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Burst image restoration aims to reconstruct a high-quality image from burst images, which are typically captured using manually designed exposure settings. Although these exposure settings significantly influence the final restoration performance, the problem of finding optimal exposure settings has been overlooked. In this paper, we present Dynamic Exposure Burst Image Restoration (DEBIR), a novel burst image restoration pipeline that enhances restoration quality by dynamically predicting exposure times tailored to the shooting environment. In our pipeline, Burst Auto-Exposure Network (BAENet) estimates the optimal exposure time for each burst image based on a preview image, as well as motion magnitude and gain. Subsequently, a burst image restoration network reconstructs a high-quality image from burst images captured using these optimal exposure times. For training, we introduce a differentiable burst simulator and a three-stage training strategy. Our experiments demonstrate that our pipeline achieves state-of-the-art restoration quality. Furthermore, we validate the effectiveness of our approach on a real-world camera system, demonstrating its practicality.