Prediction, learning, and games

1. Introduction 2. Prediction with expert advice 3. Tight bounds for specific losses 4. Randomized prediction 5. Efficient forecasters for large classes of experts 6. Prediction with limited feedback 7. Prediction and playing games 8. Absolute loss 9. Logarithmic loss 10. Sequential investment 11. Linear pattern recognition 12. Linear classification 13. Appendix.

[1]  A E Bostwick,et al.  THE THEORY OF PROBABILITIES. , 1896, Science.

[2]  J. Littlewood ON BOUNDED BILINEAR FORMS IN AN INFINITE NUMBER OF VARIABLES , 1930 .

[3]  J. Neumann,et al.  Theory of Games and Economic Behavior. , 1945 .

[4]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[5]  N. Aronszajn Theory of Reproducing Kernels. , 1950 .

[6]  G. Brier VERIFICATION OF FORECASTS EXPRESSED IN TERMS OF PROBABILITY , 1950 .

[7]  J. Robinson AN ITERATIVE METHOD OF SOLVING A GAME , 1951, Classics in Game Theory.

[8]  J. Nash NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[9]  H. Robbins Some aspects of the sequential design of experiments , 1952 .

[10]  K Fan,et al.  Minimax Theorems. , 1953, Proceedings of the National Academy of Sciences of the United States of America.

[11]  H. Robbins,et al.  Asymptotic Solutions of the Compound Decision Problem for Two Completely Specified Distributions , 1955 .

[12]  J. J. Kelly A new interpretation of information rate , 1956 .

[13]  D. Blackwell An analog of the minimax theorem for vector payoffs. , 1956 .

[14]  M. Sion On general minimax theorems , 1958 .

[15]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

[16]  James Hannan,et al.  4. APPROXIMATION TO RAYES RISK IN REPEATED PLAY , 1958 .

[17]  L. Breiman Optimal Gambling Systems for Favorable Games , 1962 .

[18]  D. Blackwell,et al.  Merging of Opinions with Increasing Information , 1962 .

[19]  A. A. Mullin,et al.  Principles of neurodynamics , 1962 .

[20]  H. D. Block The perceptron: a model for brain functioning. I , 1962 .

[21]  V. Vapnik Pattern recognition using generalized portrait method , 1963 .

[22]  L. Shapley SOME TOPICS IN TWO-PERSON GAMES , 1963 .

[23]  E. Samuel Asymptotic Solutions of the Sequential Compound Decision Problem , 1963 .

[24]  W. Hoeffding Probability Inequalities for sums of Bounded Random Variables , 1963 .

[25]  Albert B Novikoff,et al.  ON CONVERGENCE PROOFS FOR PERCEPTRONS , 1963 .

[26]  Michel Loève,et al.  Probability Theory I , 1977 .

[27]  E. Samuel Convergence of the Losses of Certain Decision Rules for the Sequential Compound Decision Problem , 1964 .

[28]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part I , 1964, Inf. Control..

[29]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part II , 1964, Inf. Control..

[30]  M. Aizerman,et al.  Theoretical Foundations of the Potential Function Method in Pattern Recognition Learning , 1964 .

[31]  Thomas M. Cover,et al.  Behavior of sequential predictors of binary sequences , 1965 .

[32]  J. V. Ryzin,et al.  The Sequential Compound Decision Problem with $m \times n$ Finite Loss Matrix , 1966 .

[33]  E. Mark Gold,et al.  Language Identification in the Limit , 1967, Inf. Control..

[34]  D. Gilliland Sequential Compound Estimation , 1968 .

[35]  P. Billingsley,et al.  Convergence of Probability Measures , 1970, The Mathematical Gazette.

[36]  A. Banos On Pseudo-Games , 1968 .

[37]  J. Hannan,et al.  On an Extended Compound Decision Problem , 1969 .

[38]  L. Levin,et al.  THE COMPLEXITY OF FINITE OBJECTS AND THE DEVELOPMENT OF THE CONCEPTS OF INFORMATION AND RANDOMNESS BY MEANS OF THE THEORY OF ALGORITHMS , 1970 .

