arXiv subjects

Xiang Yu

Publications and source records attributed to Xiang Yu.

At least 91 records · Page 5Linked to original sources

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

Continuous-time q-learning for mean-field control problems

This paper studies the q-learning, recently coined as the continuous time counterpart of Q-learning by Jia and Zhou (2023), for continuous time Mckean-Vlasov control problems in the setting of entropy-regularized reinforcement learning. In contrast to the single agent's control problem in Jia and Zhou (2023), the mean-field interaction of agents renders the definition of the q-function more subtle, for which we reveal that two distinct q-functions naturally arise: (i) the integrated q-function (denoted by $q$) as the first-order approximation of the integrated Q-function introduced in Gu, Guo, Wei and Xu (2023), which can be learnt by a weak martingale condition involving test policies; and (ii) the essential q-function (denoted by $q_e$) that is employed in the policy improvement iterations. We show that two q-functions are related via an integral representation under all test policies. Based on the weak martingale condition and our proposed searching method of test policies, some model-free learning algorithms are devised. In two examples, one in LQ control framework and one beyond LQ control framework, we can obtain the exact parameterization of the optimal value function and q-functions and illustrate our algorithms with simulation experiments.

cs.LG↗

arXiv2024

On optimal tracking portfolio in incomplete markets: The reinforcement learning approach

This paper studies an infinite horizon optimal tracking portfolio problem using capital injection in incomplete market models. The benchmark process is modelled by a geometric Brownian motion with zero drift driven by some unhedgeable risk. The relaxed tracking formulation is adopted where the fund account compensated by the injected capital needs to outperform the benchmark process at any time, and the goal is to minimize the cost of the discounted total capital injection. When model parameters are known, we formulate the equivalent auxiliary control problem with reflected state dynamics, for which the classical solution of the HJB equation with Neumann boundary condition is obtained explicitly. When model parameters are unknown, we introduce the exploratory formulation for the auxiliary control problem with entropy regularization and develop the continuous-time q-learning algorithm in models of reflected diffusion processes. In some illustrative numerical example, we show the satisfactory performance of the q-learning algorithm.

q-fin.PM↗

arXiv2024

On the incremental equations in surface elasticity

We derive the incremental equations for a hyperelastic solid that incorporate surface tension effect by assuming that the surface energy is a general function of the surface deformation gradient. The incremental equations take the same simple form as their purely mechanical counterparts and are valid for any geometry. In particular, for isotropic materials, the extra surface elastic moduli are expressed in terms of the surface energy function and the two surface principal stretches. The effectiveness of the resulting incremental theory is illustrated by applying it to study the Plateau--Rayleigh and Wilkes instabilities in a solid cylinder.

cond-mat.soft↗

arXiv2024

An asymptotically consistent morphoelastic shell model for compressible biological structures with finite-strain deformations

We derive an asymptotically consistent morphoelastic shell model to describe the finite deformations of biological tissues using the variational asymptotical method. Biological materials may exhibit remarkable compressibility when under large deformations, and we take this factor into account for accurate predictions of their morphoelastic changes. The morphoelastic shell model combines the growth model of Rodriguez et al. and a novel shell model developed by us. We start from the three-dimensional (3D) morphoelastic model and construct the optimal shell energy based on a series expansion around the middle surface. A two-step variational method is applied that retains the leading-order expansion coefficient while eliminating the higher-order ones. The main outcome is a two-dimensional (2D) shell energy depending on the stretching and bending strains of the middle surface. The derived morphoelastic shell model is asymptotically consistent with three-dimensional morphoelasticity and can recover various shell models in literature. Several examples are shown for the verification and illustration.

cond-mat.soft↗

arXiv2024

QComp: A QSAR-Based Data Completion Framework for Drug Discovery

In drug discovery, in vitro and in vivo experiments reveal biochemical activities related to the efficacy and toxicity of compounds. The experimental data accumulate into massive, ever-evolving, and sparse datasets. Quantitative Structure-Activity Relationship (QSAR) models, which predict biochemical activities using only the structural information of compounds, face challenges in integrating the evolving experimental data as studies progress. We develop QSAR-Complete (QComp), a data completion framework to address this issue. Based on pre-existing QSAR models, QComp utilizes the correlation inherent in experimental data to enhance prediction accuracy across various tasks. Moreover, QComp emerges as a promising tool for guiding the optimal sequence of experiments by quantifying the reduction in statistical uncertainty for specific endpoints, thereby aiding in rational decision-making throughout the drug discovery process.

