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

Maria-Florina Balcan · Mikhail Khodak · Dravyansh Sharma · Ameet Talwalkar

Keywords: [ Online Learning ] [ Meta Learning ] [ Machine Learning ] [ Robustness ] [ Optimization ]


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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