[39]  Vladimir Vapnik,et al.  Chervonenkis: On the uniform convergence of relative frequencies of events to their probabilities , 1971 .

[40]  Norbert Sauer,et al.  On the Density of Families of Sets , 1972, J. Comb. Theory, Ser. A.

[41]  S. Shelah A combinatorial problem; stability and order for models and theories in infinitary languages. , 1972 .

[42]  R. Aumann Subjectivity and Correlation in Randomized Strategies , 1974 .

[43]  Kumpati S. Narendra,et al.  Adaptation and learning in automatic systems , 1974 .

[44]  R. Serfling Probability Inequalities for the Sum in Sampling without Replacement , 1974 .

[45]  D. Freedman On Tail Probabilities for Martingales , 1975 .

[46]  X. Fernique Regularite des trajectoires des fonctions aleatoires gaussiennes , 1975 .

[47]  J. Neveu,et al.  Discrete Parameter Martingales , 1975 .

[48]  R. Rockafellar Monotone Operators and the Proximal Point Algorithm , 1976 .

[49]  S. Szarek On the best constants in the Khinchin inequality , 1976 .

[50]  Jorma Rissanen,et al.  Generalized Kraft Inequality and Arithmetic Coding , 1976, IBM J. Res. Dev..

[51]  Abraham Lempel,et al.  A universal algorithm for sequential data compression , 1977, IEEE Trans. Inf. Theory.

[52]  J. D. T. Oliveira,et al.  The Asymptotic Theory of Extreme Order Statistics , 1979 .

[53]  E. Slud Distribution Inequalities for the Binomial Law , 1977 .

[54]  丸山 徹 Convex Analysisの二,三の進展について , 1977 .

[55]  R. Dudley Central Limit Theorems for Empirical Measures , 1978 .

[56]  H. Robbins,et al.  Strong consistency of least squares estimates in multiple regression , 1978 .

[57]  Jacob Ziv,et al.  Coding theorems for individual sequences , 1978, IEEE Trans. Inf. Theory.

[58]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[59]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[60]  N. Megiddo On repeated games with incomplete information played by non-Bayesian players , 1980 .

[61]  Jacob Ziv,et al.  Distortion-rate theory for individual sequences , 1980, IEEE Trans. Inf. Theory.

[62]  Glen G. Langdon,et al.  Universal modeling and coding , 1981, IEEE Trans. Inf. Theory.

[63]  Raphail E. Krichevsky,et al.  The performance of universal encoding , 1981, IEEE Trans. Inf. Theory.

[64]  T. Lai,et al.  Least Squares Estimates in Stochastic Regression Models with Applications to Identification and Control of Dynamic Systems , 1982 .

[65]  A. Dawid The Well-Calibrated Bayesian , 1982 .

[66]  G. Pisier Some applications of the metric entropy condition to harmonic analysis , 1983 .

[67]  John Darzentas,et al.  Problem Complexity and Method Efficiency in Optimization , 1983 .

[68]  X. Fernique Regularite de fonctions aleatoires non Gaussiennes , 1983 .

[69]  Jorma Rissanen,et al.  Universal coding, information, prediction, and estimation , 1984, IEEE Trans. Inf. Theory.

[70]  H. Robbins,et al.  Asymptotically efficient adaptive allocation rules , 1985 .

[71]  H. Robbins Asymptotically Subminimax Solutions of Compound Statistical Decision Problems , 1985 .

[72]  David Oakes,et al.  Self-Calibrating Priors Do Not Exist , 1985 .

[73]  A. Dawid Calibration-Based Empirical Probability , 1985 .

[74]  Jorma Rissanen,et al.  Complexity of strings in the class of Markov sources , 1986, IEEE Trans. Inf. Theory.

[75]  J. Rissanen Stochastic Complexity and Modeling , 1986 .

[76]  Thomas M. Cover,et al.  Empirical Bayes stock market portfolios , 1986 .

[77]  R. Aumann Correlated Equilibrium as an Expression of Bayesian Rationality Author ( s ) , 1987 .

