Hierarchies of Relaxations for Online Prediction Problems with Evolving Constraints
published: Aug. 20, 2015, recorded: July 2015, views: 1713
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We propose a framework for online prediction with a benchmark defined through an evolving constraint set. We analyze a method based on random playout. While computing the optimal decision in hindsight might be hard due to the combinatorial constraints, we provide polynomial-time prediction algorithms based on Lasserre semidefinite hierarchy. Since the predictions are improper, the algorithm only needs the value of an online relaxation and not the integral solution. We provide a generic regret bound based on the integrality gap of Lasserre hierarchy at level $r$, thus establishing a link between the time required for solving the semidefinite relaxation and the associated regret bound in terms of Rademacher complexity. Our results are applicable for problems involving prediction over evolving graphs with stochastic side information.
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