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Online vector balancing and geometric discrepancy

Nikhil Bansal, Haotian Jiang, Sahil Singla, Makrand Sinha
2020 Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing  
In particular, this lets us obtain a poly(n, logT ) bound for online vector balancing under arbitrary input distributions, and a polylog(T ) bound for online interval discrepancy.  ...  We consider an online vector balancing question where T vectors, chosen from an arbitrary distribution over [−1, 1] n , arrive one-byone and must be immediately given a ± sign.  ...  Then, we apply these bounds in §5 to obtain our vector balancing result (Theorem 1.4). In §6, we again apply these bounds to obtain our geometric discrepancy results (Theorems 1.2 and 1.3).  ... 
doi:10.1145/3357713.3384280 dblp:conf/stoc/BansalJ0S20 fatcat:662jnfqvsnhxzhn7r3bgvpq4qm

Online Vector Balancing and Geometric Discrepancy [article]

Nikhil Bansal, Haotian Jiang, Sahil Singla, Makrand Sinha
2020 arXiv   pre-print
This lets us obtain a poly(n, log T) bound for online vector balancing under arbitrary input distributions, and a poly(log T) bound for online interval discrepancy.  ...  We consider an online vector balancing question where T vectors, chosen from an arbitrary distribution over [-1,1]^n, arrive one-by-one and must be immediately given a ± sign.  ...  In particular, this lets us obtain a poly(n, log T ) bound for online vector balancing under arbitrary input distributions, and a polylog(T ) bound for online interval discrepancy.  ... 
arXiv:1912.03350v2 fatcat:f6qyelc2uzepdd63o3x4pp5mxm

Discrepancy Minimization via a Self-Balancing Walk [article]

Ryan Alweiss, Yang P. Liu, Mehtaab Sawhney
2020 arXiv   pre-print
As corollaries, we obtain bounds which are tight up to logarithmic factors for several problems in online vector balancing posed by Bansal, Jiang, Singla, and Sinha (STOC 2020), as well as linear time  ...  We study discrepancy minimization for vectors in R^n under various settings. The main result is the analysis of a new simple random process in multiple dimensions through a comparison argument.  ...  Acknowledgements The authors thank Noga Alon, Vishesh Jain, Mark Sellke, Aaron Sidford, and Yufei Zhao for helpful comments regarding the manuscript.  ... 
arXiv:2006.14009v2 fatcat:3hn664zfvvgbveokmplr3ybsnu

Online Balanced Experimental Design [article]

David Arbour, Drew Dimmery, Tung Mai, Anup Rao
2022 arXiv   pre-print
In this work, we present algorithms that build on recent advances in online discrepancy minimization which accommodate both arbitrary treatment probabilities and multiple treatments.  ...  e consider the experimental design problem in an online environment, an important practical task for reducing the variance of estimates in randomized experiments which allows for greater precision, and  ...  Online Assignment of Treatments Weighted Online Discrepancy Minimization: We consider a variant of the online Komlós problem [Spencer, 1977] , where vectors x 1 , . . . x n arrive one by one and must  ... 
arXiv:2203.02025v1 fatcat:kgsylxzfinfxdf5yi5dzw4b7iq

Online Geometric Discrepancy for Stochastic Arrivals with Applications to Envy Minimization [article]

Haotian Jiang, Janardhan Kulkarni, Sahil Singla
2019 arXiv   pre-print
On arrival of a point, the problem is to immediately and irrevocably color it in {+1,-1} while ensuring that every interval [a,b] ⊆ [0,1] is nearly-balanced.  ...  We show that the discrepancy of the above problem is sub-polynomial in n and that no algorithm can achieve a constant discrepancy.  ...  We are grateful to Alex Psomas and Ariel Procaccia for introducing us to the online envy minimization problem.  ... 
arXiv:1910.01073v1 fatcat:oaobsh4jujf6hgk64o4unz42si

Pigeonhole Design: Balancing Sequential Experiments from an Online Matching Perspective [article]

Jinglong Zhao, Zijie Zhou
2022 arXiv   pre-print
For online web-facing firms, however, it still remains challenging in balancing covariate information when experimental units arrive sequentially in online field experiments.  ...  the total discrepancy, which is defined as the minimum weight perfect matching between the two groups.  ...  In an online vector balancing problem, users with unknown vector information arrive one by one.  ... 
arXiv:2201.12936v3 fatcat:dtfi7farcfcytk4jyzwakmxbcu

Online Carpooling using Expander Decompositions [article]

Anupam Gupta, Ravishankar Krishnaswamy, Amit Kumar, Sahil Singla
2020 arXiv   pre-print
We consider the online carpooling problem: given n vertices, a sequence of edges arrive over time.  ...  the absolute difference between its in-degree and out-degree.  ...  Acknowledgments We thank atchaphol Saranurak for explaining and pointing us to [BvdBG + 20, eorem 5.6]. e last author would like to thank Navin Goyal for introducing him to [AAN + 98].  ... 
arXiv:2007.10545v2 fatcat:qzdbk2b3gvcjzjjglghihv5pyi

Online Discrepancy Minimization for Stochastic Arrivals [article]

