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Bandit Algorithms for Prophet Inequality and Pandora's Box
The goal is to minimize the regret, which is the difference over $T$ rounds in the total value of the optimal algorithm that knows the distributions vs. the total value of our algorithm that learns the distributions from the partial feedback.
Online Learning with Vector Costs and Bandits with Knapsacks
We study \OLVCp in both stochastic and adversarial arrival settings, and give a general procedure to reduce the problem from $d$ dimensions to a single dimension.
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