Online Learning and Competitive Analysis: a Unified Approach

1 Abbreviations and Notations 3

[1]  Zhiyi Huang,et al.  Welfare Maximization with Production Costs: A Primal Dual Approach , 2014, SODA.

[2]  Jack Edmonds,et al.  Matroids and the greedy algorithm , 1971, Math. Program..

[3]  S. F. Kapoor,et al.  The Many Facets of Graph Theory , 1969 .

[4]  Joseph Naor,et al.  Towards the randomized k-server conjecture: a primal-dual approach , 2010, SODA '10.

[5]  Yossi Azar,et al.  Online Mixed Packing and Covering , 2012, SODA.

[6]  Anupam Gupta,et al.  Changing Bases: Multistage Optimization for Matroids and Matchings , 2014, ICALP.

[7]  Manfred K. Warmuth,et al.  Exponentiated Gradient Versus Gradient Descent for Linear Predictors , 1997, Inf. Comput..

[8]  Enoch Peserico,et al.  Online paging with arbitrary associativity , 2003, SODA '03.

[9]  Martin Zinkevich,et al.  Online Convex Programming and Generalized Infinitesimal Gradient Ascent , 2003, ICML.

[10]  Amos Fiat,et al.  Competitive Paging Algorithms , 1991, J. Algorithms.

[11]  Shie Mannor,et al.  Online Learning for Global Cost Functions , 2009, COLT.

[12]  Artur Czumaj,et al.  An O(log k)-Competitive Algorithm for Generalized Caching , 2012, SODA.

[13]  Joseph Naor,et al.  Competitive Analysis via Regularization , 2014, SODA.

[14]  Joseph Naor,et al.  Simplex partitioning via exponential clocks and the multiway cut problem , 2013, STOC '13.

[15]  Peter L. Bartlett,et al.  A Regularization Approach to Metrical Task Systems , 2010, ALT.

[16]  Laszlo A. Belady,et al.  A Study of Replacement Algorithms for Virtual-Storage Computer , 1966, IBM Syst. J..

[17]  Seshadhri Comandur,et al.  Efficient learning algorithms for changing environments , 2009, ICML '09.

[18]  Noga Alon,et al.  A general approach to online network optimization problems , 2004, SODA '04.

[19]  Ambuj Tewari,et al.  Online Learning: Beyond Regret , 2010, COLT.

[20]  Joseph Naor,et al.  Randomized competitive algorithms for generalized caching , 2008, STOC.

[21]  H. Whitney.  On the Abstract Properties of Linear Dependence , 1935 .

[22]  Geoffrey J. Gordon.  Regret bounds for prediction problems , 1999, COLT '99.

[23]  Joseph Naor,et al.  The Design of Competitive Online Algorithms via a Primal-Dual Approach , 2009, Found. Trends Theor. Comput. Sci..

[24]  Alexander Rakhlin,et al.  Lecture Notes on Online Learning DRAFT , 2009 .

[25]  Joseph Naor,et al.  Online Primal-Dual Algorithms for Covering and Packing , 2009, Math. Oper. Res..

[26]  Joseph Naor,et al.  Online Primal-Dual Algorithms for Covering and Packing Problems , 2005, ESA.

[27]  Elad Hazan,et al.  Logarithmic regret algorithms for online convex optimization , 2006, Machine Learning.

[28]  Joseph Naor,et al.  Competitive Algorithms for Restricted Caching and Matroid Caching , 2014, ESA.

[29]  Joseph Naor,et al.  Online Packing and Covering Framework with Convex Objectives , 2014, ArXiv.

[30]  Marek Chrobak,et al.  Competitive analysis of randomized paging algorithms , 2000, Theor. Comput. Sci..

[31]  R. Latala.  Estimation of moments of sums of independent real random variables , 1997 .

[32]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[33]  Jennifer Wortman Vaughan,et al.  Efficient Market Making via Convex Optimization, and a Connection to Online Learning , 2013, TEAC.

[34]  Shai Shalev-Shwartz,et al.  Online Learning and Online Convex Optimization , 2012, Found. Trends Mach. Learn..

[35]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[36]  Chandra Chekuri,et al.  Submodular function maximization via the multilinear relaxation and contention resolution schemes , 2011, STOC '11.

[37]  Manor Mendel,et al.  Online Companion Caching , 2002, ESA.

