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An average-value-at-risk criterion for Markov decision processes with unbounded costs

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Frontiers of Mathematics in China 2022年第4期17卷 673-687页

作者： Qiuli LIU Wai-Ki CHING Junyu ZHANG Hongchu WANG School of Mathematical Sciences South China Normal UniversityGuangzhou510631China Advanced Modeling and Applied Computing Laboratory Department of MathematicsThe University of Hong KongHong KongChina School of Mathematics Sun Yat-Sen UniversityGuangzhou510275China

We study the Markov decision processes under the average-value-at-risk *** state space and the action space are Borel spaces,the costs are admitted to be unbounded from above,and the discount factors are state-action *** suitable conditions,we establish the existence of optimal deterministic stationary ***,we apply our main results to a cash-balance model.

关键词： Markov decision processes average-value-at-risk(AVaR) state-action dependent discount factors optimal policy

A discrete perspective towards the construction of sparse probabilistic Boolean networks

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Information Sciences 2025年 718卷

作者： Christopher H. Fok Chi-Wing Wong Wai-Ki Ching Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Pokfulam Hong Kong China

The construction problem of sparse probabilistic Boolean networks (PBNs) has important applications in areas such as gene regulatory network inference and financial risk modeling. Many of the existing methods for solving this problem do not output sparse decompositions or are associated with high time complexity. We propose a new Entry-Removal-Type (ERT) algorithm called the Greedy Entry Removal algorithm (GER) for solving the construction problem. The key idea behind GER is to maximize the reduction in the number of positive entries in the residue matrix at each iteration, resulting in fewer iterations needed for the residue matrix to become the zero matrix and allowing GER to output sparse decompositions. We establish new upper bounds for two existing ERT algorithms and GER, providing theoretical guarantees for their performance. In numerical experiments based on both synthetic and real-world data, GER outperforms state-of-the-art sparse PBN construction algorithms by producing the sparsest decompositions for most of the tested transition probability matrices. Additionally, we are the first to study the lower bound problem related to sparse PBN construction and derive a series of theoretical results, which can inform future algorithm design and set realistic expectations for the sparsity achievable in practical scenarios.

关键词： Digital arithmetic

A Column-Wise Update Algorithm for Sparse Stochastic Matrix Factorization

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arXiv 2021年

作者： Xiao, Guiyun Bai, Zheng-Jian Ching, Wai-Ki School of Mathematical Sciences Xiamen University Xiamen361005 China School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing Xiamen University Xiamen361005 China Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong

Nonnegative matrix factorization arises widely in machine learning and data analysis. In this paper, for a given factorization of rank r, we consider the sparse stochastic matrix factorization (SSMF) of decomposing a prescribed m-by-n stochastic matrix V into a product of an m-by-r stochastic matrix W and an r-by-n stochastic matrix H, where both W and H are required to be sparse. With the prescribed sparsity level, we reformulate the SSMF as an unconstrained nonconvex-nonsmooth minimization problem and introduce a column-wise update algorithm for solving the minimization problem. We show that our algorithm converges globally. The main advantage of our algorithm is that the generated sequence converges to a special critical point of the cost function, which is nearly a global minimizer over each column vector of the W-factor and is a global minimizer over the H-factor as a whole if there is no sparsity requirement on H. Numerical experiments on both synthetic and real data sets are given to demonstrate the effectiveness of our proposed *** Codes 65K05, 90C06, 90C26 Copyright © 2021, The Authors. All rights reserved.

关键词： Gradient methods

HOMOGENIZATION OF THE DISTRIBUTION-DEPENDENT STOCHASTIC ABSTRACT FLUID MODELS

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arXiv 2023年

作者： Chen, Junlong Qiu, Zhaoyang Tang, Yanbin School of Sciences Great Bay University Great Bay Institute for Advanced Study Dongguan523000 China School of Mathematics University of Science and Technology of China Anhui Hefei230026 China School of Applied Mathematics Nanjing University of Finance and Economics Nanjing210046 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