[78]  N. Littlestone Learning Quickly When Irrelevant Attributes Abound: A New Linear-Threshold Algorithm , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[79]  M. Talagrand Regularity of gaussian processes , 1987 .

[80]  T. Cover,et al.  Asymptotic optimality and asymptotic equipartition properties of log-optimum investment , 1988 .

[81]  Bernard Widrow,et al.  Adaptive switching circuits , 1988 .

[82]  Saburou Saitoh,et al.  Theory of Reproducing Kernels and Its Applications , 1988 .

[83]  Alfredo De Santis,et al.  Learning probabilistic prediction functions , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[84]  P. Odifreddi Classical recursion theory , 1989 .

[85]  Sergiu Hart,et al.  Existence of Correlated Equilibria , 1989, Math. Oper. Res..

[86]  Michael Biehl,et al.  The AdaTron: An Adaptive Perceptron Algorithm , 1989 .

[87]  Christian M. Ernst,et al.  Multi-armed Bandit Allocation Indices , 1989 .

[88]  David A. Cohn,et al.  Training Connectionist Networks with Queries and Selective Sampling , 1989, NIPS.

[89]  Andrew R. Barron,et al.  Information-theoretic asymptotics of Bayes methods , 1990, IEEE Trans. Inf. Theory.

[90]  Donald F. Specht,et al.  Probabilistic neural networks and the polynomial Adaline as complementary techniques for classification , 1990, IEEE Trans. Neural Networks.

[91]  J. Bather,et al.  Multi‐Armed Bandit Allocation Indices , 1990 .

[92]  Vladimir Vovk,et al.  Aggregating strategies , 1990, COLT '90.

[93]  F. Forges Correlated Equilibrium in Two-Person Zero-Sum Games , 1990 .

[94]  J. Jordan,et al.  Bayesian learning in normal form games , 1991 .

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

[96]  Meir Feder,et al.  Gambling using a finite state machine , 1991, IEEE Trans. Inf. Theory.

[97]  Dean Phillips Foster Prediction in the Worst Case , 1991 .

[98]  Nick Littlestone,et al.  Redundant noisy attributes, attribute errors, and linear-threshold learning using winnow , 1991, COLT '91.

[99]  M. Talagrand,et al.  Probability in Banach spaces , 1991 .

[100]  Bernhard E. Boser,et al.  A training algorithm for optimal margin classifiers , 1992, COLT '92.

[101]  P. Algoet UNIVERSAL SCHEMES FOR PREDICTION, GAMBLING AND PORTFOLIO SELECTION' , 1992 .

[102]  A. Barron,et al.  Jeffreys' prior is asymptotically least favorable under entropy risk , 1994 .

[103]  A. P. Dawid,et al.  Prequential data analysis , 1992 .

[104]  Neri Merhav,et al.  Universal prediction of individual sequences , 1992, IEEE Trans. Inf. Theory.

[105]  N. Vieille,et al.  Weak Approachability , 1992, Math. Oper. Res..

[106]  Paul Tseng,et al.  On the convergence of the exponential multiplier method for convex programming , 1993, Math. Program..

[107]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[108]  D. Fudenberg,et al.  Steady state learning and Nash equilibrium , 1993 .

[109]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 2019, Texts in Computer Science.

[110]  Neri Merhav,et al.  Universal schemes for sequential decision from individual data sequences , 1993, IEEE Trans. Inf. Theory.

[111]  E. Kalai,et al.  Rational Learning Leads to Nash Equilibrium , 1993 .

[112]  Paul H. Algoet,et al.  The strong law of large numbers for sequential decisions under uncertainty , 1994, IEEE Trans. Inf. Theory.

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

[114]  T. H. Chung Minimax learning in iterated games via distributional majorization , 1994 .

[115]  Thomas H. Chung,et al.  Approximate methods for sequential decision making using expert advice , 1994, COLT '94.

[116]  Neri Merhav,et al.  Optimal sequential probability assignment for individual sequences , 1994, IEEE Trans. Inf. Theory.

[117]  Manfred K. Warmuth,et al.  A comparison of new and old algorithms for a mixture estimation problem , 1995, COLT '95.

