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Spectral Sparsification and Regret Minimization Beyond Matrix Multiplicative Updates [article]

Zeyuan Allen-Zhu and Zhenyu Liao and Lorenzo Orecchia
2015 arXiv   pre-print
The fundamental conceptual novelty of our work is the leveraging of a strong connection between sparsification and a regret minimization problem over density matrices.  ...  This connection was known to provide an interpretation of the randomized sparsifiers of Spielman and Srivastava [SS11] via the application of matrix multiplicative weight updates (MWU) [CHS11, Vis14].  ...  Acknowledgement We thank Richard Peng, Nikhil Srivastava, and Nisheeth Vishnoi for helpful conversations.  ... 
arXiv:1506.04838v1 fatcat:cofi6qa5vzextpz75ll47pm5ee

Using Optimization to Obtain a Width-Independent, Parallel, Simpler, and Faster Positive SDP Solver

Zeyuan Allen-Zhu, Yin Tat Lee, Lorenzo Orecchia
2015 Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms  
. • Z.Allen-Zhu, Z.Liao and L.Orecchia. Linear-Sized Spectral Sparsification in Almost Quadratic Time and Regret Minimization Beyond Matrix Multiplicative Weight Updates. STOC'15: ACM Proc. Symp.  ...  • Z.Allen-Zhu, Y.T.Lee and L. Orecchia . Using Optimization to Obtain a Width-Independent, Parallel, Simpler, and Faster Positive SDP Solver. SODA'16: ACM-SIAM Proc.  ...  Organizer of semester-long program "Bridging Continuous and Discrete Optimization" at the Simons Institute for Theoretical Computer Science, to run in Fall 2017.  ... 
doi:10.1137/1.9781611974331.ch127 dblp:conf/soda/Allen-ZhuLO16 fatcat:hilpefptv5gw7bkb7bnjk4kvwu

Distributed Learning with Sublinear Communication [article]

Jayadev Acharya and Christopher De Sa and Dylan J. Foster and Karthik Sridharan
2019 arXiv   pre-print
In distributed statistical learning, N samples are split across m machines and a learner wishes to use minimal communication to learn as well as if the examples were on a single machine.  ...  This result is based on a family of algorithms that combine mirror descent with randomized sparsification/quantization of iterates, and extends to the general stochastic convex optimization model.  ...  Acknowledgements Part of this work was completed while DF was a student at Cornell University and supported by the Facebook PhD fellowship.  ... 
arXiv:1902.11259v2 fatcat:6a4ndvdsjzg7ngcir72ifua7ei

Near-Optimal Design of Experiments via Regret Minimization

Zeyuan Allen-Zhu, Yuanzhi Li, Aarti Singh, Yining Wang
2017 International Conference on Machine Learning  
Numerical results on synthetic and real-world design problems verify the practical effectiveness of the proposed algorithm.  ...  Acknowledgement This work is supported by NSF grants CAREER IIS-1252412 and CCF-1563918.  ...  We thank Adams Wei Yu for providing an efficient implementation of the projection step, and other useful discussions.  ... 
dblp:conf/icml/Allen-ZhuLSW17 fatcat:wbhz6ktx2ndsvk33hd5ncxz3qq

Taking the Human Out of the Loop: A Review of Bayesian Optimization

Bobak Shahriari, Kevin Swersky, Ziyu Wang, Ryan P. Adams, Nando de Freitas
2016 Proceedings of the IEEE  
Big data applications are typically associated with systems involving large numbers of users, massive complex software systems, and large-scale heterogeneous computing and storage architectures.  ...  It promises greater automation so as to increase both product quality and human productivity.  ...  efficient posterior updating.  ... 
doi:10.1109/jproc.2015.2494218 fatcat:dcdmezhogrd45ippmdaslddlxa

Stochastic Optimization for Machine Learning [article]

Andrew Cotter
2013 arXiv   pre-print
often outperform one which performs a smaller number of much "smarter" but computationally-expensive updates.  ...  "has cancer" or "doesn't have cancer"), and the learning problem is to find a linear classifier which is best at predicting the label.  ...  Ultimately, the cost of finding W = W + ηxx T , and maintaining an eigendecomposition during this update, is the cost of the matrix multiplication defining the new set of eigenvectors U : O (k ) 2 d .  ... 
arXiv:1308.3509v1 fatcat:tx5rpluajfcexgiqz52cnfigmi

Design of large polyphase filters in the Quadratic Residue Number System

Gian Carlo Cardarilli, Alberto Nannarelli, Yann Oster, Massimo Petricca, Marco Re
2010 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers  
., schemes that minimize the rate at which regret accumulates with time), and/or adaptive schemes that come arbitrarily close to the minimum rate.  ...  Based on this soft clustering, we update K linear filters per data sample and combine the outputs to minimize squared error.  ... 
doi:10.1109/acssc.2010.5757589 fatcat:ccxnu5owr5fyrcjcqukumerueq

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 bound the regret by Õ(√(T dln(1/σ)) + d√(ln(T/σ))). This answers open questions of [RST11,Hag18].  ...  [ALO15] Zeyuan Allen-Zhu, Zhenyu Liao, and Lorenzo Orecchia. Spectral sparsification and regret minimization beyond matrix multiplicative updates.  ... 
arXiv:2102.08446v2 fatcat:eq3326qer5aohmxnqmirqc3wcq

