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In this book, I introduce the concepts of online learning through a modern view based on convex optimization.
A. Mokhtari, A. Ozdaglar, and S. Pattathil · 1901
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Combining online learning guarantees
A. Cutkosky · 1902
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Online convex optimization for sequential decision processes and extensive-form games
G. Farina, C. Kroer, and T. Sandholm · 1925
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Zur theorie der gesellschaftsspiele
J. von Neumann · 1928
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Étude critique de la notion de collectif
J. Ville · 1939
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Theory of games and economic behavior
J. von Neumann and O. Morgenstern · 1944
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Sequential tests of statistical hypotheses
A. Wald · 1945
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Statistical decision functions
A. Wald · 1950
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Games against nature
J. Milnor · 1951
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The theory of statistical decision
L. J. Savage · 1951
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Some aspects of the sequential design of experiments
H. Robbins · 1952
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The foundations of statistics
L. J. Savage · 1954
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A remark on stirling’s formula
H. Robbins · 1955
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An algorithm for quadratic programming
M. Frank and P. Wolfe · 1956
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A new interpretation of information rate
J. L. Kelly, jr · 1956
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Approximation to Bayes risk in repeated play
J. Hannan · 1957
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The Perceptron: A probabilistic model for information storage and organization in the brain
F. Rosenblatt · 1958
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On general minimax theorems
M. Sion · 1958
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The Perceptron: A model for brain functioning. I
H.-D. Block · 1962
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On convergence proofs for perceptrons
A. B Novikoff · 1962
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Convex functions and dual extremum problems
R. T. Rockafellar · 1963
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Theoretical foundations of the potential function method in pattern recognition learning
M. A. Aizerman, E. M. Braverrnan, and L. I. Rozonoer · 1964
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On the structure of algorithms for the numerical solution of optimal planning and design problems (in Russian)
N. Shor · 1964
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Behavior of sequential predictors of binary sequences
T. Cover · 1965
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Existence theorems and convergence of minimizing sequences in extremum problems with restrictions
B. Polyak · 1966
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The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming
L. M. Bregman · 1967
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Convex Analysis
R. T. Rockafellar · 1970
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A unified approach to the definition of random sequences
C.-P. Schnorr · 1971
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On the amount of variance needed to escape from a strip
D. Blackwell and D. Freedman · 1973
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Universal gambling schemes and the complexity measures of Kolmogorov and Chaitin
T. M Cover · 1974
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The expected sample size of some tests of power one
H. Robbins and D. Siegmund · 1974
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The extragradient method for finding saddle points and other problems
G. M. Korpelevich · 1976
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Uniform tests of randomness
L. A. Levin · 1976
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A modification of the Arrow-Hurwicz method for search of saddle points
L. D. Popov · 1980
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The best constants in the Khintchine inequality
U. Haagerup · 1981
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The performance of universal encoding
R. Krichevsky and V. Trofimov · 1981
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Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems
T. L. Lai and C. Z. Wei · 1982
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Problem complexity and method efficiency in optimization
A. S. Nemirovskij and D. Yudin · 1983
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Differential-Geometrical Methods in Statistics
S. Amari · 1985
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Asymptotically efficient adaptive allocation rules
T. L. Lai and H. Robbins · 1985
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Adaptive treatment allocation and the multi-armed bandit problem
T. L. Lai · 1987
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Thoughts on hypothesis boosting
M. Kearns · 1988
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Learning boolean formulae or finite automata is as hard as factoring
M. Kearns and L. G. Valiant · 1988
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The strength of weak learnability
R. E. Schapire · 1990
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Aggregating strategies
V. G. Vovk · 1990
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Universal portfolios
T. M. Cover · 1991
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How to use expert advice
N. Cesa-Bianchi, Y. Freund, D. P. Helmbold, D. Haussler, R. E. Schapire, and M. K Warmuth · 1993
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Convergence analysis of a proximal-like minimization algorithm using Bregman functions
G. Chen and M. Teboulle · 1993
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A logic of probability, with application to the foundations of statistics
V. G. Vovk · 1993
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On the Rademacher series
P. Hitczenko and S. Kwapień · 1994
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The weighted majority algorithm
N. Littlestone and M. K. Warmuth · 1994
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A desicion-theoretic generalization of on-line learning and an application to boosting