[118]  Luc Devroye,et al.  Lower bounds in pattern recognition and learning , 1995, Pattern Recognit..

[119]  Frans M. J. Willems,et al.  The context-tree weighting method: basic properties , 1995, IEEE Trans. Inf. Theory.

[120]  J. Jordan Bayesian Learning in Repeated Games , 1995 .

[121]  John Nachbar Prediction, optimization, and learning in repeated games , 1997 .

[122]  Robert E. Schapire,et al.  Predicting Nearly as Well as the Best Pruning of a Decision Tree , 1995, COLT.

[123]  Vladimir Vovk,et al.  A game of prediction with expert advice , 1995, COLT '95.

[124]  L. Shapley,et al.  Fictitious Play Property for Games with Identical Interests , 1996 .

[125]  Xiaohong Chen,et al.  Laws of Large Numbers for Hilbert Space-Valued Mixingales with Applications , 1996, Econometric Theory.

[126]  Erik Ordentlich,et al.  Universal portfolios with side information , 1996, IEEE Trans. Inf. Theory.

[127]  László Györfi,et al.  A Probabilistic Theory of Pattern Recognition , 1996, Stochastic Modelling and Applied Probability.

[128]  Philip M. Long,et al.  Worst-case quadratic loss bounds for prediction using linear functions and gradient descent , 1996, IEEE Trans. Neural Networks.

[129]  Amos Fiat,et al.  Making commitments in the face of uncertainty: how to pick a winner almost every time (extended abstract) , 1996, STOC '96.

[130]  T. Cover Universal Portfolios , 1996 .

[131]  Ehud Lehrer,et al.  Merging and learning , 1996 .

[132]  Dean P. Foster,et al.  Calibrated Learning and Correlated Equilibrium , 1997 .

[133]  Yoav Freund,et al.  Predicting a binary sequence almost as well as the optimal biased coin , 2003, COLT '96.

[134]  Yoram Singer,et al.  On‐Line Portfolio Selection Using Multiplicative Updates , 1998, ICML.

[135]  Jorma Rissanen,et al.  Fisher information and stochastic complexity , 1996, IEEE Trans. Inf. Theory.

[136]  Manfred K. Warmuth,et al.  How to use expert advice , 1997, JACM.

[137]  A. Blum,et al.  Universal portfolios with and without transaction costs , 1997, COLT '97.

[138]  Vladimir Vovk,et al.  Derandomizing Stochastic Prediction Strategies , 1997, COLT '97.

[139]  S. Hart,et al.  A simple adaptive procedure leading to correlated equilibrium , 2000 .

[140]  Yoram Singer,et al.  Using and combining predictors that specialize , 1997, STOC '97.

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

[142]  David P. Helmbold,et al.  Some label efficient learning results , 1997, COLT '97.

[143]  Yoav Freund,et al.  A decision-theoretic generalization of on-line learning and an application to boosting , 1997, EuroCOLT.

[144]  Philip M. Long On-line evaluation and prediction using linear functions , 1997, COLT '97.

[145]  J. Hannan ON BLACKWELL'S MINIMAX THEOREM AND THE COMPOUND DECISION METHOD , 1997 .

[146]  D. Haussler,et al.  MUTUAL INFORMATION, METRIC ENTROPY AND CUMULATIVE RELATIVE ENTROPY RISK , 1997 .

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

[148]  Tom Bylander,et al.  Worst-Case Absolute Loss Bounds for Linear Learning Algorithms , 1997, AAAI/IAAI.

[149]  G. Lugosi,et al.  Minimax lower bounds for the two-armed bandit problem , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[150]  Yoram Singer,et al.  Switching Portfolios , 1998, Int. J. Neural Syst..

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

[152]  David Haussler,et al.  Sequential Prediction of Individual Sequences Under General Loss Functions , 1998, IEEE Trans. Inf. Theory.

[153]  Kenji Yamanishi,et al.  A Decision-Theoretic Extension of Stochastic Complexity and Its Applications to Learning , 1998, IEEE Trans. Inf. Theory.

