We propose DoE2Vec, a variational autoencoder (VAE)-based methodology to learn optimization landscape characteristics for downstream meta-learning tasks, e.g., automated selection of optimization algorithms. Principally, using large training data sets generated with a random function generator, DoE2Vec self-learns an informative latent representation for any design of experiments (DoE). Unlike the classical exploratory landscape analysis (ELA) method, our approach does not require any feature engineering and is easily applicable for high dimensional search spaces. For validation, we inspect the quality of latent reconstructions and analyze the latent representations using different experiments. The latent representations not only show promising potentials in identifying similar (cheap-to-evaluate) surrogate functions, but also can significantly boost performances when being used complementary to the classical ELA features in classification tasks.