Y. Freund and R. E. Schapire · 1995
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Consistency and cautious fictitious play
D. Fudenberg and D. K. Levine · 1995
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Worst-case quadratic loss bounds for prediction using linear functions and gradient descent
N. Cesa-Bianchi, P. M. Long, and M. K. Warmuth · 1996
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Universal portfolios with side information
T. M. Cover and E. Ordentlich · 1996
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Game theory, on-line prediction and boosting
Y. Freund and R. E. Schapire · 1996
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Legendre functions and the method of random Bregman projections
H. H. Bauschke and J. M. Borwein · 1997
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Empirical support for Winnow and weighted-majority algorithms: Results on a calendar scheduling domain
A. Blum · 1997
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Universal portfolios with and without transaction costs
A. Blum and A. Kalai · 1997
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How to use expert advice
N. Cesa-Bianchi, Y. Freund, D. Haussler, D. P. Helmbold, R. E. Schapire, and M. K. Warmuth · 1997
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A decision-theoretic generalization of on-line learning and an application to boosting
Y. Freund and R. E. Schapire · 1997
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Using and combining predictors that specialize
Y. Freund, R. E. Schapire, Y. Singer, and M. K. Warmuth · 1997
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General convergence results for linear discriminant updates
A. J. Grove, N. Littlestone, and D. Schuurmans · 1997
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Exponentiated gradient versus gradient descent for linear predictors
J. Kivinen and M. Warmuth · 1997
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Continuous and discrete-time nonlinear gradient descent: Relative loss bounds and convergence
M. K. Warmuth and A. K. Jagota · 1997
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Large margin classification using the Perceptron algorithm
Y. Freund and R. E. Schapire · 1998
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On-line portfolio selection using multiplicative updates
D. P. Helmbold, R. E. Schapire, Y. Singer, and M. K. Warmuth · 1998
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Tracking the best expert
M. Herbster and M. K. Warmuth · 1998
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Universal portfolio selection
V. Vovk and C. Watkins · 1998
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Adaptive regression and model selection in data mining problems
S. Bakin · 1999
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Universal portfolios with and without transaction costs
A. Blum and A. Kalai · 1999
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Beating the hold-out: Bounds for k k -fold and progressive cross-validation
A. Blum, A. Kalai, and J. Langford · 1999
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Analysis of two gradient-based algorithms for on-line regression
N. Cesa-Bianchi · 1999
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The robustness of the p p -norm algorithms
C. Gentile and N. Littlestone · 1999
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Averaging expert predictions
J. Kivinen and M. K. Warmuth · 1999
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A simple adaptive procedure leading to correlated equilibrium
S. Hart and A. Mas-Colell · 2000
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Relative loss bounds for on-line density estimation with the exponential family of distributions
K. S. Azoury and M. K. Warmuth · 2001
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The ordered subsets mirror descent optimization method with applications to tomography
A. Ben-Tal, T. Margalit, and A. Nemirovski · 2001
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General convergence results for linear discriminant updates
A. J. Grove, N. Littlestone, and D. Schuurmans · 2001
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Tracking the best linear predictor
M. Herbster and M. K. Warmuth · 2001
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Probability and finance: it’s only a game!
G. Shafer and V. Vovk · 2001
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Competitive on-line statistics
V. Vovk · 2001
Cited alongside, same era.
Disentangling adaptive gradient methods from learning rates
N. Agarwal, R. Anil, E. Hazan, T. Koren, and C. Zhang · 2002
Cited alongside, same era.
Efficient algorithms for universal portfolios
A. T. Kalai and S. Vempala · 2002
Cited alongside, same era.
S. Lacoste-Julien, M. Schmidt, and F. Bach · 2002
Cited alongside, same era.
Bregman monotone optimization algorithms
H. H. Bauschke, J. M. Borwein, and P. L. Combettes · 2003
Cited alongside, same era.
Mirror descent and nonlinear projected subgradient methods for convex optimization
Stochastic proximal iteration: a non-asymptotic improvement upon stochastic gradient descent
E. K. Ryu and S. Boyd · 2014
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Adaptivity and optimism: An improved exponentiated gradient algorithm
J. Steinhardt and P. Liang · 2014
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Fighting bandits with a new kind of smoothness
J. D. Abernethy, C. Lee, and A. Tewari · 2015
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Heads-up limit hold’em poker is solved
M. Bowling, N. Burch, M. Johanson, and O. Tammelin · 2015
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Strongly adaptive online learning
A. Daniely, A. Gonen, and S. Shalev-Shwartz · 2015
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Second-order quantile methods for experts and combinatorial games
W. M. Koolen and T. van Erven · 2015
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A. Beck and M. Teboulle · 2003
Cited alongside, same era.
The robustness of the p p -norm algorithms
C. Gentile · 2003
Cited alongside, same era.
Online convex programming and generalized infinitesimal gradient ascent
M. Zinkevich · 2003
Cited alongside, same era.
Convex Optimization
S. Boyd and L. Vandenberghe · 2004
Cited alongside, same era.
On the generalization ability of on-line learning algorithms
N. Cesa-Bianchi, A. Conconi, and C. Gentile · 2004
Cited alongside, same era.
Fundamentals of convex analysis
Jean-Baptiste Hiriart-Urruty and Claude Lemaréchal · 2004
Cited alongside, same era.
