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学者姓名：徐大川
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Abstract ：
In this paper, we study online diminishing return submodular (DR-submodular for short) maximization in the bandit setting. Our focus is on problems where the reward functions can be non-monotone, and the constraint set is a general convex set. We first present the Single-sampling Non-monotone Frank-Wolfe algorithm. This algorithm only requires a single call to each reward function, and it computes the stochastic gradient to make it suitable for large-scale settings where full gradient information might not be available. We provide an analysis of the approximation ratio and regret bound of the proposed algorithm. We then propose the Bandit Online Non-monotone Frank-Wolfe algorithm to adjust for problems in the bandit setting, where each reward function returns the function value at a single point. We take advantage of smoothing approximations to reward functions to tackle the challenges posed by the bandit setting. Under mild assumptions, our proposed algorithm can reach 14(1-minx is an element of P '& Vert;x & Vert;infinity)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{4} (1- \min _{x\in {\mathcal {P}}'}\Vert x\Vert _\infty )$$\end{document}-approximation with regret bounded by O(T5min{1,gamma}+56min{1,gamma}+5)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O (T<^>{\frac{5 \min \{1, \gamma \}+5 }{6 \min \{1, \gamma \}+5}})$$\end{document}, where the positive parameter gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} is related to the "safety domain" P '\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {P}}'$$\end{document}. To the best of our knowledge, this is the first work to address online non-monotone DR-submodular maximization over a general convex set in the bandit setting.
Keyword ：
Non-monotone function Non-monotone function DR submodular maximization DR submodular maximization Bandit setting Bandit setting Regret bound Regret bound Approximation algorithm Approximation algorithm
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| GB/T 7714 | Ju, Jiachen , Wang, Xiao , Xu, Dachuan . Online non-monotone diminishing return submodular maximization in the bandit setting [J]. | JOURNAL OF GLOBAL OPTIMIZATION , 2024 , 90 (3) : 619-649 . |
| MLA | Ju, Jiachen 等. "Online non-monotone diminishing return submodular maximization in the bandit setting" . | JOURNAL OF GLOBAL OPTIMIZATION 90 . 3 (2024) : 619-649 . |
| APA | Ju, Jiachen , Wang, Xiao , Xu, Dachuan . Online non-monotone diminishing return submodular maximization in the bandit setting . | JOURNAL OF GLOBAL OPTIMIZATION , 2024 , 90 (3) , 619-649 . |
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Abstract ：
This study investigates electricity trading in a deregulated retail market, aiming to coordinate the energy consumption behavior of end-users through demand response (DR) and carbon emission mechanisms under dynamic pricing. The objective is to minimize integrated energy system (IES) operating cost while maintaining a supply-demand balance. The IES schematic includes generation, dispatch, and consumption, as well as their physical and communication connections, corresponding to the grid, retailer, and multiple PV producers and consumers. Beyond the hierarchical decision-making between the retailer and PV prosumers, the challenge lies in the non-cooperative and competitive interdependence among prosumers. Therefore, the problem is formulated as a Stackelberg-Nash game (SNG) model, with the retailer as leader and PV prosumers as followers. Emphasizing that allowing fair energy trading between prosumers in the Nash game can have a positive impact on pricing decisions. Carbon trading and DR mechanisms enhance the flexibility of coordinating energy system supply-demand balance. An efficient iterative distributed algorithm is proposed for SNG strategy, it can complete real-time scheduling and privacy protection at the same time. Finally, the validity of the model is verified by a case study, which demonstrates that its effectiveness in adapting to changes in energy prices with practicality and economic benefits. Furthermore, we also show that the transactions between prosumers and the DR policies can reduce their operating costs by 12% and 9%, respectively.
Keyword ：
Demand response Demand response Smart grids Smart grids PV prosumers PV prosumers Distributed algorithm Distributed algorithm Stackelberg-Nash game Stackelberg-Nash game
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| GB/T 7714 | Wu, Yan , Tian, Xiaoyun , Gai, Ling et al. Energy management for PV prosumers inside microgrids based on Stackelberg-Nash game considering demand response [J]. | SUSTAINABLE ENERGY TECHNOLOGIES AND ASSESSMENTS , 2024 , 68 . |
| MLA | Wu, Yan et al. "Energy management for PV prosumers inside microgrids based on Stackelberg-Nash game considering demand response" . | SUSTAINABLE ENERGY TECHNOLOGIES AND ASSESSMENTS 68 (2024) . |
| APA | Wu, Yan , Tian, Xiaoyun , Gai, Ling , Lim, Boon-Han , Wu, Tingdong , Xu, Dachuan et al. Energy management for PV prosumers inside microgrids based on Stackelberg-Nash game considering demand response . | SUSTAINABLE ENERGY TECHNOLOGIES AND ASSESSMENTS , 2024 , 68 . |
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An established fact with far-reaching implications in the field of submodular maximization is that the validity of the Jensen-type inequality with probability measures is only necessary but not sufficient for DR-submodular functions. This work aims to demonstrate that a characterization of DR-submodular functions can be achieved by allowing signed measures. We prove this result by leveraging the Lyapunov function approach, which holds independent interest as a general method for deriving inequalities.