In this paper, we study the homogenization of the distribution-dependent stochastic abstract fluid models by combining the two−scale convergence and martingale representative approach. A general framework of the homogenization research is established for stochastic abstract fluid models which are the type of nonlinear partial differential equations including the (distribution-dependent) stochastic Navier-Stokes equations, stochastic magneto-hydrodynamic equations, stochastic Boussinesq equations, stochastic micropolar equations, stochastic Allen-Cahn equations. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

Distributed Pinning Set Stabilization of Large-Scale Boolean Networks

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arXiv 2022年

作者： Zhu, Shiyong Lu, Jianquan Sun, Liangjie Cao, Jinde The Department of Systems Science School of Mathematics Southeast University Nanjing210096 China The Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Hong Kong The School of Mathematics Frontiers Science Center for Mobile Information Communication and Security Southeast University Nanjing210096 China The Purple Mountain Laboratories Nanjing211111 China The Yonsei Frontier Lab Yonsei University Seoul03722 Korea Republic of

In this article, we design the distributed pinning controllers to globally stabilize a Boolean network (BN), specially a sparsely connected large-scale one, towards a preassigned subset of state space through the node-to-node message exchange. Given an appointed state set, system nodes are partitioned into two disjoint parts, which respectively gather the nodes whose states are fixed or arbitrary with respect to the given state set. With such node division, three parts of pinned nodes are selected and the state feedback controllers are accordingly designed such that the resulting BN satisfies three conditions: the states of the other nodes cannot affect the nodal dynamics of fixed-state nodes, the subgraph of network structure induced by the fixed-state nodes is acyclic, and the steady state of the subnetwork induced by the fixed-state nodes lies in the state set given beforehand. If the BN after control is acyclic, the stabilizing time is revealed to be no more than the length of the longest path in the current network structure plus one. This enables us to further design the pinning controllers with the constraint of stabilizing time. Noting that the overall procedure runs in an exponentially increasing time with respect to the largest number of functional variables in the dynamics of pinned nodes, the sparsely-connected large-scale BNs can be well addressed in a reasonable amount of time. Finally, we demonstrate the applications of our theoretical results in a T-LGL survival signal network with 29 nodes and T-cell receptor signaling network with 90 nodes. Copyright © 2022, The Authors. All rights reserved.

关键词： Controllers

A modified orthogonal matching pursuit for construction of sparse probabilistic Boolean networks

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arXiv 2020年

Probabilistic Boolean Networks play a remarkable role in the modelling and control of gene regulatory networks. In this paper, we consider the inverse problem of constructing a sparse probabilistic Boolean network from the prescribed transition probability matrix. We propose a modified orthogonal matching pursuit for solving the inverse problem. We provide some conditions under which the proposed algorithm can recover a sparse probabilistic Boolean network. We also report some numerical results to illustrate the effectiveness of the proposed algorithm. Copyright © 2020, The Authors. All rights reserved.

关键词： Inverse problems

A Markov-Driven Portfolio Execution Strategy with Market Impact

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高等学校计算数学学报（英文版） 2018年第4期11卷 701-728页

作者： Qingqing Yang Wai-Ki Ching Tak-Kuen Siu Zhiwen Zhang Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong Department of Applied Finance and Actuarial Studies Faculty of Business and Economics Macquarie University Sydney NSW 2109 Australia

In this paper,we propose a framework for studying optimal agency execution strategies in a Limit Order Book (LOB) under a Markov-modulated market *** Almgren-Chriss's market impact model [1] is extended to a more general situation where multiple venues are available for investors to submit *** the assumption of risk-neutrality,a compact recursive formula is derived,using the value iterative method,to calculate the optimal agency execution *** original optimal control problem is then converted to a constrained quadratic optimization problem,which can be solved by using the Quadratic Programming (Qp) *** examples are given to illustrate the efficiency and effective of our proposed methods.