cs.LG↗

arXiv2024

Stochastic control problems with state-reflections arising from relaxed benchmark tracking

This paper studies stochastic control problems motivated by optimal consumption with wealth benchmark tracking. The benchmark process is modeled by a combination of a geometric Brownian motion and a running maximum process, indicating its increasing trend in the long run. We consider a relaxed tracking formulation such that the wealth compensated by the injected capital always dominates the benchmark process. The stochastic control problem is to maximize the expected utility of consumption deducted by the cost of the capital injection under the dynamic floor constraint. By introducing two auxiliary state processes with reflections, an equivalent auxiliary control problem is formulated and studied, which leads to the HJB equation with two Neumann boundary conditions. We establish the existence of a unique classical solution to the dual PDE using some novel probabilistic representations involving the local time of some dual processes together with a tailor-made decomposition-homogenization technique. The proof of the verification theorem on the optimal feedback control can be carried out by some stochastic flow analysis and technical estimations of the optimal control.

math.OC↗

arXiv2024

Reduced model and nonlinear analysis of localized instabilities of residually stressed cylinders under axial stretch

In this paper we present a dimensional reduction to obtain a one-dimensional model to analyze localized necking or bulging in a residually stressed circular cylindrical solid. The nonlinear theory of elasticity is first specialized to obtain the equations governing the homogeneous deformation. Then, to analyze the non-homogeneous part, we include higher order correction terms of the axisymmetric displacement components leading to a three-dimensional form of the total potential energy functional. Details of the reduction to the one-dimensional form are given. We focus on a residually stressed Gent material and use numerical methods to solve the governing equations. Two loading conditions are considered. In the first, the residual stress is maintained constant, while the axial stretch is used as the loading parameter. In the second, we keep the pre-stretch constant and monotonically increase the residual stress until bifurcation occurs. We specify initial conditions, find the critical values for localized bifurcation and compute the change in radius during localized necking or bulging growth. Finally, we optimize material properties and use the one-dimensional model to simulate necking or bulging until the Maxwell values of stretch are reached.

cond-mat.soft↗

arXiv2024

Optimal consumption with loss aversion and reference to past spending maximum

This paper studies an optimal consumption problem for a loss-averse agent with reference to past consumption maximum. To account for loss aversion on relative consumption, an S-shaped utility is adopted that measures the difference between the non-negative consumption rate and a fraction of the historical spending peak. We consider the concave envelope of the utility with respect to consumption, allowing us to focus on an auxiliary HJB variational inequality on the strength of concavification principle and dynamic programming arguments. By applying the dual transform and smooth-fit conditions, the auxiliary HJB variational inequality is solved in piecewise closed-form and some thresholds of the wealth variable are obtained. The optimal consumption and investment control can be derived in the piecewise feedback form. The rigorous verification proofs on optimality and concavification principle are provided. Some numerical sensitivity analysis and financial implications are also presented.

math.OC↗

arXiv2024

A mean field game approach to equilibrium consumption under external habit formation

This paper studies the equilibrium consumption under external habit formation in a large population of agents. We first formulate problems under two types of conventional habit formation preferences, namely linear and multiplicative external habit formation, in a mean field game framework. In a log-normal market model with the asset specialization, we characterize one mean field equilibrium in analytical form in each problem, allowing us to understand some quantitative properties of the equilibrium strategy and conclude some financial implications caused by consumption habits from a mean-field perspective. In each problem with n agents, we construct an approximate Nash equilibrium for the n-player game using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained.

q-fin.MF↗

arXiv2024

Optimal portfolio under ratio-type periodic evaluation in incomplete markets with stochastic factors

This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is periodically evaluated on the relative ratio of two adjacent wealth levels over an infinite horizon. For both power and logarithmic utilities, we formulate the auxiliary one-period optimization problems with modified utility functions, for which we develop the martingale duality approach to establish the existence of the optimal portfolio processes and the dual minimizers can be identified as the "least favorable" completion of the market. With the help of the duality results in the auxiliary problems and some fixed point arguments, we further derive and verify the optimal portfolio processes in a periodic manner for the original periodic evaluation problems over an infinite horizon.

