arXiv - MATH - Optimization and Control最新文献_第4页

Addressing misspecification in contextual optimization 解决情境优化中的误规范问题

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10479

Omar Bennouna, Jiawei Zhang, Saurabh Amin, Asuman Ozdaglar

{"title":"Addressing misspecification in contextual optimization","authors":"Omar Bennouna, Jiawei Zhang, Saurabh Amin, Asuman Ozdaglar","doi":"arxiv-2409.10479","DOIUrl":"https://doi.org/arxiv-2409.10479","url":null,"abstract":"We study a linear contextual optimization problem where a decision maker has\u0000access to historical data and contextual features to learn a cost prediction\u0000model aimed at minimizing decision error. We adopt the predict-then-optimize\u0000framework for this analysis. Given that perfect model alignment with reality is\u0000often unrealistic in practice, we focus on scenarios where the chosen\u0000hypothesis set is misspecified. In this context, it remains unclear whether\u0000current contextual optimization approaches can effectively address such model\u0000misspecification. In this paper, we present a novel integrated learning and\u0000optimization approach designed to tackle model misspecification in contextual\u0000optimization. This approach offers theoretical generalizability, tractability,\u0000and optimality guarantees, along with strong practical performance. Our method\u0000involves minimizing a tractable surrogate loss that aligns with the performance\u0000value from cost vector predictions, regardless of whether the model\u0000misspecified or not, and can be optimized in reasonable time. To our knowledge,\u0000no previous work has provided an approach with such guarantees in the context\u0000of model misspecification.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Realistic Extreme Behavior Generation for Improved AV Testing 生成逼真的极端行为，改进视听测试

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10669

Robert Dyro, Matthew Foutter, Ruolin Li, Luigi Di Lillo, Edward Schmerling, Xilin Zhou, Marco Pavone

{"title":"Realistic Extreme Behavior Generation for Improved AV Testing","authors":"Robert Dyro, Matthew Foutter, Ruolin Li, Luigi Di Lillo, Edward Schmerling, Xilin Zhou, Marco Pavone","doi":"arxiv-2409.10669","DOIUrl":"https://doi.org/arxiv-2409.10669","url":null,"abstract":"This work introduces a framework to diagnose the strengths and shortcomings\u0000of Autonomous Vehicle (AV) collision avoidance technology with synthetic yet\u0000realistic potential collision scenarios adapted from real-world, collision-free\u0000data. Our framework generates counterfactual collisions with diverse crash\u0000properties, e.g., crash angle and velocity, between an adversary and a target\u0000vehicle by adding perturbations to the adversary's predicted trajectory from a\u0000learned AV behavior model. Our main contribution is to ground these adversarial\u0000perturbations in realistic behavior as defined through the lens of\u0000data-alignment in the behavior model's parameter space. Then, we cluster these\u0000synthetic counterfactuals to identify plausible and representative collision\u0000scenarios to form the basis of a test suite for downstream AV system\u0000evaluation. We demonstrate our framework using two state-of-the-art behavior\u0000prediction models as sources of realistic adversarial perturbations, and show\u0000that our scenario clustering evokes interpretable failure modes from a baseline\u0000AV policy under evaluation.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"54 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A first-order greedy algorithm for A-optimal experimental design with optimality guarantee 具有最优性保证的 A 优化实验设计一阶贪婪算法

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.09963

Christian Aarset

引用次数: 0

Efficient approximation schemes for scheduling on a stochastic number of machines 随机机器数量调度的高效近似方案

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10155

Leah Epstein, Asaf Levin

{"title":"Efficient approximation schemes for scheduling on a stochastic number of machines","authors":"Leah Epstein, Asaf Levin","doi":"arxiv-2409.10155","DOIUrl":"https://doi.org/arxiv-2409.10155","url":null,"abstract":"We study three two-stage optimization problems with a similar structure and\u0000different objectives. In the first stage of each problem, the goal is to assign\u0000input jobs of positive sizes to unsplittable bags. After this assignment is\u0000decided, the realization of the number of identical machines that will be\u0000available is revealed. Then, in the second stage, the bags are assigned to\u0000machines. The probability vector of the number of machines in the second stage\u0000is known to the algorithm as part of the input before making the decisions of\u0000the first stage. Thus, the vector of machine completion times is a random\u0000variable. The goal of the first problem is to minimize the expected value of\u0000the makespan of the second stage schedule, while the goal of the second problem\u0000is to maximize the expected value of the minimum completion time of the\u0000machines in the second stage solution. The goal of the third problem is to\u0000minimize the ell_p norm for a fixed p>1, where the norm is applied on\u0000machines' completion times vectors. Each one of the first two problems admits a\u0000PTAS as Buchem et al. showed recently. Here we significantly improve all their\u0000results by designing an EPTAS for each one of these problems. We also design an\u0000EPTAS for ell_p norm minimization for any p>1.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Improving the Solution of Indefinite Quadratic Programs and Linear Programs with Complementarity Constraints by a Progressive MIP Method 用渐进式 MIP 方法改进带互补约束的不定二次程序和线性程序的求解方法

