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

TL;DR

This paper develops a meta-learning framework for non-convex piecewise-Lipschitz functions, enabling the learning of initializations and step-sizes across multiple tasks with guarantees based on task similarity.

Contribution

It generalizes regret bounds to be initialization-dependent and introduces a practical meta-learning method for non-convex functions with theoretical guarantees.

Findings

The method learns initialization and step-size from multiple tasks.

Regret scales with task similarity, measuring overlap of near-optimal regions.

Guarantees are provided for robust meta-learning and multi-task algorithm design.

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.