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Supermartingales in prediction with expert advice

Alexey Chernov, Yuri Kalnishkan, Fedor Zhdanov, Vladimir Vovk
2010 Theoretical Computer Science  
The paper applies the method of defensive forecasting, based on the use of game-theoretic supermartingales, to prediction with expert advice.  ...  The paper also discusses a new setting where the experts can give advice conditional on the learner's future decision.  ...  Discussions with Alex Gammerman, Glenn Shafer, and Alexander Shen, and detailed comments of the anonymous referees for the conference version [4] and the journal version have helped us improve the paper  ... 
doi:10.1016/j.tcs.2010.04.003 fatcat:kk7nzm67vvgqpik2hwi4auwmwi

Supermartingales in Prediction with Expert Advice [article]

Alexey Chernov, Yuri Kalnishkan, Fedor Zhdanov, Vladimir Vovk
2010 arXiv   pre-print
We apply the method of defensive forecasting, based on the use of game-theoretic supermartingales, to prediction with expert advice.  ...  We discuss also a new setting where the experts can give advice conditional on the learner's future decision.  ...  Discussions with Alex Gammerman, Glenn Shafer, and Alexander Shen, and detailed comments of the anonymous referees for the conference version [4] and for a journal submission have helped us improve the  ... 
arXiv:1003.2218v1 fatcat:nwknxlnwlbbbtbfiytmjtayi2y

Supermartingales in Prediction with Expert Advice [chapter]

Alexey Chernov, Yuri Kalnishkan, Fedor Zhdanov, Vladimir Vovk
2008 Lecture Notes in Computer Science  
The paper applies the method of defensive forecasting, based on the use of game-theoretic supermartingales, to prediction with expert advice.  ...  The paper also discusses a new setting where the experts can give advice conditional on the learner's future decision.  ...  Discussions with Alex Gammerman, Glenn Shafer, and Alexander Shen, and detailed comments of the anonymous referees for the conference version [4] and the journal version have helped us improve the paper  ... 
doi:10.1007/978-3-540-87987-9_19 fatcat:yz7n6rlkfncj7irebtlt3pu3g4

Defensive forecasting for optimal prediction with expert advice [article]

Vladimir Vovk
2007 arXiv   pre-print
The method of defensive forecasting is applied to the problem of prediction with expert advice for binary outcomes.  ...  It turns out that defensive forecasting is not only competitive with the Aggregating Algorithm but also handles the case of "second-guessing" experts, whose advice depends on the learner's prediction;  ...  The protocol of prediction with expert advice becomes: Prediction with expert advice under log loss L 0 := 0. λ (ω n , p n ) − λ (ω n , γ n (p n )) is a supermartingale in the binary forecasting protocol  ... 
arXiv:0708.1503v1 fatcat:isxogd56tbgxlcur236vcit7pq

Prediction with expert evaluators' advice [article]

Alexey Chernov, Vladimir Vovk
2009 arXiv   pre-print
We introduce a new protocol for prediction with expert advice in which each expert evaluates the learner's and his own performance using a loss function that may change over time and may be different from  ...  Aggregating Algorithm in the standard setting and known to be optimal.  ...  Acknowledgements We are grateful to the anonymous Eurocrat who coined the term "expert evaluator". This work was supported in part by EPSRC grant EP/F002998/1.  ... 
arXiv:0902.4127v2 fatcat:3ee25xru5bayfcaqbwmoxfy42e

Prediction with Advice of Unknown Number of Experts [article]

Alexey Chernov, Vladimir Vovk
2014 arXiv   pre-print
In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts.  ...  In contrast to the Normal- Hedge bound, which mainly depends on the effective number of experts but also weakly depends on the nominal one, we obtain a bound that does not contain the nominal number of  ...  In Section 2 we describe the setup of prediction with expert advice and of decision-theoretic online learning, and define thequantile regret.  ... 
arXiv:1408.2040v1 fatcat:yno2b3np35cq3bwg66ut4ggwc4

Prediction with Advice of Unknown Number of Experts [article]

Alexey Chernov, Vladimir Vovk
2010 arXiv   pre-print
In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts.  ...  In contrast to the NormalHedge bound, which mainly depends on the effective number of experts and also weakly depends on the nominal one, we obtain a bound that does not contain the nominal number of experts  ...  Introduction We consider the problem of prediction with expert advice (PEA) and its variant, decision-theoretic online learning (DTOL).  ... 
arXiv:1006.0475v1 fatcat:wfip7fvlnjas7kt5td6ulochku

A Cardinal Comparison of Experts [article]