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.09964

Xinyao Zhang, Shaoning Han, Jong-Shi Pang

{"title":"Improving the Solution of Indefinite Quadratic Programs and Linear Programs with Complementarity Constraints by a Progressive MIP Method","authors":"Xinyao Zhang, Shaoning Han, Jong-Shi Pang","doi":"arxiv-2409.09964","DOIUrl":"https://doi.org/arxiv-2409.09964","url":null,"abstract":"Indefinite quadratic programs (QPs) are known to be very difficult to be\u0000solved to global optimality, so are linear programs with linear complementarity\u0000constraints. Treating the former as a subclass of the latter, this paper\u0000presents a progressive mixed integer linear programming method for solving a\u0000general linear program with linear complementarity constraints (LPCC). Instead\u0000of solving the LPCC with a full set of integer variables expressing the\u0000complementarity conditions, the presented method solves a finite number of\u0000mixed integer subprograms by starting with a small fraction of integer\u0000variables and progressively increasing this fraction. After describing the PIP\u0000(for progressive integer programming) method and its various implementations,\u0000we demonstrate, via an extensive set of computational experiments, the superior\u0000performance of the progressive approach over the direct solution of the\u0000full-integer formulation of the LPCCs. It is also shown that the solution\u0000obtained at the termination of the PIP method is a local minimizer of the LPCC,\u0000a property that cannot be claimed by any known non-enumerative method for\u0000solving this nonconvex program. In all the experiments, the PIP method is\u0000initiated at a feasible solution of the LPCC obtained from a nonlinear\u0000programming solver, and with high likelihood, can successfully improve it.\u0000Thus, the PIP method can improve a stationary solution of an indefinite QP,\u0000something that is not likely to be achievable by a nonlinear programming\u0000method. Finally, some analysis is presented that provides a better\u0000understanding of the roles of the LPCC suboptimal solutions in the local\u0000optimality of the indefinite QP.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Quantile Fourier regressions for decision making under uncertainty 用于不确定情况下决策的量子傅立叶回归

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10455

Arash Khojaste, Geoffrey Pritchard, Golbon Zakeri

引用次数: 0

Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Neumann Boundary Condition with a Point-Wise Control 半平面内受诺伊曼边界条件控制的热方程的可控性问题与点式控制

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10169

Larissa Fardigola, Kateryna Khalina

{"title":"Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Neumann Boundary Condition with a Point-Wise Control","authors":"Larissa Fardigola, Kateryna Khalina","doi":"arxiv-2409.10169","DOIUrl":"https://doi.org/arxiv-2409.10169","url":null,"abstract":"In the paper, the problems of controllability and approximate controllability\u0000are studied for the control system $w_t=Delta w$,\u0000$w_{x_1}(0,x_2,t)=u(t)delta(x_2)$, $x_1>0$, $x_2inmathbb R$, $tin(0,T)$,\u0000where $uin L^infty(0,T)$ is a control. To this aid, it is investigated the\u0000set $mathcal{R}_T(0)subset L^2((0,+infty)timesmathbb R)$ of its end states\u0000which are reachable from $0$. It is established that a function\u0000$finmathcal{R}_T(0)$ can be represented in the form $f(x)=gbig(|x|^2big)$\u0000a.e. in $(0,+infty)timesmathbb R$ where $gin L^2(0,+infty)$. In fact, we\u0000reduce the problem dealing with functions from $L^2((0,+infty)timesmathbb\u0000R)$ to a problem dealing with functions from $L^2(0,+infty)$. Both a necessary\u0000and sufficient condition for controllability and a sufficient condition for\u0000approximate controllability in a given time $T$ under a control $u$ bounded by\u0000a given constant are obtained in terms of solvability of a Markov power moment\u0000problem. Using the Laguerre functions (forming an orthonormal basis of\u0000$L^2(0,+infty)$), necessary and sufficient conditions for approximate\u0000controllability and numerical solutions to the approximate controllability\u0000problem are obtained. It is also shown that there is no initial state that is\u0000null-controllable in a given time $T$. The results are illustrated by an\u0000example.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"187 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Online Nonconvex Bilevel Optimization with Bregman Divergences 利用布雷格曼发散进行在线非凸双曲优化

