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Language agents have shown some ability to interact with an external environment, e.g., a virtual world such as ScienceWorld, to perform complex tasks, e.g., growing a plant, without the startup costs of reinforcement learning. While recent work, e.g., Reflexion, has demonstrated how such agents can also self-improve by adding a textual memory of ''hints'' learned from prior experience, such improvements have been limited both in size and scope. In contrast, our goal is a language agent that can robustly improve performance over time, including when both the task and environment are varied. Our approach is to have the agent learn a textual representation of how the world works (rather than just isolated hints), expressed as a memory of causal abstractions, to guide future decision-making. In experiments, we find CLIN is able to continually improve on repeated trials on the same task and environment, outperforming state-of-the-art reflective language agents like Reflexion by 23 points in ScienceWorld and 1.4 points in ALFWorld benchmarks. CLIN can also transfer its learning to new environments and tasks, enhancing performance by 21 points in ScienceWorld and 11 points in ALFWorld. This suggests that language agents with a textual causal memory can play a significant role in interactive environments, including being able to rapidly improve over time.