[154]  T. Cover,et al.  Universal portfolios with short sales and margin , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[155]  Claudio Gentile,et al.  Linear Hinge Loss and Average Margin , 1998, NIPS.

[156]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

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

[158]  Neri Merhav,et al.  Universal Prediction , 1998, IEEE Trans. Inf. Theory.

[159]  Erik Ordentlich,et al.  The Cost of Achieving the Best Portfolio in Hindsight , 1998, Math. Oper. Res..

[160]  W. Szpankowski ON ASYMPTOTICS OF CERTAIN RECURRENCES ARISING IN UNIVERSAL CODING , 1998 .

[161]  Jorma Rissanen,et al.  The Minimum Description Length Principle in Coding and Modeling , 1998, IEEE Trans. Inf. Theory.

[162]  Yoav Freund,et al.  Large Margin Classification Using the Perceptron Algorithm , 1998, COLT.

[163]  Manfred K. Warmuth,et al.  Efficient Learning With Virtual Threshold Gates , 1995, Inf. Comput..

[164]  G. Lugosi,et al.  On Prediction of Individual Sequences , 1998 .

[165]  Vladimir Vovk,et al.  Universal portfolio selection , 1998, COLT' 98.

[166]  Kenji Yamanishi,et al.  Minimax relative loss analysis for sequential prediction algorithms using parametric hypotheses , 1998, COLT' 98.

[167]  G. Lugosi,et al.  On Prediction of Individual Sequences , 1998 .

[168]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[169]  Y. Freund,et al.  Adaptive game playing using multiplicative weights , 1999 .

[170]  William W. Cohen,et al.  Context-sensitive learning methods for text categorization , 1999, TOIS.

[171]  Nicolò Cesa-Bianchi,et al.  Analysis of Two Gradient-Based Algorithms for On-Line Regression , 1999 .

[172]  Geoffrey J. Gordon,et al.  Approximate solutions to markov decision processes , 1999 .

[173]  D. Haussler,et al.  Worst Case Prediction over Sequences under Log Loss , 1999 .

[174]  A. Rustichini Minimizing Regret : The General Case , 1999 .

[175]  E. Kalai,et al.  Calibrated Forecasting and Merging , 1999 .

[176]  Manfred K. Warmuth,et al.  Averaging Expert Predictions , 1999, EuroCOLT.

[177]  D. Fudenberg,et al.  An Easier Way to Calibrate , 1999 .

[178]  Dean P. Foster,et al.  A Proof of Calibration Via Blackwell's Approachability Theorem , 1999 .

[179]  Jürgen Forster,et al.  On Relative Loss Bounds in Generalized Linear Regression , 1999, FCT.

[180]  S. Hart,et al.  A General Class of Adaptive Strategies , 1999 .

[181]  Dean P. Foster,et al.  Regret in the On-Line Decision Problem , 1999 .

[182]  Manfred K. Warmuth,et al.  Relative loss bounds for single neurons , 1999, IEEE Trans. Neural Networks.

[183]  Nello Cristianini,et al.  Query Learning with Large Margin Classifiers , 2000, ICML.

[184]  Daphne Koller,et al.  Support Vector Machine Active Learning with Application sto Text Classification , 2000, ICML.

[185]  Manfred K. Warmuth,et al.  The Minimax Strategy for Gaussian Density Estimation. pp , 2000, COLT.

[186]  Nello Cristianini,et al.  An introduction to Support Vector Machines , 2000 .

[187]  Thore Graepel,et al.  From Margin to Sparsity , 2000, NIPS.

[188]  Garud Iyengar,et al.  Growth optimal investment in horse race markets with costs , 2000, IEEE Trans. Inf. Theory.

[189]  Yishay Mansour,et al.  Nash Convergence of Gradient Dynamics in General-Sum Games , 2000, UAI.

[190]  Philip M. Long,et al.  Apple Tasting , 2000, Inf. Comput..

[191]  A. E. Hoerl,et al.  Ridge regression: biased estimation for nonorthogonal problems , 2000 .

