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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.  ...  For Tusnády's problem of minimizing the discrepancy of axis-aligned boxes, we obtain an O(log^d+4 T) bound for arbitrary distribution over points.  ...  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

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

Haotian Jiang, Janardhan Kulkarni, Sahil Singla
2019 arXiv   pre-print
This generalization allows us to improve recent results of Benade et al. for the online envy minimization problem when the arrivals are stochastic.  ...  If all the arriving points were known upfront then we can color them alternately to achieve a discrepancy of 1. What is the minimum possible expected discrepancy when we color the points online?  ...  We are grateful to Alex Psomas and Ariel Procaccia for introducing us to the online envy minimization problem.  ... 
arXiv:1910.01073v1 fatcat:oaobsh4jujf6hgk64o4unz42si

Online Carpooling using Expander Decompositions [article]

Anupam Gupta, Ravishankar Krishnaswamy, Amit Kumar, Sahil Singla
2020 arXiv   pre-print
This provides the first polylogarithmic bounds for the online (stochastic) carpooling problem.  ...  Prior to this work, the best known bounds were O(√(n log n))-discrepancy for any adversarial sequence of arrivals, or O(loglog n)-discrepancy bounds for the stochastic arrivals when G is the complete graph  ...  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 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  
One must utilize the stochasticity as in the worst-case scenario it is known that discrepancy is Ω(T 1/2 ) for any online algorithm.  ...  ] that gives a non-trivial O(T 1/log log T ) bound for online interval discrepancy.  ...  The authors are thankful to Janardhan Kulkarni for several discussions on this project. The authors would also like to thank the anonymous ref-  ... 
doi:10.1145/3357713.3384280 dblp:conf/stoc/BansalJ0S20 fatcat:662jnfqvsnhxzhn7r3bgvpq4qm

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.  ...  In this problem, experimental units with heterogeneous covariate information arrive sequentially and must be immediately assigned into either the control or the treatment group, with an objective of minimizing  ...  The online vector balancing problem minimizes the total signed prefix-sum, whereas our online blocking problem minimizes the size of the minimum weight perfect matching.  ... 
arXiv:2201.12936v3 fatcat:dtfi7farcfcytk4jyzwakmxbcu

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  ...  Harshaw et al. [2020] do that for an offline discrepancy minimization algorithm, and here we do it for an online version.  ... 
arXiv:2203.02025v1 fatcat:kgsylxzfinfxdf5yi5dzw4b7iq

MACRO: A Meta-Algorithm for Conditional Risk Minimization [article]

Alexander Zimin, Christoph Lampert
2018 arXiv   pre-print
We study conditional risk minimization (CRM), i.e. the problem of learning a hypothesis of minimal risk for prediction at the next step of sequentially arriving dependent data.  ...  In this work, we introduce MACRO, a meta-algorithm for CRM that does not suffer from this shortcoming, but nevertheless offers learning guarantees.  ...  Conditional risk minimization has many application for learning tasks in which data arrives sequentially and decisions have to be made quickly, e.g. frame-wise classification of video streams.  ... 
arXiv:1801.00507v2 fatcat:4dclc7m2djgkzerwqm2mo5snu4

Smoothed Analysis with Adaptive Adversaries [article]

Nika Haghtalab, Tim Roughgarden, Abhishek Shetty
2021 arXiv   pre-print
-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.  ...  We prove novel algorithmic guarantees for several online problems in the smoothed analysis model.  ...  Online geometric discrepancy for stochastic arrivals with applications to envy minimization. CoRR, abs/1910.01073, 2019.  ... 
arXiv:2102.08446v2 fatcat:eq3326qer5aohmxnqmirqc3wcq

Scheduling (Dagstuhl Seminar 18101)

