A popular approach for online decision-making in large MDPs is time-bounded tree search. The effectiveness of tree search, however, is largely influenced by the action branching factor, which limits the search depth given a time bound. An obvious way to reduce action branching is to consider only a subset of potentially good actions at each state as specified by a provided partial policy. In this work, we consider offline learning of such partial policies with the goal of speeding up search without significantly reducing decision-making quality. Our first contribution consists of reducing the learning problem to set learning. We give a reduction-style analysis of three such algorithms, each making different assumptions, which relates the set learning objectives to the sub-optimality of search using the learned partial policies. Our second contribution is to describe concrete implementations of the algorithms within the popular framework of Monte-Carlo tree search. Finally, the third contribution is to evaluate the learning algorithms on two challenging MDPs with large action branching factors. The results show that the learned partial policies can significantly improve the anytime performance of Monte-Carlo tree search.