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arXiv 2022年

作者： Chen, Qinyi Golrezaei, Negin Susan, Fransisca Operations Research Center Massachusetts Institute of Technology CambridgeMA02139 United States Sloan School of Management Massachusetts Institute of Technology CambridgeMA02139 United States

Many online platforms, ranging from online retail stores to social media platforms, employ algorithms to optimize their offered assortment of items (e.g., products and contents). These algorithms often focus exclusively on achieving the platforms’ objectives, highlighting items with the highest popularity or revenue. This approach, however, can compromise the equality of opportunities for the rest of the items, in turn leading to less content diversity and increased regulatory scrutiny for the platform. Motivated by this, we introduce and study a fair assortment planning problem that enforces equality of opportunities via pairwise fairness, which requires any two items to be offered similar outcomes. We show that the problem can be formulated as a linear program (LP), called (FAIR), that optimizes over the distribution of all feasible assortments. To find a near-optimal solution to (FAIR), we propose a framework based on the Ellipsoid method, which requires a polynomial-time separation oracle to the dual of the LP. We show that finding an optimal separation oracle to the dual problem is an NP-complete problem, and hence we propose a series of approximate separation oracles, which then result in a 1/2-approx. algorithm and an FPTAS for Problem (FAIR). The approximate separation oracles are designed by (i) showing the separation oracle to the dual of the LP is equivalent to solving an infinite series of parameterized knapsack problems, and (ii) leveraging the structure of knapsack problems. Finally, we perform numerical studies on both synthetic data and real-world MovieLens data, showcasing the effectiveness of our algorithms and providing insights into the platform’s price of fairness. Copyright © 2022, The Authors. All rights reserved.

关键词： optimization algorithms

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RATE-DISTORTION OPTIMIZED OPTICAL FLOW ESTIMATION

RATE-DISTORTION OPTIMIZED OPTICAL FLOW ESTIMATION

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IEEE International Conference on Image Processing

作者： Sean I. Young David Taubman University of NSW

ISBN: (纸本)9781479983407

We propose a general framework for rate-distortion optimized estimation of optical flow, taking heed of the optimality conditions when both the residue and the motion coefficients are quantized and coded. The framework is particularly well suited for wavelet estimation of motion, where the estimated coefficients can additionally be coded in a scalable fashion. We also give a summary of two majorization-minimization type of optimization algorithms that can be used to solve our non-linear and non-convex rate-distortion optimization problem. We show experimentally that the proposed scheme produces motion descriptions that are superior to those produced by other optical flow algorithms, in the rate and distortion sense.

关键词： Video compression Optical flow Motion estimation Wavelets Rate-distortion optimization Optic Flow Video compression wavelets Rate distortion motion estimation Traffic estimation optimization algorithms

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A Family of Penalty Functions for Structured Sparsity 10

A Family of Penalty Functions for Structured Sparsity

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Annual Conference on Neural Information Processing Systems

作者： Charles A. Micchelli Jean M. Morales Massimiliano Pontil Department of Mathematics City University of Hong Kong 83 Tat Chee Avenue Kowloon Tong Hong Kong Department of Computer Science University College London Gower Street London WC1E England UK

ISBN: (纸本)9781617823800

We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. We present a family of convex penalty functions, which encode this prior knowledge by means of a set of constraints on the absolute values of the regression coefficients. This family subsumes the e_1 norm and is flexible enough to include different models of sparsity patterns, which are of practical and theoretical importance. We establish some important properties of these functions and discuss some examples where they can be computed explicitly. Moreover, we present a convergent optimization algorithm for solving regularized least squares with these penalty functions. Numerical simulations highlight the benefit of structured sparsity and the advantage offered by our approach over the Lasso and other related methods.

关键词： penalty function regression coefficients optimization algorithms family penalty alachlor Absolute value

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FAST EMPIRICAL SCENARIOS

arXiv

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arXiv 2023年

作者： Multerer, Michael Schneider, Paul Sen, Rohan Euler Institute USI Lugano Via la Santa 1 Lugano6962 Switzerland USI Lugano and SFI Via Buffi 6 Lugano6900 Switzerland

We seek to extract a small number of representative scenarios from large panel data that are consistent with sample moments. Among two novel algorithms, the first identifies scenarios that have not been observed before, and comes with a scenario-based representation of covariance matrices. The second proposal selects important data points from states of the world that have already realized, and are consistent with higher-order sample moment information. Both algorithms are efficient to compute and lend themselves to consistent scenario-based modeling and multi-dimensional numerical integration that can be used for interpretable decision-making under uncertainty. Extensive numerical benchmarking studies and an application in portfolio optimization favor the proposed *** Codes 11C20, 41A55, 46E22, 46N30, 60-08, 68W25 Copyright © 2023, The Authors. All rights reserved.