[38]  Joseph Naor,et al.  A primal-dual randomized algorithm for weighted paging , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[39]  Kirk Pruhs,et al.  Speed scaling for weighted flow time , 2007, SODA '07.

[40]  Amit Kumar,et al.  Resource augmentation for weighted flow-time explained by dual fitting , 2012, SODA.

[41]  Jan Vondrák,et al.  Maximizing a Monotone Submodular Function Subject to a Matroid Constraint , 2011, SIAM J. Comput..

[42]  Noga Alon,et al.  The online set cover problem , 2003, STOC '03.

[43]  Anupam Gupta,et al.  Approximating Sparse Covering Integer Programs Online , 2012, Math. Oper. Res..

[44]  Ambuj Tewari,et al.  Regularization Techniques for Learning with Matrices , 2009, J. Mach. Learn. Res..

[45]  Santosh S. Vempala,et al.  Efficient algorithms for online decision problems , 2005, J. Comput. Syst. Sci..

[46]  Allan Borodin,et al.  An optimal on-line algorithm for metrical task system , 1992, JACM.

[47]  Kirk Pruhs,et al.  Speed Scaling with an Arbitrary Power Function , 2009, TALG.

[48]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[49]  Yoav Freund,et al.  A decision-theoretic generalization of on-line learning and an application to boosting , 1995, EuroCOLT.

[50]  Richard J. Enbody,et al.  On-line Restricted Caching , 2001, SODA '01.

[51]  Robert D. Carr,et al.  Strengthening integrality gaps for capacitated network design and covering problems , 2000, SODA '00.

[52]  BansalNikhil,et al.  A Polylogarithmic-Competitive Algorithm for the k-Server Problem , 2015 .

[53]  Lyle A. McGeoch,et al.  A strongly competitive randomized paging algorithm , 1991, Algorithmica.

[54]  Gábor Lugosi,et al.  Prediction, learning, and games , 2006 .

[55]  Dale Schuurmans,et al.  General Convergence Results for Linear Discriminant Updates , 1997, COLT '97.

[56]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[57]  Niv Buchbinder,et al.  Incentive Compatible Mulit-Unit Combinatorial Auctions: A Primal Dual Approach , 2013, Algorithmica.

[58]  Yuval Rabani,et al.  A Decomposition Theorem for Task Systems and Bounds for Randomized Server Problems , 2000, SIAM J. Comput..

[59]  Nathan Linial,et al.  On convex body chasing , 1993, Discret. Comput. Geom..

[60]  Avrim Blum,et al.  On-line Learning and the Metrical Task System Problem , 1997, COLT '97.

[61]  Yossi Azar,et al.  Online Covering with Convex Objectives and Applications , 2014, ArXiv.

[62]  Leah Epstein,et al.  Calculating lower bounds for caching problems , 2007, Computing.

[63]  William H. Cunningham,et al.  Testing membership in matroid polyhedra , 1984, J. Comb. Theory, Ser. B.

[64]  Lachlan L. H. Andrew,et al.  A tale of two metrics: simultaneous bounds on competitiveness and regret , 2013, SIGMETRICS '13.

[65]  Elad Hazan.  The convex optimization approach to regret minimization , 2011 .

[66]  Jack Edmonds,et al.  Submodular Functions, Matroids, and Certain Polyhedra , 2001, Combinatorial Optimization.

[67]  J. Borwein,et al.  Convex Analysis And Nonlinear Optimization , 2000 .

[68]  Robert E. Tarjan,et al.  Amortized efficiency of list update and paging rules , 1985, CACM.

[69]  Manfred K. Warmuth,et al.  The Weighted Majority Algorithm , 1994, Inf. Comput..

[70]  Joseph Naor,et al.  Unified Algorithms for Online Learning and Competitive Analysis , 2012, COLT.

[71]  Adam Tauman Kalai,et al.  Finely-competitive paging , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[72]  Yishay Mansour,et al.  Welfare and Profit Maximization with Production Costs , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[73]  Mark Herbster,et al.  Tracking the Best Expert , 1995, Machine Learning.

[74]  Adam Tauman Kalai,et al.  Online convex optimization in the bandit setting: gradient descent without a gradient , 2004, SODA '05.

[75]  Kirk Pruhs,et al.  Online Primal-Dual for Non-linear Optimization with Applications to Speed Scaling , 2011, WAOA.

[76]  Adam Tauman Kalai,et al.  Static Optimality and Dynamic Search-Optimality in Lists and Trees , 2002, SODA '02.