Nikhil Bansal, Haotian Jiang, Raghu Meka, Sahil Singla, Makrand Sinha
2020 arXiv   pre-print
In the stochastic online vector balancing problem, vectors v_1,v_2,...,v_T chosen independently from an arbitrary distribution in R^n arrive one-by-one and must be immediately given a ± sign.  ...  We consider some of the most well-known problems in discrepancy theory in the above online stochastic setting, and give algorithms that match the known offline bounds up to polylog(nT) factors.  ...  Online Komlós and Tusnády settings. We first consider Komlós' setting for online discrepancy minimization where the vectors have 2 -norm at most 1.  ... 
arXiv:2007.10622v1 fatcat:5rkwteoctfccfc3kdindpbal5u

DEM-Aided Block Adjustment for Satellite Images With Weak Convergence Geometry

Tee-Ann Teo, Liang-Chien Chen, Chien-Liang Liu, Yi-Chung Tung, Wan-Yu Wu
2010 IEEE Transactions on Geoscience and Remote Sensing  
Experimental results indicate that using the DEM as an elevation control can significantly improve the geometric accuracy as well as the geometric discrepancies between images.  ...  His research activities are focused on the domain of digital photogrammetry, geometrical data processing for remotely sensed data, image feature extraction, lidar processing, and terrain analysis.  ...  Geometric consistency is maintained between images by utilizing residual vectors on the TPs to reduce the image discrepancy. Thus, we need to compute the residual vectors for TPs.  ... 
doi:10.1109/tgrs.2009.2033935 fatcat:tejg6rmmarf2lnc7rnorqhmdne

Online Discrepancy with Recourse for Vectors and Graphs [article]

Anupam Gupta, Vijaykrishna Gurunathan, Ravishankar Krishnaswamy, Amit Kumar, Sahil Singla
2021 arXiv   pre-print
The vector-balancing problem is a fundamental problem in discrepancy theory: given T vectors in [-1,1]^n, find a signing σ(a) ∈{± 1} of each vector a to minimize the discrepancy ∑_aσ(a) · a _∞.  ...  Since vector balancing has also been greatly studied for sparse vectors, we then give algorithms for low-discrepancy edge orientation, where we dynamically maintain signings for 2-sparse vectors.  ...  In Section 6 we give a generic reduction that can maintain near-optimal discrepancy for O V B against adaptive adversaries, with small recourse. eorem 1.4 (Arrivals Only: Online Vector Balancing with Recourse  ... 
arXiv:2111.06308v1 fatcat:kncn52uy3fdg5htrqtmg4exxfe

Smoothed Analysis with Adaptive Adversaries [article]

Nika Haghtalab, Tim Roughgarden, Abhishek Shetty
2021 arXiv   pre-print
We bound the ℓ_∞ norm of the discrepancy vector by Õ(ln^2( nT/σ) ).  ...  -Online discrepancy minimization: We consider the online Komlós problem, where the input is generated from an adaptive sequence of σ-smooth and isotropic distributions on the ℓ_2 unit ball.  ...  [BJSS20] Nikhil Bansal, Haotian Jiang, Sahil Singla, and Makrand Sinha. Online vector balanc- ing and geometric discrepancy.  ... 
arXiv:2102.08446v2 fatcat:eq3326qer5aohmxnqmirqc3wcq

Linear Regression under Fixed-Rank Constraints: A Riemannian Approach

Gilles Meyer, Silvere Bonnabel, Rodolphe Sepulchre
2011 International Conference on Machine Learning  
The proposed algorithms have many applications, scale to highdimensional problems, enjoy local convergence properties and confer a geometric basis to recent contributions on learning fixedrank matrices  ...  We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop efficient line-search algorithms.  ...  Acknowledgments This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by  ... 
dblp:conf/icml/MeyerBS11 fatcat:bwov435ewnfujcxsp6a6z4h64m

Self-polarizing terahertz liquid crystal phase shifter

Xiao-wen Lin, Jing-bo Wu, Wei Hu, Zhi-gang Zheng, Zi-jian Wu, Ge Zhu, Fei Xu, Biao-bing Jin, Yan-qing Lu
2011 AIP Advances  
Using sub-wavelength metallic gratings as both transparent electrodes and broadband high-efficiency polarizers, a highly-compact self-polarizing phase shifter is demonstrated by electrically tuning the  ...  The thickness of the gratings was set to be 30 nm for an optimum balance between transparency, conductivity and polarizing efficiency.  ...  Precise measurements are thus desired to resolve the discrepancy between theory and experiment. IV.  ... 
doi:10.1063/1.3626560 fatcat:6dsrvx6etvaonn5uj4dptfs2tm

Assessing Dataset Bias in Computer Vision [article]

Athiya Deviyani
2022 arXiv   pre-print
We will apply several augmentation techniques on a sample of the UTKFace dataset, such as undersampling, geometric transformations, variational autoencoders (VAEs), and generative adversarial networks  ...  We also found that training on geometrically transformed images lead to a similar performance with a much quicker training time.  ...  The two vectors are the a vector of means µ, and another vector of standard deviations σ.  ... 
arXiv:2205.01811v1 fatcat:nerm3uxlbngqfbi7fsll6zjtre

Multiqubit symmetric states with high geometric entanglement

J. Martin, O. Giraud, P. A. Braun, D. Braun, T. Bastin
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
and how their entanglement behaves asymptotically for large N.  ...  We show that much higher geometric entanglement with improved asymptotical behavior can be obtained in comparison with the highly entangled balanced Dicke states studied previously.  ...  Thus one should not expect to find a unique measure of quantumness, and the discrepancy between the LBQ and the MQ states should come as no surprise. VI.  ... 
doi:10.1103/physreva.81.062347 fatcat:airgbapnfjf4ditgj6pp4bevsa
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