Linear Stochastic Bandits over a Bit-Constrained Channel [article]

Aritra Mitra, Hamed Hassani, George J. Pappas
2022 arXiv   pre-print
The goal of the server is to take actions based on these estimates to minimize cumulative regret.  ...  To this end, we develop a novel and general algorithmic framework that hinges on two main components: (i) an adaptive encoding mechanism that exploits statistical concentration bounds, and (ii) a decision-making  ...  Third, we plan to extend the ideas and results in our paper to more complex distributed/federated settings involving multiple agents.  ... 
arXiv:2203.01198v1 fatcat:dco27nfyj5gzhahxhswnsswn2a

Positive Semidefinite Programming: Mixed, Parallel, and Width-Independent [article]

Arun Jambulapati, Yin Tat Lee, Jerry Li, Swati Padmanabhan, Kevin Tian
2021 arXiv   pre-print
For a given multiplicative accuracy of ϵ, our algorithm takes O(log^3(ndρ) ·ϵ^-3) parallelizable iterations, where n, d are dimensions of the problem and ρ is a width parameter of the instance, generalizing  ...  Crucial to our analysis are a simplification of existing algorithms for mixed positive linear programs, achieved by removing an asymmetry caused by modifying covering constraints, and a suite of matrix  ...  AJ and KT would like to thank Kiran Shiragur for helpful conversations, and Aaron Sidford for bringing this problem to our attention, as well as his continued encouragement through this project.  ... 
arXiv:2002.04830v3 fatcat:hkpukrmkxra77ijb4owsv6lnia

Contributions to Representation Learning with Graph Autoencoders and Applications to Music Recommendation [article]

Guillaume Salha-Galvan
2022 arXiv   pre-print
such as link prediction and community detection.  ...  Furthermore, we argue that GAE and VGAE models are often unnecessarily complex, and we propose to simplify them by leveraging linear encoders.  ...  p×p : the matrix multiplication of M and N ( = N M in general).  ... 
arXiv:2205.14651v2 fatcat:3decglpamjc65p3i7jdx5h2eiu

Noncommutative analysis, Multivariable spectral theory for operators in Hilbert space, Probability, and Unitary Representations [article]

Palle Jorgensen, Feng Tian
2015 arXiv   pre-print
in a way that minimizes the need for prerequisites.  ...  And neighboring areas, probability/statistics (for example stochastic processes, Ito and Malliavin calculus), physics (representation of Lie groups, quantum field theory), and spectral theory for Schr\  ...  A story: Selfadjoint operators, and the gulf between the lingo and culture of mathematics and of physics: Peter Lax relates the following conversation in German between K.O. Friedrichs and W.  ... 
arXiv:1408.1164v8 fatcat:ltmzpyj3gzfjpizdfrjsdxdw3y

Mixed-Variable Bayesian Optimization [article]

Erik Daxberger, Anastasia Makarova, Matteo Turchetta, Andreas Krause
2019 arXiv   pre-print
The optimization of expensive to evaluate, black-box, mixed-variable functions, i.e. functions that have continuous and discrete inputs, is a difficult and yet pervasive problem in science and engineering  ...  We propose two methods to optimize its acquisition function, a challenging problem for mixed-variable domains, and we show that MiVaBo can handle complex constraints over the discrete part of the domain  ...  Komodakis, N., Paragios, N., and Tziritas, G. (2011). MRF Henrández-Lobato, J. M., Hoffman, M. W., and Ghahra- energy minimization and beyond via dual decomposi- mani, Z. (2014).  ... 
arXiv:1907.01329v3 fatcat:srdpkrqzpvc4bjdypnlrzupxza

Resource-constrained, scalable learning [article]

Ioannis Mitliagkas
Specifically, x t = Az t + w t , (3.1) where A ∈ R p×k is a fixed matrix, z t ∈ Prior Work Online-PCA for regret minimization is considered in several papers, most recently in [75] .  ...  Beyond the CPU, and depending on the platform, problem, algorithm and implementation, other resources turn out to be the limiting factor: main memory, storage and over-the-network communication are the  ...  This means that teleportation happens with probability p T and the walk is described by the transition probability matrix (TPM) Q, as defined in Section 2.6.  ... 
doi:10.15781/t2hp6w fatcat:5upssqxsyzejhjacfopmg6kz4y

Selective Data Acquisition in Learning and Decision Making Problems

Yining Wang
Classical statistics and machine learning posit that data are passively collected, usually assumed to be independently and identically distributed.  ...  In sequential decision making problems, data such as feedback or utility depend on the particular decisions which can be adaptively and selectively made.  ...  Perhaps the most famous choice of ψ is the matrix entropy ψpAq xA, log A ¡ Iy, and the resulting MD strategy is referred to as matrix multiplicative weight updates (Arora & Kale, 2007) .  ... 
doi:10.1184/r1/8342630.v1 fatcat:7juwf653n5eg5ngsjra7dg3gfe
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