Adaptive gradient methods are the most popular method for optimization in machine learning, but existing bounds didn't take (possible) changing environments into consideration. We study the problem of learning a local preconditioner, that can change as the data is changing along the optimization trajectory. We propose an adaptive gradient method that has provable adaptive regret guarantees vs. the best local preconditioner. To derive this guarantee, we prove a new adaptive regret bound in online learning that improves upon previous adaptive online learning methods. We demonstrate the robustness of our method in automatically choosing the optimal learning rate schedule for popular benchmarking tasks in vision and language domains. Without the need to manually tune a learning rate schedule, our method can, in a single run, achieve comparable and stable task accuracy as a fine-tuned optimizer.

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