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| GB/T 7714 | Du,Donglei , Xu,Dachuan . A characterization of DR-submodularity via Jensen-type inequality with signed measure [R]. 2024. (2024-05-07). |
| MLA | Du,Donglei et al. "A characterization of DR-submodularity via Jensen-type inequality with signed measure" 2024. (2024-05-07). |
| APA | Du,Donglei , Xu,Dachuan . A characterization of DR-submodularity via Jensen-type inequality with signed measure 2024. (2024-05-07). |
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Abstract ：
Purpose: The formulation and optimization of radiation therapy plans are complex and time-consuming processes that heavily rely on the expertise of medical physicists. Consequently, there is an urgent need for automated optimization methods. Recent advancements in reinforcement learning, particularly deep reinforcement learning (DRL), show great promise for automating radiotherapy planning. This review summarizes the current state of DRL applications in this field, evaluates their effectiveness, and identifies challenges and future directions. Methods: A systematic search was conducted in Google Scholar, PubMed, IEEE Xplore, and Scopus using keywords such as "deep reinforcement learning", "radiation therapy", and "treatment planning". The extracted data were synthesized for an overview and critical analysis. Results: The application of deep reinforcement learning in radiation therapy plan optimization can generally be divided into three categories: optimizing treatment planning parameters, directly optimizing machine parameters, and adaptive radiotherapy. From the perspective of disease sites, DRL has been applied to cervical cancer, prostate cancer, vestibular schwannoma, and lung cancer. Regarding types of radiation therapy, it has been used in HDRBT, IMRT, SBRT, VMAT, GK, and Cyberknife. Conclusions: Deep reinforcement learning technology has played a significant role in advancing the automated optimization of radiation therapy plans. However, there is still a considerable gap before it can be widely applied in clinical settings due to three main reasons: inefficiency, limited methods for quality assessment, and poor interpretability. To address these challenges, significant research opportunities exist in the future, such as constructing evaluators, parallelized training, and exploring continuous action spaces.
Keyword ：
Radiation therapy Radiation therapy Treatment planning Treatment planning Deep reinforcement learning Deep reinforcement learning
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| GB/T 7714 | Li, Can , Guo, Yuqi , Lin, Xinyan et al. Deep reinforcement learning in radiation therapy planning optimization: A comprehensive review [J]. | PHYSICA MEDICA-EUROPEAN JOURNAL OF MEDICAL PHYSICS , 2024 , 125 . |
| MLA | Li, Can et al. "Deep reinforcement learning in radiation therapy planning optimization: A comprehensive review" . | PHYSICA MEDICA-EUROPEAN JOURNAL OF MEDICAL PHYSICS 125 (2024) . |
| APA | Li, Can , Guo, Yuqi , Lin, Xinyan , Feng, Xuezhen , Xu, Dachuan , Yang, Ruijie . Deep reinforcement learning in radiation therapy planning optimization: A comprehensive review . | PHYSICA MEDICA-EUROPEAN JOURNAL OF MEDICAL PHYSICS , 2024 , 125 . |
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In this paper, we study the problem of maximizing a nonmonotone nonnegative one-sided sigma-smooth (OSS) function G(x). For a downwards-closed basis polyhedron constraint, we propose two classes of parallel algorithms under deterministic and random settings. For the deterministic nonmonotone OSS problem, we design the Jump-Start Parallel Frank Wolfe (JSPFW) algorithm and obtain an approximation solution of (e(-1) - e(-2) - O(epsilon)). The JSPFW algorithm has (O(log n/epsilon(2))) adaptive rounds and O(n log n/epsilon(2)) queries about function and its gradient value. For the stochastic OSS problem, we design the Stochastic Parallel Frank Wolfe (SPFW) algorithm and get the (e(-1) - e(-2))(1 - O(epsilon))(1 - o(1)) approximation solution. The SPFW algorithm needs O(n(2)) adaptive rounds and consumes O(n(2)) queries about gradient function value.
