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Large language models (LLMs) deployed as agents solve user-specified tasks over multiple steps while keeping the required manual engagement to a minimum. Crucially, such LLMs need to ground their generations in any feedback obtained to reliably achieve the desired outcomes. We propose an end-to-end reinforcement learning method for teaching models to leverage execution feedback in the realm of code synthesis, where state-of-the-art LLMs struggle to improve code iteratively compared to independent sampling. We benchmark on competitive programming tasks and achieve large performance gains with both small (8B parameters) and large (70B) models, outperforming previous work while reducing the number of samples required by an order of magnitude. Our analysis of inference-time behavior demonstrates that our method produces LLMs that effectively leverage automatic feedback over multiple steps.