Introductory lectures on convex optimization: A basic course , volume 87
Y. Nesterov · 2004
Cited alongside, same era.
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Achieving all with no parameters: AdaNormalHedge
H. Luo and R. E. Schapire · 2015
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Projected reflected gradient methods for monotone variational inequalities
Y. Malitsky · 2015
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Quasi-monotone subgradient methods for nonsmooth convex minimization
Y. Nesterov and V. Shikhman · 2015
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Scale-free algorithms for online linear optimization
F. Orabona and D. Pál · 2015
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Optimal non-asymptotic lower bound on the minimax regret of learning with expert advice
F. Orabona and D. Pál · 2015
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F. Orabona and D. Pál · 2015
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A generalized online mirror descent with applications to classification and regression
F. Orabona, K. Crammer, and N. Cesa-Bianchi · 2015
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Solving heads-up limit Texas hold’em
O. Tammelin, N. Burch, M. Johanson, and M. Bowling · 2015
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A closer look at adaptive regret
D. Adamskiy, W. M. Koolen, A. Chernov, and V. Vovk · 2016
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Distributed algorithms via gradient descent for Fisher markets
B. Birnbaum, N. R. Devanur, and L. Xiao · 2016
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Fast projection onto the simplex and the 𝒍 𝟏 \boldsymbol{l}_{\mathbf{1}} ball
L. Condat · 2016
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Accelerating online convex optimization via adaptive prediction
M. Mohri and S. Yang · 2016
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Coin betting and parameter-free online learning
F. Orabona and D. Pál · 2016
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MetaGrad: Multiple learning rates in online learning
T. van Erven and W. M. Koolen · 2016
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Dual averaging methods for regularized stochastic learning and online optimization
L. Xiao · 2016
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On Frank-Wolfe and equilibrium computation
J. D. Abernethy and J.-K. Wang · 2017
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A descent lemma beyond lipschitz gradient continuity: first-order methods revisited and applications
H. H. Bauschke, J. Bolte, and M. Teboulle · 2017
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Efficient online bandit multiclass learning with O ~ ( T ) \tilde{O}(\sqrt{T}) regret
A. Beygelzimer, F. Orabona, and C. Zhang · 2017
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Parameter-free online learning via model selection
D. J. Foster, S. Kale, M. Mohri, and K. Sridharan · 2017
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A modular analysis of adaptive (non-)convex optimization: Optimism, composite objectives, and variational bounds
P. Joulani, A. György, and C. Szepesvári · 2017
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A survey of algorithms and analysis for adaptive online learning
H B. McMahan · 2017
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Training deep networks without learning rates through coin betting
F. Orabona and T. Tommasi · 2017
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On equivalence of martingale tail bounds and deterministic regret inequalities
A. Rakhlin and K. Sridharan · 2017
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A version of the mirror descent method to solve variational inequalities
V. V. Semenov · 2017
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Algorithms and Lower Bounds for Parameter-free Online Learning
A. Cutkosky · 2018
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Black-box reductions for parameter-free online learning in Banach spaces
A. Cutkosky and F. Orabona · 2018
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Training GANs with optimism
C. Daskalakis, A. Ilyas, V. Syrgkanis, and H. Zeng · 2018
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Test martingales for bounded random variables
H. Hendriks · 2018
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Relatively smooth convex optimization by first-order methods, and applications
H. Lu, R. M. Freund, and Y. Nesterov · 2018
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On the convergence of Adam and beyond
S. J. Reddi, S. Kale, and S. Kumar · 2018
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Adaptive online learning in dynamic environments
L. Zhang, S. Lu, and Z.-H. Zhou · 2018
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Revisiting CFR+ and alternating updates
N. Burch, M. Moravcik, and M. Schmid · 2019
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Last-iterate convergence: Zero-sum games and constrained min-max optimization
C. Daskalakis and I. Panageas · 2019
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A variational inequality perspective on generative adversarial networks
G. Gidel, H. Berard, G. Vignoud, P. Vincent, and S. Lacoste-Julien · 2019
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On the convergence of single-call stochastic extra-gradient methods
Y.-G. Hsieh, F. Iutzeler, J. Malick, and P. Mertikopoulos · 2019
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The implicit bias of gradient descent on nonseparable data
Z. Ji and M. Telgarsky · 2019
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Parameter-free online convex optimization with sub-exponential noise
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Interaction matters: A note on non-asymptotic local convergence of generative adversarial networks
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Temporal variability in implicit online learning
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Better full-matrix regret via parameter-free online learning
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Online parameter-free learning of multiple low variance tasks
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Regret minimization with function approximation in extensive-form games
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Lipschitz and comparator-norm adaptivity in online learning
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Comparator-adaptive convex bandits
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Dynamic regret of convex and smooth functions
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Online learning with optimism and delay
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