Keyword ：
Parallel algorithm Parallel algorithm Frank Wolfe Frank Wolfe OSS function OSS function Down-closed Down-closed
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| GB/T 7714 | Zhang, Hongxiang , Xu, Dachuan , Zhang, Yapu et al. Parallelized maximization of nonmonotone one-sided sigma-smooth function [J]. | COMPUTERS & ELECTRICAL ENGINEERING , 2023 , 105 . |
| MLA | Zhang, Hongxiang et al. "Parallelized maximization of nonmonotone one-sided sigma-smooth function" . | COMPUTERS & ELECTRICAL ENGINEERING 105 (2023) . |
| APA | Zhang, Hongxiang , Xu, Dachuan , Zhang, Yapu , Zhang, Zhenning . Parallelized maximization of nonmonotone one-sided sigma-smooth function . | COMPUTERS & ELECTRICAL ENGINEERING , 2023 , 105 . |
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Lower bounded correlation clustering problem (LBCorCP) is a new generalization of the correlation clustering problem (CorCP). In the LBCorCP, we are given an integer L and a complete labelled graph. Each edge in the graph is either positive or negative based on the similarity of its two endpoints. The goal is to find a clustering of the vertices, each cluster contains at least L vertices, so as to minimize the sum of the number of positive cut edges and negative uncut edges. In this paper, we first introduce the LBCorCP and give three algorithms for this problem. The first algorithm is a random algorithm, which is designed for the instances of the LBCorCP with fewer positive edges. The second one is that we let the set V itself as a cluster and prove that the algorithm works well on two specially instances with fewer negative edges. The last one is an LP-rounding based iterative algorithm, which is also provided for the instances with fewer negative edges. The above three algorithms can quickly solve some special instances in polynomial time and obtain a smaller approximation ratio. In addition, we conduct simulations to evaluate the performance of our algorithms.
Keyword ：
Correlation clustering Correlation clustering Lower bounded Lower bounded LP-rounding LP-rounding Approximation algorithm Approximation algorithm Polynomial time Polynomial time
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| GB/T 7714 | Ji, Sai , Dong, Yinhong , Du, Donglei et al. Approximation algorithms for the lower bounded correlation clustering problem [J]. | JOURNAL OF COMBINATORIAL OPTIMIZATION , 2023 , 45 (1) . |
| MLA | Ji, Sai et al. "Approximation algorithms for the lower bounded correlation clustering problem" . | JOURNAL OF COMBINATORIAL OPTIMIZATION 45 . 1 (2023) . |
| APA | Ji, Sai , Dong, Yinhong , Du, Donglei , Wang, Dongzhao , Xu, Dachuan . Approximation algorithms for the lower bounded correlation clustering problem . | JOURNAL OF COMBINATORIAL OPTIMIZATION , 2023 , 45 (1) . |
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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- epsilon approximation after O(epsilon(-1)) iterations and O(epsilon(-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- minx (x is an element of C)||x||(infinity))OPT- epsilon approximation withO(epsilon(-1)) iterations and O(epsilon (-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.
Keyword ：
Frank-Wolfe algorithm Frank-Wolfe algorithm DR-Submodular DR-Submodular Gradient estimator Gradient estimator Variance reduction Variance reduction Stochastic algorithm Stochastic algorithm
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| GB/T 7714 | Lian, Yuefang , Du, Donglei , Wang, Xiao et al. Stochastic Variance Reduction for DR-Submodular Maximization [J]. | ALGORITHMICA , 2023 , 86 (5) : 1335-1364 . |
| MLA | Lian, Yuefang et al. "Stochastic Variance Reduction for DR-Submodular Maximization" . | ALGORITHMICA 86 . 5 (2023) : 1335-1364 . |
| APA | Lian, Yuefang , Du, Donglei , Wang, Xiao , Xu, Dachuan , Zhou, Yang . Stochastic Variance Reduction for DR-Submodular Maximization . | ALGORITHMICA , 2023 , 86 (5) , 1335-1364 . |
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The Correlation Clustering Problem (CorCP) is a significant clustering problem based on the similarity of data. It has significant applications in different fields, such as machine learning, biology, and data mining, and many different problems in other areas. In this paper, the Balanced 2-CorCP (B2-CorCP) is introduced and examined, and a new interesting variant of the CorCP is described. The goal of this clustering problem is to partition the vertex set into two clusters with equal size, such that the number of disagreements is minimized. We first present a polynomial time algorithm for the B2-CorCP on $M$-positive edge dominant graphs ($M\geqslant 3$). Then, we provide a series of numerical experiments, and the results show the effectiveness of our algorithm.