关键词： Hamilton-Jacobi-Bellman (HJB) equation Limit Order Book (LOB) Dynamic Programming (DP) principle market impact Quadratic Programming (Qp) regime-switching value iteration method

DeePMD-kit v2: A software package for Deep Potential models

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arXiv 2023年

作者： Zeng, Jinzhe Zhang, Duo Lu, Denghui Mo, Pinghui Li, Zeyu Chen, Yixiao Rynik, Marián Huang, Li'ang Li, Ziyao Shi, Shaochen Wang, Yingze Ye, Haotian Tuo, Ping Yang, Jiabin Ding, Ye Li, Yifan Tisi, Davide Zeng, Qiyu Bao, Han Xia, Yu Huang, Jiameng Muraoka, Koki Wang, Yibo Chang, Junhan Yuan, Fengbo Bore, Sigbjørn Løland Cai, Chun Lin, Yinnian Wang, Bo Xu, Jiayan Zhu, Jia-Xin Luo, Chenxing Zhang, Yuzhi Goodall, Rhys E.A. Liang, Wenshuo Singh, Anurag Kumar Yao, Sikai Zhang, Jingchao Wentzcovitch, Renata Han, Jiequn Liu, Jie Jia, Weile York, Darrin M. Weinan, E. Car, Roberto Zhang, Linfeng Wang, Han Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine Department of Chemistry and Chemical Biology Rutgers University PiscatawayNJ08854 United States AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China HEDPS CAPT College of Engineering Peking University Beijing100871 China College of Electrical and Information Engineering Hunan University Changsha China Yuanpei College Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Department of Experimental Physics Comenius University Mlynská Dolina F2 Bratislava842 48 Slovakia Center for Quantum Information Institute for Interdisciplinary Information Sciences Tsinghua University Beijing100084 China Center for Data Science Peking University Beijing100871 China ByteDance Research Zhonghang Plaza No. 43 North 3rd Ring West Road Haidian District Beijing China College of Chemistry and Molecular Engineering Peking University Beijing100871 China Baidu Inc. Beijing China Key Laboratory of Structural Biology of Zhejiang Province School of Life Sciences Westlake University Zhejiang Hangzhou China Westlake AI Therapeutics Lab Westlake Laboratory of Life Sciences and Biomedicine Zhejiang Hangzhou China Department of Chemistry Princeton University PrincetonNJ08544 United States SISSA Scuola Internazionale Superiore di Studi Avanzati Trieste34136 Italy Laboratory of Computational Science and Modeling Institute of Materials École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland Department of Physics National University of Defense Technology Hunan Changsha410073 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China School of Electronics Engineerin

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, Deep Potential - Range Correction (DPRc), Deep Potential Long Range (DPLR), GPU support for customized operators, model compression, non-von Neumann molecular dynamics (NVNMD), and improved usability, including documentation, compiled binary packages, graphical user interfaces (GUI), and application programming interfaces (API). This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, the article benchmarks the accuracy and efficiency of different models and discusses ongoing developments. © 2023, CC BY-NC-ND.

关键词： Molecular dynamics

Optimal liquidation problems in a randomly-Terminated horizon

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arXiv 2017年

作者： Yang, Qing-Qing Ching, Wai-Ki Gu, Jia-Wen Wong, Tak Kwong Advanced Modeling and Applied Computing Laboratory Department of Mathematics University of Hong Kong Pokfulam Road Hong Kong Hong Kong Advanced Modeling and Applied Computing Laboratory Department of Mathematics University of Hong Kong Pokfulam Road Hong Kong Hong Kong Hughes Hall Wollaston Road Cambridge United Kingdom School of Economics and Management Beijing University of Chemical Technology North Third Ring Road Beijing China Department of Mathematics Southern University of Science and Technology Shenzhen China Department of Mathematics University of Hong Kong Pokfulam Road Hong Kong Hong Kong

In this paper, we study optimal liquidation problems in a randomly-Terminated horizon. We consider the liquidation of a large single-Asset portfolio with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. Three different scenarios are analyzed under Almgren-Chriss's market impact model to explore the relation between opti-mal liquidation strategies and potential inventory risk arising from the uncertainty of the liquidation horizon. For cases where no closed-form solutions can be obtained, we verify comparison principles for viscosity solutions and characterize the value function as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation. Copyright © 2017, The Authors. All rights reserved.

关键词： Dynamic programming