关键词： optimization algorithms

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Bayesian Optimisation with Unknown Hyperparameters: Regret Bounds Logarithmically Closer to Optimal

arXiv

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arXiv 2024年

作者： Ziomek, Juliusz Adachi, Masaki Osborne, Michael A. Machine Learning Research Group University of Oxford United Kingdom Toyota Motor Corporation Japan

Bayesian optimization (BO) is widely used for optimising black-box functions but requires us to specify the length scale hyperparameter, which defines the smoothness of the functions the optimizer will consider. Most current BO algorithms choose this hyperparameter by maximizing the marginal likelihood of the observed data, albeit risking misspecification if the objective function is less smooth in regions we have not yet explored. The only prior solution addressing this problem with theoretical guarantees was A-GP-UCB, proposed by Berkenkamp et al. (2019). This algorithm progressively decreases the length scale, expanding the class of functions considered by the optimizer. However, A-GP-UCB lacks a stopping mechanism, leading to over-exploration and slow convergence. To overcome this, we introduce Length scale Balancing (LB)—a novel approach, aggregating multiple base surrogate models with varying length scales. LB intermittently adds smaller length scale candidate values while retaining longer scales, balancing exploration and exploitation. We formally derive a cumulative regret bound of LB and compare it with the regret of an oracle BO algorithm using the optimal length scale. Denoting the factor by which the regret bound of A-GP-UCB was away from oracle as g(T), we show that LB is only log g(T) away from oracle regret. We also empirically evaluate our algorithm on synthetic and real-world benchmarks and show it outperforms A-GP-UCB, maximum likelihood estimation and MCMC. © 2024, CC BY.

关键词： optimization algorithms

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MATRIX RECOVERY FROM QUANTIZED AND CORRUPTED MEASUREMENTS

MATRIX RECOVERY FROM QUANTIZED AND CORRUPTED MEASUREMENTS

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Andrew S. Lan Christoph Studer Richard G. Baraniuk Rice University Cornell University

ISBN: (纸本)9781479928941

This paper deals with the recovery of an unknown, low-rank matrix from quantized and (possibly) corrupted measurements of a subset of its entries. We develop statistical models and corresponding (multi-)convex optimization algorithms for quantized matrix completion (Q-MC) and quantized robust principal component analysis (Q-RPCA). In order to take into account the quantized nature of the available data, we jointly learn the underlying quantization bin boundaries and recover the low-rank matrix, while removing potential (sparse) corruptions. Experimental results on synthetic and two real-world collaborative filtering datasets demonstrate that directly operating with the quantized measurements--rather than treating them as real values--results in (often significantly) lower recovery error if the number of quantization bins is less than about 10.

关键词： rank of matrix system recovery optimization algorithms statistical models (nuclear) entry quantizer Quantization matrix SYNTHETICS available data matrices Subset

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Self-organized UAV traffic in realistic environments

Self-organized UAV traffic in realistic environments

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IEEE/RSJ International Conference on Intelligent Robots and Systems

作者： Csaba Viragh Mate Nagy Carlos Gershenson Gabor Vasarhelyi Biological Physics Department Eotvos University Budapest Hungary MTA-ELTE Statistical and Biological Physics Research Group Budapest Hungary IIMAS & C3 UNAM Mexico City Mexico

ISBN: (纸本)9781509037636

e investigated different dense multirotor UAV traffic simulation scenarios in open 2D and 3D space, under realistic environments with the presence of sensor noise, communication delay, limited communication range, limited sensor update rate and finite inertia. We implemented two fundamental self-organized algorithms: one with constant direction and one with constant velocity preference to reach a desired target. We performed evolutionary optimization on both algorithms in five basic traffic scenarios and tested the optimized algorithms under different vehicle densities. We provide optimal algorithm and parameter selection criteria and compare the maximal flux and collision risk of each solution and situation. We found that i) different scenarios and densities require different algorithmic approaches, i.e., UAVs have to behave differently in sparse and dense environments or when they have common or different targets;ii) a slower-is-faster effect is implicitly present in our models, i.e., the maximal flux is achieved at densities where the average speed is far from maximal;iii) communication delay is the most severe destabilizing environmental condition that has a fundamental effect on performance and needs to be taken into account when designing algorithms to be used in real life.

