraint. Our control problem is an extension of the one considered in Bahman et al. (2019) to the model with a finite horizon and an extension of the one considered in Jeon and Oh (2022) to the model with zero interest rate. Contrary to Bahman et al. (2019), we encounter a parabolic nonlinear HJB variational inequality with a gradient constraint, in which some time-dependent free boundaries complicate the analysis significantly. Meanwhile, our methodology is built on technical PDE arguments, which differs from the martingale approach in Jeon and Oh (2022). Using the dual transform and considering the auxiliary variational inequality with gradient and function constraints, we establish the existence and uniqueness of the classical solution to the HJB variational inequality after the dimension reduction, and the associated free boundaries can be characterized in analytical form. Consequently, the piecewise optimal feedback controls and the time-dependent thresholds for the ratio of wealth and historical consumption peak can be obtained.

math.OC↗

arXiv2024

Sui Lutris: A Blockchain Combining Broadcast and Consensus

Sui Lutris is the first smart-contract platform to sustainably achieve sub-second finality. It achieves this significant decrease by employing consensusless agreement not only for simple payments but for a large variety of transactions. Unlike prior work, Sui Lutris neither compromises expressiveness nor throughput and can run perpetually without restarts. Sui Lutris achieves this by safely integrating consensuless agreement with a high-throughput consensus protocol that is invoked out of the critical finality path but ensures that when a transaction is at risk of inconsistent concurrent accesses, its settlement is delayed until the total ordering is resolved. Building such a hybrid architecture is especially delicate during reconfiguration events, where the system needs to preserve the safety of the consensusless path without compromising the long-term liveness of potentially misconfigured clients. We thus develop a novel reconfiguration protocol, the first to provably show the safe and efficient reconfiguration of a consensusless blockchain. Sui Lutris is currently running in production and underpins the Sui smart-contract platform. Combined with the use of Objects instead of accounts it enables the safe execution of smart contracts that expose objects as a first-class resource. In our experiments Sui Lutris achieves latency lower than 0.5 seconds for throughput up to 5,000 certificates per second (150k ops/s with transaction blocks), compared to the state-of-the-art real-world consensus latencies of 3 seconds. Furthermore, it gracefully handles validators crash-recovery and does not suffer visible performance degradation during reconfiguration.

cs.DC↗