[192]  E. Takimoto,et al.  The Minimax Strategy for Gaussian Density Estimation , 2000 .

[193]  Santosh S. Vempala,et al.  Efficient algorithms for universal portfolios , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[194]  Brendan J. Frey,et al.  Factor graphs and the sum-product algorithm , 2001, IEEE Trans. Inf. Theory.

[195]  Claudio Gentile,et al.  A New Approximate Maximal Margin Classification Algorithm , 2002, J. Mach. Learn. Res..

[196]  V. Vovk Competitive On‐line Statistics , 2001 .

[197]  Manfred K. Warmuth,et al.  Tracking a Small Set of Experts by Mixing Past Posteriors , 2003, J. Mach. Learn. Res..

[198]  Christos H. Papadimitriou,et al.  Algorithms, games, and the internet , 2001, STOC '01.

[199]  Mark Herbster,et al.  Tracking the Best Linear Predictor , 2001, J. Mach. Learn. Res..

[200]  S. Hart,et al.  A Reinforcement Procedure Leading to Correlated Equilibrium , 2001 .

[201]  Tsachy Weissman,et al.  Twofold universal prediction schemes for achieving the finite-state predictability of a noisy individual binary sequence , 2001, IEEE Trans. Inf. Theory.

[202]  Bernhard Schölkopf,et al.  Learning with kernels , 2001 .

[203]  R. Solomonoff A PRELIMINARY REPORT ON A GENERAL THEORY OF INDUCTIVE INFERENCE , 2001 .

[204]  Daphne Koller,et al.  Support Vector Machine Active Learning with Applications to Text Classification , 2002, J. Mach. Learn. Res..

[205]  Vladimir Vovk,et al.  Predicting nearly as well as the best pruning of a decision tree through dynamic programming scheme , 2001, Theor. Comput. Sci..

[206]  Bin Yu,et al.  Model Selection and the Principle of Minimum Description Length , 2001 .

[207]  Christian Schindelhauer,et al.  Discrete Prediction Games with Arbitrary Feedback and Loss , 2001, COLT/EuroCOLT.

[208]  E. Lehrer Any Inspection is Manipulable , 2001 .

[209]  Claudio Gentile,et al.  Adaptive and Self-Confident On-Line Learning Algorithms , 2000, J. Comput. Syst. Sci..

[210]  Peter Auer,et al.  Using Confidence Bounds for Exploitation-Exploration Trade-offs , 2003, J. Mach. Learn. Res..

[211]  Peter Auer,et al.  The Nonstochastic Multiarmed Bandit Problem , 2002, SIAM J. Comput..

[212]  Microeconomics-Charles W. Upton Repeated games , 2020, Game Theory.

[213]  Mehryar Mohri,et al.  Semiring Frameworks and Algorithms for Shortest-Distance Problems , 2002, J. Autom. Lang. Comb..

[214]  Neri Merhav,et al.  On sequential strategies for loss functions with memory , 2002, IEEE Trans. Inf. Theory.

[215]  William H. Sandholm,et al.  ON THE GLOBAL CONVERGENCE OF STOCHASTIC FICTITIOUS PLAY , 2002 .

[216]  W. Szpankowski,et al.  A Combinatorial Problem Arising in Information Theory: Precise Minimax Redundancy for Markov Sources , 2002 .

[217]  Andrew C. Singer,et al.  Universal linear least squares prediction: Upper and lower bounds , 2002, IEEE Trans. Inf. Theory.

[218]  Manfred K. Warmuth,et al.  Predicting nearly as well as the best pruning of a planar decision graph , 2002, Theor. Comput. Sci..

[219]  Gábor Lugosi,et al.  Pattern Classification and Learning Theory , 2002 .

[220]  S. Sorin A First Course on Zero Sum Repeated Games , 2002 .

[221]  Yishay Mansour,et al.  Efficient Nash Computation in Large Population Games with Bounded Influence , 2002, UAI.

[222]  Sidney J. Yakowitz,et al.  Iterative nonparametric estimation of a log-optimal portfolio selection function , 2002, IEEE Trans. Inf. Theory.