Magnús M. Halldórson, Nicole Megow, Clifford Stein, Michael Wagner
2018 Dagstuhl Reports  
Deterministic Discrepancy Minimization via the Multiplicative Weight Update Method A well-known theorem of Spencer shows that any set system with n sets over n elements admits a coloring of discrepancy  ...  Overview of Talks Improved Online Algorithm for Weighted Flow Time We study the classical scheduling problem of assigning jobs to machines in order to minimize the makespan.  ...  Online Machine Minimization (Phillips et al., STOC 1997 ) is a fundamental online scheduling problem: Jobs arrive over time at their release dates and need to be scheduled preemptively on parallel machines  ... 
doi:10.4230/dagrep.8.3.1 dblp:journals/dagstuhl-reports/HalldorssonMS18 fatcat:xlfjfzwt3fdpdk3ryxr2ldra5m

Variable Metric Stochastic Approximation Theory [article]

Peter Sunehag, Jochen Trumpf, S.V.N. Vishwanathan, Nicol Schraudolph
2009 arXiv   pre-print
In doing so, we provide a convergence theory for a large class of online variable metric methods including the recently introduced online versions of the BFGS algorithm and its limited-memory LBFGS variant  ...  We provide a variable metric stochastic approximation theory.  ...  Acknowledgements The authors are very grateful to Leon Bottou at NEC Labs in Princeton, NJ for his help with the main theorem.  ... 
arXiv:0908.3529v1 fatcat:loao3wzthbcltirg4gub5b3yae

Online Stochastic and Robust Optimization [chapter]

Russell Bent, Pascal Van Hentenryck
2004 Lecture Notes in Computer Science  
This paper considers online stochastic optimization problems where uncertainties are characterized by a distribution that can be sampled and where time constraints severely limit the number of offline  ...  Robustness results are also presented for multiple vehicle routing.  ...  Happy birthday, Jean-Louis, and thank you for being such an inspiration for so many of us! This research is partially supported by NSF ITR Award DMI-0121495.  ... 
doi:10.1007/978-3-540-30502-6_21 fatcat:ms4jem3lnbcprp4kylggmnltcy

Discrepancy Minimization via a Self-Balancing Walk [article]

Ryan Alweiss, Yang P. Liu, Mehtaab Sawhney
2020 arXiv   pre-print
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.  ...  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  ...  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 Bin Packing with Known T [article]

Shang Liu, Xiaocheng Li
2021 arXiv   pre-print
In the online bin packing problem, a sequence of items is revealed one at a time, and each item must be packed into an available bin instantly upon its arrival.  ...  For the latter one, our analysis provides an alternative (probably simpler) treatment and tightens the analysis of the asymptotic benchmark of the stochastic bin packing problem in Rhee and Talagrand (  ...  Uniform loss algorithms for online stochastic decision- making with applications to bin packing.  ... 
arXiv:2112.03200v1 fatcat:37nelr2365ftrkvscqaoyk5rby

Optimally Compressed Nonparametric Online Learning [article]

Alec Koppel, Amrit Singh Bedi, Ketan Rajawat, Brian M. Sadler
2020 arXiv   pre-print
We survey online compression tools which bring their memory under control and attain approximate convergence.  ...  Unfortunately, when used online, nonparametric methods suffer a "curse of dimensionality" which precludes their use: their complexity scales at least with the time index.  ...  A new sample arrives and is incorporated as either functional stochastic gradient method, maximum a posteriori estimation, or Monte Carlo particle generation.  ... 
arXiv:1909.11555v2 fatcat:z2tl34d7nbazdlzfmwrsw5rzfu

Applying Particle Filtering in Both Aggregated and Age-structured Population Compartmental Models of Pre-vaccination Measles [article]

Xiaoyan Li, Alexander Doroshenko, Nathaniel D. Osgood
2018 bioRxiv   pre-print
The results indicate that, when used with a suitable dynamic model, particle filtering can offer high predictive capacity for measles dynamics and outbreak occurrence in a low vaccination context.  ...  In this paper, we apply the Sequential Monte Carlo approach of particle filtering, incorporating reported measles incidence for Saskatchewan during the pre-vaccination era, using an adaptation of a previously  ...  Acknowledgments 697 We thank Weicheng Qian and Anahita Safarishahrbijari for the suggestions of building 698 models; we also thank Lujie Duan for the help of debugging the models.  ... 
doi:10.1101/340661 fatcat:sgo53ne6lfa4xfik7mwd7yr6mi
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