q-fin.PM↗

arXiv2024

Application of 2D Homography for High Resolution Traffic Data Collection using CCTV Cameras

Traffic cameras remain the primary source data for surveillance activities such as congestion and incident monitoring. To date, State agencies continue to rely on manual effort to extract data from networked cameras due to limitations of the current automatic vision systems including requirements for complex camera calibration and inability to generate high resolution data. This study implements a three-stage video analytics framework for extracting high-resolution traffic data such vehicle counts, speed, and acceleration from infrastructure-mounted CCTV cameras. The key components of the framework include object recognition, perspective transformation, and vehicle trajectory reconstruction for traffic data collection. First, a state-of-the-art vehicle recognition model is implemented to detect and classify vehicles. Next, to correct for camera distortion and reduce partial occlusion, an algorithm inspired by two-point linear perspective is utilized to extracts the region of interest (ROI) automatically, while a 2D homography technique transforms the CCTV view to bird's-eye view (BEV). Cameras are calibrated with a two-layer matrix system to enable the extraction of speed and acceleration by converting image coordinates to real-world measurements. Individual vehicle trajectories are constructed and compared in BEV using two time-space-feature-based object trackers, namely Motpy and BYTETrack. The results of the current study showed about +/- 4.5% error rate for directional traffic counts, less than 10% MSE for speed bias between camera estimates in comparison to estimates from probe data sources. Extracting high-resolution data from traffic cameras has several implications, ranging from improvements in traffic management and identify dangerous driving behavior, high-risk areas for accidents, and other safety concerns, enabling proactive measures to reduce accidents and fatalities.

cs.CV↗

arXiv2024

3D Object Detection and High-Resolution Traffic Parameters Extraction Using Low-Resolution LiDAR Data

Traffic volume data collection is a crucial aspect of transportation engineering and urban planning, as it provides vital insights into traffic patterns, congestion, and infrastructure efficiency. Traditional manual methods of traffic data collection are both time-consuming and costly. However, the emergence of modern technologies, particularly Light Detection and Ranging (LiDAR), has revolutionized the process by enabling efficient and accurate data collection. Despite the benefits of using LiDAR for traffic data collection, previous studies have identified two major limitations that have impeded its widespread adoption. These are the need for multiple LiDAR systems to obtain complete point cloud information of objects of interest, as well as the labor-intensive process of annotating 3D bounding boxes for object detection tasks. In response to these challenges, the current study proposes an innovative framework that alleviates the need for multiple LiDAR systems and simplifies the laborious 3D annotation process. To achieve this goal, the study employed a single LiDAR system, that aims at reducing the data acquisition cost and addressed its accompanying limitation of missing point cloud information by developing a Point Cloud Completion (PCC) framework to fill in missing point cloud information using point density. Furthermore, we also used zero-shot learning techniques to detect vehicles and pedestrians, as well as proposed a unique framework for extracting low to high features from the object of interest, such as height, acceleration, and speed. Using the 2D bounding box detection and extracted height information, this study is able to generate 3D bounding boxes automatically without human intervention.

cs.CV↗

arXiv2023

Optimal Portfolio with Ratio Type Periodic Evaluation under Short-Selling Prohibition

This paper studies some unconventional utility maximization problems when the ratio type relative portfolio performance is periodically evaluated over an infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks. Our goal is to understand the impact of the periodic reward structure on the long-run constrained portfolio strategy. For power and logarithmic utilities, we can reformulate the original problem into an auxiliary one-period optimization problem. To cope with the auxiliary problem with no short-selling, the dual control problem is introduced and studied, which gives the characterization of the candidate optimal portfolio within one period. With the help of the results from the auxiliary problem, the value function and the optimal constrained portfolio for the original problem with periodic evaluation can be derived and verified, allowing us to discuss some financial implications under the new performance paradigm.

