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Research map / Learning theory and algorithms / Prediction and decision losses

Learning Predictions for Algorithms with Predictions

NeurIPS 2022 · Learning theory and algorithms › Prediction and decision losses · approach: Algorithms with explicit predictors

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Apply online learning to a convex upper bound on algorithm cost that depends on prediction qualityAlgorithms with predictions across matching, page migration, scheduling, and ski-rental · Adversarial online instancesregret: Table 1 gives regret bounds of \mathcal O\left(n\sqrt T\right), \mathcal O\left(\sqrt{mT\log(mT)}\right), and problem-spHelped
Use online-to-batch conversion of the online learning procedureMinimum-weight bipartite matching · I.i.d. cost instancessample complexity: a \tilde{\mathcal O}(n) lower sample complexityHelped
Relax discrete request predictions to probability vectors and optimize the convex maximum-over-expectations boundOnline page migration · Request sequencescompetitive ratio: \mathcal O\left(\frac{\log n}{\gamma D}\right) additive error over [cite] in the case of a perfect predictorHelped
Learn a linear map from instance features to predictionsAlgorithms with predictions · Feature-dependent instanceslearning guaranteesHelped
Use KT-OCO without a bounded predictor domainOnline job scheduling · Adversarial machine-weight and feature pairsregret: \|\*A\|_F\sqrt{T\log(1+24T^2\|\*A\|_F^2)}+1Helped
Tune the robustness-consistency parameter with an exponential forecasterPreferential round-robin job scheduling · Online job scheduling with predictionsregret: 9B\left(1+\sqrt{\frac T2\log T}\right)Helped
Jointly learn the buy threshold and trade-off parameterDiscrete ski-rental · Ski-rental with integer daysregret: 6N\sqrt{T\log(BNT)}Helped
Use a dispersion assumption to learn discontinuous threshold lossesContinuous ski-rental · β-dispersed ski-daysregret: \tilde{\mathcal O}\left(\sqrt{T\log(NT)}+(N+B)^2T^{1-\beta}\right)Helped
Replace the log-concave data assumption with β-dispersionContinuous ski-rental · I.i.d. ski-daysassumption strengthHelped
Replace the maximum in the prediction-error objective with a simple sumOnline page migration · Request sequencesworst-case bound: \mathcal O\left(\frac n{\gamma D}\right)Hurt

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