[223]  Alvaro Sandroni,et al.  Calibration with Many Checking Rules , 2003, Math. Oper. Res..

[224]  Nimrod Megiddo,et al.  How to Combine Expert (and Novice) Advice when Actions Impact the Environment? , 2003, NIPS.

[225]  Marc Teboulle,et al.  Mirror descent and nonlinear projected subgradient methods for convex optimization , 2003, Oper. Res. Lett..

[226]  Ehud Lehrer,et al.  Approachability in infinite dimensional spaces , 2003, Int. J. Game Theory.

[227]  Ehud Lehrer,et al.  A wide range no-regret theorem , 2003, Games Econ. Behav..

[228]  A. Barron,et al.  Efficient Universal Portfolios for Past‐Dependent Target Classes , 2003 .

[229]  Shie Mannor,et al.  On-Line Learning with Imperfect Monitoring , 2003, COLT.

[230]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[231]  S. Hart,et al.  Uncoupled Dynamics Do Not Lead to Nash Equilibrium , 2003 .

[232]  Allan Borodin,et al.  Can We Learn to Beat the Best Stock , 2003, NIPS.

[233]  John Langford,et al.  Correlated equilibria in graphical games , 2003, EC '03.

[234]  Y. Singer,et al.  Ultraconservative online algorithms for multiclass problems , 2003 .

[235]  H. Peyton Young,et al.  Learning, hypothesis testing, and Nash equilibrium , 2003, Games Econ. Behav..

[236]  Manfred K. Warmuth,et al.  Path kernels and multiplicative updates , 2003 .

[237]  H. Sebastian Seung,et al.  Selective Sampling Using the Query by Committee Algorithm , 1997, Machine Learning.

[238]  Peter Auer,et al.  Tracking the Best Disjunction , 1998, Machine Learning.

[239]  Vladimir Vovk,et al.  A Criterion for the Existence of Predictive Complexity for Binary Games , 2004, ALT.

[240]  Claudio Gentile,et al.  The Robustness of the p-Norm Algorithms , 2003, Machine Learning.

[241]  Yoram Singer,et al.  An Efficient Extension to Mixture Techniques for Prediction and Decision Trees , 1997, COLT '97.

[242]  Manfred K. Warmuth,et al.  Relative Loss Bounds for Multidimensional Regression Problems , 1997, Machine Learning.

[243]  Michael Drmota,et al.  Precise minimax redundancy and regret , 2004, IEEE Transactions on Information Theory.

[244]  Peter Auer,et al.  Finite-time Analysis of the Multiarmed Bandit Problem , 2002, Machine Learning.

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

[246]  Baruch Awerbuch,et al.  Adaptive routing with end-to-end feedback: distributed learning and geometric approaches , 2004, STOC '04.

[247]  G. Lugosi,et al.  Global Nash Convergence of Foster and Young's Regret Testing , 2004 .

[248]  Yi Li,et al.  The Relaxed Online Maximum Margin Algorithm , 1999, Machine Learning.

[249]  Claudio Gentile,et al.  Worst-Case Analysis of Selective Sampling for Linear-Threshold Algorithms , 2004, NIPS.

[250]  Philip M. Long,et al.  Structural Results About On-line Learning Models With and Without Queries , 1999, Machine Learning.

[251]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[252]  Manfred K. Warmuth,et al.  Relative Loss Bounds for On-Line Density Estimation with the Exponential Family of Distributions , 1999, Machine Learning.

[253]  Alvaro Sandroni,et al.  Belief-based equilibrium , 2004, Games Econ. Behav..

[254]  Ran El-Yaniv,et al.  How to Better Use Expert Advice , 2004, Machine Learning.

[255]  Sham M. Kakade,et al.  Online Bounds for Bayesian Algorithms , 2004, NIPS.

[256]  Nicolò Cesa-Bianchi,et al.  Worst-Case Bounds for the Logarithmic Loss of Predictors , 1999, Machine Learning.

[257]  Amotz Cahn,et al.  General procedures leading to correlated equilibria , 2004, Int. J. Game Theory.