Itay Kavaler, Rann Smorodinsky
2020 arXiv   pre-print
Furthermore, using results on the rate of convergence of supermartingales, we show that whenever the two experts' advice are sufficiently distinct, the proposed test will detect the informed expert in  ...  In various situations, decision makers face experts that may provide conflicting advice. This advice may be in the form of probabilistic forecasts over critical future events.  ...  uninformed expert made excellent predictions along the play path.  ... 
arXiv:1908.10649v3 fatcat:2u34d42vxrh6dpb2owsxsqmqqu

Probability theory for the Brier game

V. Vovk
2001 Theoretical Computer Science  
The usual theory of prediction with expert advice does not di erentiate between good and bad "experts": its typical results only assert that it is possible to e ciently merge not too extensive pools of  ...  On the other hand, it is natural to expect that good experts' predictions will in some way agree with the actual outcomes (e.g., they will be accurate on the average).  ...  This problem can be solved, however, using the techniques of the theory of prediction with expert advice: it turns out that there exists a simple strategy for transforming the expert's predictions t which  ... 
doi:10.1016/s0304-3975(00)00133-x fatcat:4gm7esgkx5gl3kfjvnocxuxppu

Guest editors' foreword

László Györfi, György Turán, Thomas Zeugmann
2010 Theoretical Computer Science  
The authors present an algorithm for prediction with expert advice under the assumption that the best expert has loss k or less.  ...  Finally, it turns out that continuous experts are only as powerful as experts making binary or no prediction in each round.  ... 
doi:10.1016/j.tcs.2010.04.001 fatcat:wkuyng23gnedbatmqa7mnoeipi

Prediction with Expert Advice under Discounted Loss [article]

Alexey Chernov, Fedor Zhdanov
2010 arXiv   pre-print
We study prediction with expert advice in the setting where the losses are accumulated with some discounting---the impact of old losses may gradually vanish.  ...  Introduction Prediction with expert advice is a framework for online sequence prediction. Predictions are made step by step.  ...  In the standard framework for prediction with expert advice (see the monograph [2] for a comprehensive review), the losses from all steps are just summed.  ... 
arXiv:1005.1918v2 fatcat:osmt6d7y7zaohaupinkpxrium4

Variable Metric Stochastic Approximation Theory [article]

Peter Sunehag, Jochen Trumpf, S.V.N. Vishwanathan, Nicol Schraudolph
2009 arXiv   pre-print
We also discuss the implications of our results for learning from expert advice.  ...  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  ...  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

Minimizing Regret With Label Efficient Prediction

N. Cesa-Bianchi, G. Lugosi, G. Stoltz
2005 IEEE Transactions on Information Theory  
Index Terms-Individual sequences, label efficient prediction, on-line learning, prediction with expert advice.  ...  We investigate label efficient prediction, a variant, proposed by Helmbold and Panizza, of the problem of prediction with expert advice.  ...  INTRODUCTION P REDICTION with expert advice, a framework introduced about 15 years ago in learning theory, may be viewed as a direct generalization of the theory of repeated games, a field pioneered by  ... 
doi:10.1109/tit.2005.847729 fatcat:kddearc6vvajrexfesbwjoytey

Minimizing Regret with Label Efficient Prediction [chapter]

Nicolò Cesa-Bianchi, Gábor Lugosi, Gilles Stoltz
2004 Lecture Notes in Computer Science  
Index Terms-Individual sequences, label efficient prediction, on-line learning, prediction with expert advice.  ...  We investigate label efficient prediction, a variant, proposed by Helmbold and Panizza, of the problem of prediction with expert advice.  ...  INTRODUCTION P REDICTION with expert advice, a framework introduced about 15 years ago in learning theory, may be viewed as a direct generalization of the theory of repeated games, a field pioneered by  ... 
doi:10.1007/978-3-540-27819-1_6 fatcat:5flerzuro5ajpjnprvpvz3xrey

The Principal-Agent Approach to Testing Experts

Wojciech Olszewski, Marcin Pęski
2011 American Economic Journal: Microeconomics  
she would obtain in the absence of any expert.  ...  Despite this negative result, we show that often exist contracts that allow a decision maker to attain the first-best payoff in the following sense: in the case in which the expert knows the stochastic  ...  The first part of (6.3) guarantees that the advice of this type of expert is valuable, if this advice is elicited in periods 1, ..., t, and then in periods t+1, t+2, ..., contingent on s t = s t (s t )  ... 
doi:10.1257/mic.3.2.89 fatcat:6ooxvl2yyzeujc6tfct4xd5wgq
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