Title: Plan2Vec: Unsupervised Representation Learning by Latent Plans. Abstract: Creating a useful representation of the world takes more than just rote memorization of individual data samples. This is because fundamentally, we use our internal representation to plan, to solve problems, and to navigate the world. For a representation to be amenable to planning, it is critical for it to embody some notion of optimality. A representation learning objective that explicitly considers some form of planning should generate representations which are more computationally valuable than those that memorize samples. In this paper, we introduce \textbf{Plan2Vec}, an unsupervised representation learning objective inspired by value-based reinforcement learning methods. By abstracting away low-level control with a learned local metric, we show that it is possible to learn plannable representations that inform long-range structures, entirely passively from high-dimensional sequential datasets without supervision. A latent space is learned by playing an ``Imagined Planning Game" on the graph formed by the data points, using a local metric function trained contrastively from context. We show that the global metric on this learned embedding can be used to plan with O(1) complexity by linear interpolation. This exponential speed-up is critical for planning with a learned representation on any problem containing non-trivial global topology. We demonstrate the effectiveness of Plan2Vec on simulated toy tasks from both proprioceptive and image states, as well as two real-world image datasets, showing that Plan2Vec can effectively plan using learned representations. Additional results and videos can be found at \url{https://sites.google.com/view/plan2vec}.