q-fin.PM↗

arXiv2023

OpEnCam: Lensless Optical Encryption Camera

Lensless cameras multiplex the incoming light before it is recorded by the sensor. This ability to multiplex the incoming light has led to the development of ultra-thin, high-speed, and single-shot 3D imagers. Recently, there have been various attempts at demonstrating another useful aspect of lensless cameras - their ability to preserve the privacy of a scene by capturing encrypted measurements. However, existing lensless camera designs suffer numerous inherent privacy vulnerabilities. To demonstrate this, we develop the first comprehensive attack model for encryption cameras, and propose OpEnCam -- a novel lensless OPtical ENcryption CAmera design that overcomes these vulnerabilities. OpEnCam encrypts the incoming light before capturing it using the modulating ability of optical masks. Recovery of the original scene from an OpEnCam measurement is possible only if one has access to the camera's encryption key, defined by the unique optical elements of each camera. Our OpEnCam design introduces two major improvements over existing lensless camera designs - (a) the use of two co-axially located optical masks, one stuck to the sensor and the other a few millimeters above the sensor and (b) the design of mask patterns, which are derived heuristically from signal processing ideas. We show, through experiments, that OpEnCam is robust against a range of attack types while still maintaining the imaging capabilities of existing lensless cameras. We validate the efficacy of OpEnCam using simulated and real data. Finally, we built and tested a prototype in the lab for proof-of-concept.

eess.IV↗

arXiv2023

On optimality of barrier dividend control under endogenous regime switching with application to Chapter 11 bankruptcy

Motivated by recent developments in risk management based on the U.S. bankruptcy code, we revisit the De Finetti's optimal dividend problem by incorporating the reorganization process and regulator's intervention documented in Chapter 11 bankruptcy. The resulting surplus process, bearing financial stress towards the more subtle concept of bankruptcy, corresponds to a non-standard spectrally negative Levy process with endogenous regime switching. Some explicit expressions of the expected present values under a barrier strategy, new to the literature, are established in terms of scale functions. With the help of these expressions, when the tail of the Levy measure is log-convex, the optimal dividend control is shown to be of the barrier type and the associated optimal barrier can be identified using scale functions of spectrally negative Levy processes. Some financial implications are also discussed in an illustrative example.

math.OC↗

arXiv2023

Augment the Pairs: Semantics-Preserving Image-Caption Pair Augmentation for Grounding-Based Vision and Language Models

Grounding-based vision and language models have been successfully applied to low-level vision tasks, aiming to precisely locate objects referred in captions. The effectiveness of grounding representation learning heavily relies on the scale of the training dataset. Despite being a useful data enrichment strategy, data augmentation has received minimal attention in existing vision and language tasks as augmentation for image-caption pairs is non-trivial. In this study, we propose a robust phrase grounding model trained with text-conditioned and text-unconditioned data augmentations. Specifically, we apply text-conditioned color jittering and horizontal flipping to ensure semantic consistency between images and captions. To guarantee image-caption correspondence in the training samples, we modify the captions according to pre-defined keywords when applying horizontal flipping. Additionally, inspired by recent masked signal reconstruction, we propose to use pixel-level masking as a novel form of data augmentation. While we demonstrate our data augmentation method with MDETR framework, the proposed approach is applicable to common grounding-based vision and language tasks with other frameworks. Finally, we show that image encoder pretrained on large-scale image and language datasets (such as CLIP) can further improve the results. Through extensive experiments on three commonly applied datasets: Flickr30k, referring expressions and GQA, our method demonstrates advanced performance over the state-of-the-arts with various metrics. Code can be found in https://github.com/amzn/augment-the-pairs-wacv2024.

cs.CV↗

arXiv2023

Domain Generalization Guided by Gradient Signal to Noise Ratio of Parameters

Overfitting to the source domain is a common issue in gradient-based training of deep neural networks. To compensate for the over-parameterized models, numerous regularization techniques have been introduced such as those based on dropout. While these methods achieve significant improvements on classical benchmarks such as ImageNet, their performance diminishes with the introduction of domain shift in the test set i.e. when the unseen data comes from a significantly different distribution. In this paper, we move away from the classical approach of Bernoulli sampled dropout mask construction and propose to base the selection on gradient-signal-to-noise ratio (GSNR) of network's parameters. Specifically, at each training step, parameters with high GSNR will be discarded. Furthermore, we alleviate the burden of manually searching for the optimal dropout ratio by leveraging a meta-learning approach. We evaluate our method on standard domain generalization benchmarks and achieve competitive results on classification and face anti-spoofing problems.

cs.CV↗