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Many practical applications, such as recommender systems and learning torank, involve solving multiple similar tasks. One example is learning ofrecommendation policies for users with similar movie preferences, where theusers may still rank the individual movies slightly differently. Such tasks canbe organized in a hierarchy, where similar tasks are related through a sharedstructure. In this work, we formulate this problem as a contextual off-policyoptimization in a hierarchical graphical model from logged bandit feedback. Tosolve the problem, we propose a hierarchical off-policy optimization algorithm(HierOPO), which estimates the parameters of the hierarchical model and thenacts pessimistically with respect to them. We instantiate HierOPO in linearGaussian models, for which we also provide an efficient implementation andanalysis. We prove per-task bounds on the suboptimality of the learnedpolicies, which show a clear improvement over not using the hierarchical model.We also evaluate the policies empirically. Our theoretical and empiricalresults show a clear advantage of using the hierarchy over solving each taskindependently.

Multi-Task Off-Policy Learning from Bandit Feedback