Keyword ：
Correlation Correlation Machine learning Machine learning balanced clustering balanced clustering Clustering algorithms Clustering algorithms Approximation algorithms Approximation algorithms positive edge dominant graphs positive edge dominant graphs Biology Biology $k$-correlation clustering $k$-correlation clustering Data mining Data mining approximation algorithm approximation algorithm Partitioning algorithms Partitioning algorithms
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| GB/T 7714 | Ji, Sai , Xu, Dachuan , Du, Donglei et al. Approximation Algorithm for the Balanced 2-Correlation Clustering Problem [J]. | TSINGHUA SCIENCE AND TECHNOLOGY , 2022 , 27 (5) : 777-784 . |
| MLA | Ji, Sai et al. "Approximation Algorithm for the Balanced 2-Correlation Clustering Problem" . | TSINGHUA SCIENCE AND TECHNOLOGY 27 . 5 (2022) : 777-784 . |
| APA | Ji, Sai , Xu, Dachuan , Du, Donglei , Gai, Ling , Zhao, Zhongrui . Approximation Algorithm for the Balanced 2-Correlation Clustering Problem . | TSINGHUA SCIENCE AND TECHNOLOGY , 2022 , 27 (5) , 777-784 . |
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Abstract ：
In this paper, we study the prize-collecting $k$-Steiner tree ($\mathsf{PC}k\mathsf{ST}$) problem. We are given a graph $G=(V, E)$ and an integer $k$. The graph is connected and undirected. A vertex $r\in V$ called root and a subset $R\subseteq V$ called terminals are also given. A feasible solution for the $\mathsf{PC}k\mathsf{ST}$ is a tree $F$ rooted at $r$ and connecting at least $k$ vertices in $R$. Excluding a vertex from the tree incurs a penalty cost, and including an edge in the tree incurs an edge cost. We wish to find a feasible solution with minimum total cost. The total cost of a tree $F$ is the sum of the edge costs of the edges in $F$ and the penalty costs of the vertices not in $F$. We present a simple approximation algorithm with the ratio of 5.9672 for the $\mathsf{PC}k\mathsf{ST}$. This algorithm uses the approximation algorithms for the prize-collecting Steiner tree (PCST) problem and the $k$-Steiner tree ($k\mathsf{ST}$) problem as subroutines. Then we propose a primal-dual based approximation algorithm and improve the approximation ratio to 5.
Keyword ：
Steiner tree Steiner tree Costs Costs Steiner trees Steiner trees Approximation algorithms Approximation algorithms prize-collecting prize-collecting approximation algorithm approximation algorithm
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| GB/T 7714 | Han, Lu , Wang, Changjun , Xu, Dachuan et al. Algorithms for the Prize-Collecting $k$-Steiner Tree Problem [J]. | TSINGHUA SCIENCE AND TECHNOLOGY , 2022 , 27 (5) : 785-792 . |
| MLA | Han, Lu et al. "Algorithms for the Prize-Collecting $k$-Steiner Tree Problem" . | TSINGHUA SCIENCE AND TECHNOLOGY 27 . 5 (2022) : 785-792 . |
| APA | Han, Lu , Wang, Changjun , Xu, Dachuan , Zhang, Dongmei . Algorithms for the Prize-Collecting $k$-Steiner Tree Problem . | TSINGHUA SCIENCE AND TECHNOLOGY , 2022 , 27 (5) , 785-792 . |
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Abstract ：
In this paper, we concentrate on a stochastic non-monotone DR-submodular maximization problem over a convex constraint C, where the objective function arises as an expectation of a set of stochastic functions. We develop an algorithm named SPIDER-FW, which is a stochastic version of the classical Frank-Wolfe algorithm with 1/4 (1- min(x epsilon C) parallel to x parallel to(infinity))F(x*) - epsilon (in expectation) approximation guarantee, the best guarantee so far for the above setting, achieved with O(1/epsilon) iterations, and O(1/epsilon(2)) first-order oracle calls.
Keyword ：
Continuous DR-submodular Continuous DR-submodular Gradient estimator Gradient estimator Frank-Wolfe algorithm Frank-Wolfe algorithm Potential function Potential function Stochastic optimization Stochastic optimization
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| GB/T 7714 | Lian, Yuefang , Xu, Dachuan , Du, Donglei et al. A Stochastic Non-monotone DR-Submodular Maximization Problem over a Convex Set [J]. | COMPUTING AND COMBINATORICS, COCOON 2022 , 2022 , 13595 : 1-11 . |
| MLA | Lian, Yuefang et al. "A Stochastic Non-monotone DR-Submodular Maximization Problem over a Convex Set" . | COMPUTING AND COMBINATORICS, COCOON 2022 13595 (2022) : 1-11 . |
| APA | Lian, Yuefang , Xu, Dachuan , Du, Donglei , Zhou, Yang . A Stochastic Non-monotone DR-Submodular Maximization Problem over a Convex Set . | COMPUTING AND COMBINATORICS, COCOON 2022 , 2022 , 13595 , 1-11 . |
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