关键词： Three-dimensional displays Two dimensional displays Roads Trajectory Mathematical model Vehicles Robot sensing systems three-dimensional displays Manipulator sensing systems vehicle Road trajectory Mathematical Model Unmanned Aerial Vehicle drone honey bees communication range Environments collision risk optimization algorithms Average speed

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Taxicab distance based best-worst method for multi-criteria decision-making: An analytical approach

arXiv

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arXiv 2024年

作者： Ratandhara, Harshit M. Kumar, Mohit Department of Basic Sciences Institute of Infrastructure Technology Research And Management Gujarat Ahmedabad380026 India

The Best-Worst Method (BWM) is a well-known distance based multi-criteria decision-making method used for computing the weights of decision criteria. This article examines a taxicab distance based model of the BWM, with the objective of developing a framework for deriving the model’s optimal weights by solving its associated optimization problem analytically. To achieve this, an optimal modification based optimization problem, equivalent to the original one, is first formulated. This reformulated problem is then solved analytically, and the optimal weight sets are derived from its solutions. Contrary to existing literature that asserts the uniqueness of optimal weight sets based on numerical examples, our findings reveal that, in some cases, the taxicab BWM leads to multiple optimal weight sets. This framework provides a solid mathematical foundation that enhances understanding of the model. It also eliminates the requirement for optimization software, improving the model’s precision and efficiency. Finally, the effectiveness of the proposed framework is demonstrated through numerical examples. © 2024, CC BY-NC-SA.

关键词： optimization algorithms

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Towards Sharper Risk Bounds for Minimax Problems

arXiv

引用

arXiv 2024年

作者： Zhu, Bowei Li, Shaojie Liu, Yong Gaoling School of Artificial Intelligence Renmin University of China Beijing China Beijing Key Laboratory of Big Data Management and Analysis Methods Beijing China

Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error and optimization error, present 1/n-rates in strongly-convex-strongly-concave (SC-SC) settings. Existing studies mainly focus on minimax problems with specific algorithms for optimization error, with only a few studies on generalization performance, which limit better excess risk bounds. In this paper, we study the generalization bounds measured by the gradients of primal functions using uniform localized convergence. We obtain a sharper high probability generalization error bound for nonconvex-strongly-concave (NC-SC) stochastic minimax problems. Furthermore, we provide dimension-independent results under Polyak-Lojasiewicz condition for the outer layer. Based on our generalization error bound, we analyze some popular algorithms such as empirical saddle point (ESP), gradient descent ascent (GDA) and stochastic gradient descent ascent (SGDA). We derive better excess primal risk bounds with further reasonable assumptions, which, to the best of our knowledge, are n times faster than exist results in minimax problems. © 2024, CC BY.

关键词： optimization algorithms

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A Novel State Estimation Formulation for Distribution Grids with Renewable Energy Sources

A Novel State Estimation Formulation for Distribution Grids ...

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IEEE Power and Energy Society General Meeting

作者： F. Shabaninia M. Vaziri S. Vadhva J. Vaziri Shiraz University California State University Sacramento CA 95819 USA UC Berkeley Berkeley CA 94720

ISBN: (纸本)9781467327275

Interconnection of Distributed Generation (DG) using renewable resources to the distribution networks in on the rise. Distribution grids having DG interconnections at higher penetration levels are challenged for more accurate monitoring and controls. In this paper a novel approach and a theoretical formulation of state estimation is proposed for distribution grids with Renewable Energy Sources (RES). The recommended formulation pertains to an optimization algorithm with variable weighting factor for a more precise estimation of the system states. The formulation can serve as as a general framework for a self-adapting dynamic estimator for improved states forecasting and thus preventive control of the distribution grid. Precisely estimated system states can also serve beneficial in;optimal scheduling, security assessment, and real time transactions.

关键词： Renewable Energy Sources RES Distributed Generation DG State Estimation Distribution Grid Power grids State estimation Renewable energy renewable energy sources optimization algorithms renewable resource

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