Hybrid Stochastic-Adversarial On-line Learning PDF
Preview Hybrid Stochastic-Adversarial On-line Learning
Onlineclassificationproblem HybridStochastic-Adversarialsetting Extensions Discussionandconclusion Hybrid Stochastic-Adversarial On-line Learning Alessandro LAZARIC andRémiMunos INRIA,SequeL(SequentialLearning)project, France ECML’09Workshop on Learningfrom non-IID data, September7,2009,Bled AlessandroLazaricandRémiMunos HybridStochastic-AdversarialOn-lineLearning Onlineclassificationproblem HybridStochastic-Adversarialsetting Extensions Discussionandconclusion Motivating example A (not-so-serious) real-life predictionproblem: AlessandroLazaricandRémiMunos HybridStochastic-AdversarialOn-lineLearning Onlineclassificationproblem HybridStochastic-Adversarialsetting Extensions Discussionandconclusion Motivating example A (not-so-serious) real-life predictionproblem: Predict: Yes,No for dinner { } tonight AlessandroLazaricandRémiMunos HybridStochastic-AdversarialOn-lineLearning Onlineclassificationproblem HybridStochastic-Adversarialsetting Extensions Discussionandconclusion Motivating example A (not-so-serious) real-life predictionproblem: Predict: Yes,No for dinner { } tonight Inputs(girls) are drawnfrom a fixed probabilitydistribution Therelationshipbetween inputsandoutputsis complex Hybrid stochastic (inputs) adversarial(outputs)problem AlessandroLazaricandRémiMunos HybridStochastic-AdversarialOn-lineLearning Onlineclassificationproblem HybridStochastic-Adversarialsetting Extensions Discussionandconclusion Motivating example A (little-bit-more-serious) real-life prediction problem: Predict: Buy,NotBuy the new { } modelofmobilephone AlessandroLazaricandRémiMunos HybridStochastic-AdversarialOn-lineLearning Onlineclassificationproblem HybridStochastic-Adversarialsetting Extensions Discussionandconclusion Motivating example A (little-bit-more-serious) real-life prediction problem: Predict: Buy,NotBuy the new { } modelofmobilephone Inputs(potentialusers) are drawnfrom a fixed probability distribution Therelationshipbetween inputsandoutputsis complex Hybrid stochastic (inputs) adversarial(outputs)problem AlessandroLazaricandRémiMunos HybridStochastic-AdversarialOn-lineLearning Onlineclassificationproblem HybridStochastic-Adversarialsetting Extensions Discussionandconclusion Outline 1 Onlineclassification problem 2 Hybrid Stochastic-Adversarial setting Finitehypothesis space Infinite hypothesisspace: the EStochAdForecaster 3 Extensions BanditInformation Applicationto Games 4 Discussion andconclusion Comparison AlessandroLazaricandRémiMunos HybridStochastic-AdversarialOn-lineLearning Onlineclassificationproblem HybridStochastic-Adversarialsetting Extensions Discussionandconclusion Online classification problem Inputspace , Outputspace = 0,1 , X Y { } Hypothesisspace = h : H { X → Y} for t = 1,2,..., Thelearnerobservesx , t ∈ X Thelearnerchoosesh andpredicts y = h (x ) , t t t t ∈H ∈ Y y is revealed, t ∈ Y Thelearnerincurs a loss ℓ(y ,y )= I y =by t t t t 6 (cid:8) (cid:9) Goal: minimize thecumulative regret: b b n n R = ℓ(y ,y ) inf ℓ(h(x ),y ) n t t t t −h∈H t=1 t=1 X X b AlessandroLazaricandRémiMunos HybridStochastic-AdversarialOn-lineLearning Onlineclassificationproblem HybridStochastic-Adversarialsetting Extensions Discussionandconclusion Known results in different settings iid Fullystochasticsetting: (x ,y ) P, t t ∼ R = O( VC( )nlogn) n H (byusinganEmpiricalRiskpMinimizeron-line) AlessandroLazaricandRémiMunos HybridStochastic-AdversarialOn-lineLearning Onlineclassificationproblem HybridStochastic-Adversarialsetting Extensions Discussionandconclusion Known results in different settings iid Fullystochasticsetting: (x ,y ) P, t t ∼ R = O( VC( )nlogn) n H (byusinganEmpiricalRiskpMinimizeron-line) Fullyadversarialsetting: (x ,y ) chosenby adversary, t t R =O( Ldim( )nlogn) n H (AgnosticOnlineLearning[pBen-David,PálandShalev-Shwartz, 2009]) AlessandroLazaricandRémiMunos HybridStochastic-AdversarialOn-lineLearning
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