The vision of a broadly capable and goal-directed agent, such as an Internet-browsing agent in the digital world and a household humanoid in the physical world, has rapidly advanced, thanks to the generalization capability of foundation models. Such a generalist agent needs to have a large and diverse skill repertoire, such as finding directions between two travel locations and buying specific items from the Internet. If each skill needs to be specified manually through a fixed set of human-annotated instructions, the agent's skill repertoire will necessarily be limited due to the quantity and diversity of human-annotated instructions. In this work, we address this challenge by proposing Proposer-Agent-Evaluator, an effective learning system that enables foundation model agents to autonomously discover and practice skills in the wild. At the heart of PAE is a context-aware task proposer that autonomously proposes tasks for the agent to practice with context information of the environment such as user demos or even just the name of the website itself for Internet-browsing agents. Then, the agent policy attempts those tasks with thoughts and actual grounded operations in the real world with resulting trajectories evaluated by an autonomous VLM-based success evaluator. The success evaluation serves as the reward signal for the agent to refine its policies through RL. We validate PAE on challenging vision-based web navigation, using both real-world and self-hosted websites from WebVoyager and WebArena.To the best of our knowledge, this work represents the first effective learning system to apply autonomous task proposal with RL for agents that generalizes real-world human-annotated benchmarks with SOTA performances. Our open-source checkpoints and code can be found in https://yanqval.github.io/PAE/