In critical systems (e.g., for core airplane functions), codes should both never fail;in particular, they should be robust to numerical instabilities, and, they should reuse certified routines. Yet, the combination of...
详细信息
This report addresses the problem of daily net revenue maximization in a fruit wholesale company. For this purpose, a linear programming model has been formulated whose objective function is the maximization of the ne...
详细信息
Several key problems in web-scale recommender systems, such as optimal matching and allocation, can be formulated as large-scale linear programs (LPs) [4, 1]. These LPs take predictions from ML models such as probabil...
详细信息
ISBN:
(纸本)9798400701030
Several key problems in web-scale recommender systems, such as optimal matching and allocation, can be formulated as large-scale linear programs (LPs) [4, 1]. These LPs take predictions from ML models such as probabilities of click, like, etc. as inputs and optimize recommendations made to users. In recent years, there has been an explosion in the research and development of large-scale recommender systems, but effective optimization of business objectives using the output of those systems remains a challenge. Although LPs can help optimize such business objectives, and algorithms for solving LPs have existed since the 1950s [5, 8], generic LP solvers cannot handle the scale of these problems. At LinkedIn, we have developed algorithms that can solve LPs of various forms with trillions of variables in a Spark-based library called "DuaLip" [7], a novel distributed solver that solves a perturbation of the LP problem at scale via gradient-based algorithms on the smooth dual of the perturbed LP. DuaLip has been deployed in production at LinkedIn and powers several very large-scale recommender systems. DuaLip is open-sourced and extensible in terms of features and algorithms. In this first-of-its-kind tutorial, we will motivate the application of LPs to improve recommender systems, cover the theory of key LP algorithms [8, 6], and introduce DuaLip (https://*** / linkedin/DuaLip), a highly performant Spark-based library that solves extreme-scale LPs for a large variety of recommender system problems. We will describe practical successes of large-scale LP in the industry [3, 2, 9], followed by a hands-on exercise to run DuaLip.
We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of t...
详细信息
We propose a linear programming method that is based on active-set changes and proximal-point iterations. The method solves a sequence of least-distance problems using a warm-started quadratic programming solver that ...
详细信息
We propose a linear programming method that is based on active-set changes and proximal-point iterations. The method solves a sequence of least-distance problems using a warm-started quadratic programming solver that can reuse internal matrix factorizations from the previously solved least-distance problem. We show that the proposed method terminates in a finite number of iterations and that it outperforms state-of-the-art LP solvers in scenarios where an extensive number of small/medium scale LPs need to be solved rapidly, occurring in, for example, multi-parametric programming algorithms. In particular, we show how the proposed method can accelerate operations such as redundancy removal, computation of Chebyshev centers and solving linear feasibility problems.
Background and objectives Flour millers often produce several flour types from a single wheat grist. Consequently, different specifications characterize each flour. For example, French standards specify six different ...
详细信息
Background and objectives Flour millers often produce several flour types from a single wheat grist. Consequently, different specifications characterize each flour. For example, French standards specify six different flour types, each classified by ash content. The proportional blending of different flour streams from a single wheat grist achieves the target flour specifications. This study explores the opportunity to improve flour blending using linear programming and compares it to sequential ash curve blending. Findings linear programming and ash curve approaches were used to meet specifications for French flour types from a wheat grist milled to produce 10 flour streams, each stream having different flour quality attributes. The first simulation set quantity targets for Types 45, 55, and 65 flour. The balance of the flour went to the lower value Types 80, 110, and 150. The flour type targets were met using linear programming. By utilizing the ash curve method, Type 65 flour was under-delivered. The second simulation aimed to maximize income using the two methods with no constraints on the amount of each flour type. The linear programming approach resulted in a 0.13% increase in revenue compared to the ash curve technique. Conclusion In the first simulation, the linear programming technique reduced the lower-value high ash flour types, generating an additional $6.16/ton of flour. In the second simulation, linear programming increased income by $0.84/ton of flour. Thus, a milling plant operating for 8,000 hr/year and processing 20 tons of wheat/hr translates to $779,000 and $107,000 per annum, respectively. Significance and novelty This study showed that linear programming could significantly improve flour blending outcomes, resulting in increased profitability and resource utilization in the milling industry.
In this paper, a decision analysis method based on time series analysis and planning model is proposed. By establishing multiple regression equations, this paper analyzes the correlation between sales volume and cost-...
详细信息
We consider online reinforcement learning in episodic Markov decision process (MDP) with unknown transition function and stochastic rewards drawn from some fixed but unknown distribution. The learner aims to learn the...
详细信息
ISBN:
(纸本)9798350301243
We consider online reinforcement learning in episodic Markov decision process (MDP) with unknown transition function and stochastic rewards drawn from some fixed but unknown distribution. The learner aims to learn the optimal policy and minimize their regret over a finite time horizon through interacting with the environment. We devise a simple and efficient model-based algorithm that achieves (O) over tilde (LX root TA) regret with high probability, where L is the episode length, T is the number of episodes, and X and A are the cardinalities of the state space and the action space, respectively. The proposed algorithm, which is based on the concept of "optimism in the face of uncertainty", maintains confidence sets of transition and reward functions and uses occupancy measures to connect the online MDP with linear programming. It achieves a tighter regret bound compared to the existing works that use a similar confidence set framework and improves computational effort compared to those that use a different framework but with a slightly tighter regret bound.
linear programming is an established, well-understood technique optimization problem; the goal of this thesis is to show that we can still use linear programming to advance the state of the art in two important blocks...
详细信息
linear programming is an established, well-understood technique optimization problem; the goal of this thesis is to show that we can still use linear programming to advance the state of the art in two important blocks of modern robotic systems, namely perception, and control. In the context of perception, we study the effects of outliers in the solution of localization problems. In its essence, this problem reduces to finding the coordinates of a set of nodes in a common reference frame starting from relative pairwise measurements and is at the core of many applications such as Structure from Motion (SfM), sensor networks, and Simultaneous Localization And Mapping (SLAM). In practical situations, the accuracy of the relative measurements is marred by noise and outliers (large-magnitude errors). In particular, outliers might introduce significant errors in the final result, hence, we have the problem of quantifying how much we should trust the solution returned by some given localization solver. In this work, we focus on the question of whether an L1-norm robust optimization formulation can recover a solution that is identical to the ground truth, under the scenario of translation-only measurements corrupted exclusively by outliers and no noise. In the context of control, we study the problem of robust path planning. Path planning deals with the problem of finding a path from an initial state toward a goal state while considering collision avoidance. We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of robust min-max linear programming problems on the elements of a cell decomposition of the environment. The optimization problems are formulated using linear Control Lyapunov Function (CLF) and Control Barrier Function (CBF) constraints, to provide stability and safety guarantees, respective
As a consequence of the impending gas shortages from sources in the Gulf of Thailand, the country will be obliged to switch to imports of LNG to achieve energy security. The gas system of Thailand is constructed as a ...
详细信息
As a consequence of the impending gas shortages from sources in the Gulf of Thailand, the country will be obliged to switch to imports of LNG to achieve energy security. The gas system of Thailand is constructed as a mathematical model. In the simulation, the output shows that reserves gas of Thailand is insufficient to face the demand in 2015-2036, while the consumption of natural gas reserves continues at a rate that indicates that LNG imports will become the primary supply in the future to meet rising demand. The linear programming approach indicates patterns in the supply of gas which will see imports of LNG expanding at a rate lower than that predicted in the plan, thus undercutting the figures for the 2021 MMSCFD under the Gas Plan. The programming described in this study, however, may serve as the foundation for further examinations of Thailand's situation regarding energy security.
暂无评论