Learning-to-learn non-convex piecewise-Lipschitz functions

Nina Balcan, Mikhail Khodak, Dravyansh Sharma, Ameet Talwalkar

Keywords: meta-learning, data-driven algorithm design, robustness, online learning, nonconvex optimization

TL;DR: Provable guarantees for learning to initialize dispersed piecewise-Lipschitz functions, with applications to algorithm configuration and robustness.

Abstract: We analyze the meta-learning of the initialization and step-size of learning algorithms for piecewise-Lipschitz functions, a non-convex setting with applications to both machine learning and algorithms. Starting from recent regret bounds for the exponential forecaster on losses with dispersed discontinuities, we generalize them to be initialization-dependent and then use this result to propose a practical meta-learning procedure that learns both the initialization and the step-size of the algorithm from multiple online learning tasks. Asymptotically, we guarantee that the average regret across tasks scales with a natural notion of task-similarity that measures the amount of overlap between near-optimal regions of different tasks. Finally, we instantiate the method and its guarantee in two important settings: robust meta-learning and multi-task data-driven algorithm design.

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