We study the placement of virtual functions aimed at minimizing the cost. We propose a novel algorithm, using ideas based on multi-armed bandits. We prove that these algorithms learn the optimal placement policy rapidly, and their regret grows at a rate at most $O( N M \sqrt{T\ln T} )$ while respecting the feasibility constraints with high probability, where $T$ is total time slots, $M$ is the number of classes of function and $N$ is the number of computation nodes. We show through numerical experiments that the proposed algorithm both has good practical performance and modest computational complexity. We propose an acceleration technique that allows the algorithm to achieve good performance also in large networks where computational power is limited. Our experiments are fully reproducible, and the code is publicly available.