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10470

Jason Bohne, David Rosenberg, Gary Kazantsev, Pawel Polak

{"title":"Online Nonconvex Bilevel Optimization with Bregman Divergences","authors":"Jason Bohne, David Rosenberg, Gary Kazantsev, Pawel Polak","doi":"arxiv-2409.10470","DOIUrl":"https://doi.org/arxiv-2409.10470","url":null,"abstract":"Bilevel optimization methods are increasingly relevant within machine\u0000learning, especially for tasks such as hyperparameter optimization and\u0000meta-learning. Compared to the offline setting, online bilevel optimization\u0000(OBO) offers a more dynamic framework by accommodating time-varying functions\u0000and sequentially arriving data. This study addresses the online\u0000nonconvex-strongly convex bilevel optimization problem. In deterministic\u0000settings, we introduce a novel online Bregman bilevel optimizer (OBBO) that\u0000utilizes adaptive Bregman divergences. We demonstrate that OBBO enhances the\u0000known sublinear rates for bilevel local regret through a novel hypergradient\u0000error decomposition that adapts to the underlying geometry of the problem. In\u0000stochastic contexts, we introduce the first stochastic online bilevel optimizer\u0000(SOBBO), which employs a window averaging method for updating outer-level\u0000variables using a weighted average of recent stochastic approximations of\u0000hypergradients. This approach not only achieves sublinear rates of bilevel\u0000local regret but also serves as an effective variance reduction strategy,\u0000obviating the need for additional stochastic gradient samples at each timestep.\u0000Experiments on online hyperparameter optimization and online meta-learning\u0000highlight the superior performance, efficiency, and adaptability of our\u0000Bregman-based algorithms compared to established online and offline bilevel\u0000benchmarks.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"201 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Provably Efficient Infinite-Horizon Average-Reward Reinforcement Learning with Linear Function Approximation 利用线性函数逼近进行可证明高效的无限视距平均回报强化学习

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10772

Woojin Chae, Dabeen Lee

引用次数: 0

A gradient flow approach for combined layout-control design of wave energy parks 波浪能公园布局与控制组合设计的梯度流方法

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10200

Marco Gambarini, Gabriele Ciaramella, Edie Miglio

{"title":"A gradient flow approach for combined layout-control design of wave energy parks","authors":"Marco Gambarini, Gabriele Ciaramella, Edie Miglio","doi":"arxiv-2409.10200","DOIUrl":"https://doi.org/arxiv-2409.10200","url":null,"abstract":"Wave energy converters (WECs) represent an innovative technology for power\u0000generation from renewable sources (marine energy). Although there has been a\u0000great deal of research into such devices in recent decades, the power output of\u0000a single device has remained low. Therefore, installation in parks is required\u0000for economic reasons. The optimal design problem for parks of WECs is\u0000challenging since it requires the simultaneous optimization of positions and\u0000control parameters. While the literature on this problem usually considers\u0000metaheuristic algorithms, we present a novel numerical framework based on a\u0000gradient-flow formulation. This framework is capable of solving the optimal\u0000design problem for WEC parks. In particular, we use a low-order adaptive\u0000Runge-Kutta scheme to integrate the gradient-flow equation and introduce an\u0000inexact solution procedure. Here, the tolerances of the linear solver used for\u0000projection on the constraint nullspace and of the time-advancing scheme are\u0000automatically adapted to avoid over-solving so that the method requires minimal\u0000tuning. We then provide the specific details of its application to the\u0000considered WEC problem: the goal is to maximize the average power produced by a\u0000park, subject to hydrodynamic and dynamic governing equations and to the\u0000constraints of available sea area, minimum distance between devices, and\u0000limited oscillation amplitude around the undisturbed free surface elevation. A\u0000suitable choice of the discrete models allows us to compute analytically the\u0000Jacobian of the state problem's residual. Numerical tests with realistic\u0000parameters show that the proposed algorithm is efficient, and results of\u0000physical interest are obtained.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"152 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0