Research on graph representation learning has received great attention in recent years. However, most of the studies so far have focused on the embedding of single-layer graphs. The few studies dealing with the problem of representation learning of multilayer structures rely on the strong hypothesis that the inter-layer links are known, and this limits the range of possible applications. Here we propose MultiSAGE, a generalization of the GraphSAGE algorithm that allows to embed multiplex networks. We show that MultiSAGE is capable to reconstruct both the intra-layer and the inter-layer connectivity, outperforming GraphSAGE, which has been designed for simple graphs. Next, through a comprehensive experimental analysis, we shed light also on the performance of the embedding, both in simple and in multiplex networks, showing that either the density of the graph or the randomness of the links strongly influences the quality of the embedding.