[258]  Sham M. Kakade,et al.  Deterministic calibration and Nash equilibrium , 2004, J. Comput. Syst. Sci..

[259]  Drew Fudenberg,et al.  Learning to Play Bayesian Games , 2001, Games Econ. Behav..

[260]  Nicolò Cesa-Bianchi,et al.  Potential-Based Algorithms in On-Line Prediction and Game Theory , 2003, Machine Learning.

[261]  Tamás Linder,et al.  Efficient algorithms and minimax bounds for zero-delay lossy source coding , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[262]  H. Peyton Young,et al.  Strategic Learning and Its Limits , 2004 .

[263]  Peter Grünwald,et al.  A tutorial introduction to the minimum description length principle , 2004, ArXiv.

[264]  Avrim Blum,et al.  Online Geometric Optimization in the Bandit Setting Against an Adaptive Adversary , 2004, COLT.

[265]  Tamás Linder,et al.  A "follow the perturbed leader"-type algorithm for zero-delay quantization of individual sequences , 2004, Data Compression Conference, 2004. Proceedings. DCC 2004.

[266]  Chamy Allenberg-Neeman,et al.  Full Information Game with Gains and Losses , 2004, ALT.

[267]  Jason Weston,et al.  Fast Kernel Classifiers with Online and Active Learning , 2005, J. Mach. Learn. Res..

[268]  G. Iyengar UNIVERSAL INVESTMENT IN MARKETS WITH TRANSACTION COSTS , 2005 .

[269]  M. Talagrand The Generic Chaining , 2005 .

[270]  Y. Mansour,et al.  Improved Second-Order Bounds for Prediction with Expert Advice , 2005, COLT.

[271]  Philip M. Long,et al.  On-line learning of linear functions , 2005, computational complexity.

[272]  Gábor Lugosi,et al.  Minimizing regret with label efficient prediction , 2004, IEEE Transactions on Information Theory.

[273]  Akimichi Takemura,et al.  Defensive Forecasting , 2005, AISTATS.

[274]  S. Hart Adaptive Heuristics , 2005 .

[275]  Tamás Linder,et al.  Tracking the Best of Many Experts , 2005, COLT.

[276]  Gábor Lugosi,et al.  Internal Regret in On-Line Portfolio Selection , 2005, Machine Learning.

[277]  Claudio Gentile,et al.  A Second-Order Perceptron Algorithm , 2002, SIAM J. Comput..

[278]  Christos H. Papadimitriou,et al.  Computing correlated equilibria in multi-player games , 2005, STOC '05.

[279]  Marcus Hutter,et al.  Adaptive Online Prediction by Following the Perturbed Leader , 2005, J. Mach. Learn. Res..

[280]  Dean P. Foster,et al.  Regret Testing: A Simple Payo-Based Procedure for Learning Nash Equilibrium , 2005 .

[281]  G. Shafer,et al.  Good randomized sequential probability forecasting is always possible , 2005 .

[282]  Nicolò Cesa-Bianchi,et al.  Regret Minimization Under Partial Monitoring , 2006, 2006 IEEE Information Theory Workshop - ITW '06 Punta del Este.

[283]  G. Lugosi,et al.  NONPARAMETRIC KERNEL‐BASED SEQUENTIAL INVESTMENT STRATEGIES , 2006 .

[284]  Nimrod Megiddo,et al.  Combining expert advice in reactive environments , 2006, JACM.

[285]  Andreu Mas-Colell,et al.  Stochastic Uncoupled Dynamics and Nash Equilibrium , 2004, Games Econ. Behav..

[286]  J. Wissel,et al.  On the Best Constants in the Khintchine Inequality , 2007 .

[287]  Yishay Mansour,et al.  From External to Internal Regret , 2005, J. Mach. Learn. Res..

[288]  Gábor Lugosi,et al.  Learning correlated equilibria in games with compact sets of strategies , 2007, Games Econ. Behav..

[289]  E. Seneta Non-negative Matrices and Markov Chains , 2008 .

[290]  Online Prediction with Experts under a Log-scoring Rule - Online Expert Prediction , 2022 .