Large language models (LLMs) have emerged as powerful and general solutions to many natural language tasks. However, many of the most important applications of language generation are interactive, where an agent has to talk to a person to reach a desired outcome.For example, a teacher might try to understand their student's current comprehension level to tailor their instruction accordingly, and a travel agent might ask questions of their customer to understand their preferences in order to recommend activities they might enjoy.LLMs trained with supervised fine-tuning or ``single-step'' RL, as with standard RLHF, might struggle which tasks that require such goal-directed behavior, since they are not trained to optimize for overall conversational outcomes after multiple turns of interaction. In this work, we explore a new method for adapting LLMs with RL for such goal-directed dialogue. Our key insight is that, though LLMs might not effectively solve goal-directed dialogue tasks out of the box, they can provide useful data for solving such tasks by simulating suboptimal but human-like behaviors. Given a textual description of a goal-directed dialogue task, we leverage LLMs to sample diverse synthetic rollouts of hypothetical in-domain human-human interactions. Our algorithm then utilizes this dataset with \emph{offline reinforcement learning} to train an interactive conversational agent that can optimize goal-directed objectives over multiple turns. In effect, the LLM produces examples of possible interactions, and RL then processes these examples to learn to perform more optimal interactions. Empirically, we show that our proposed approach achieves state-of-the-art performance in various goal-directed dialogue tasks that include teaching and preference elicitation.