Papers › Gradient Methods with Online Scaling
Gradient Methods with Online Scaling
Wenzhi Gao, Ya-Chi Chu, Yinyu Ye, Madeleine Udell
We introduce a framework to accelerate the convergence of gradient-based methods with online learning. The framework learns to scale the gradient at each iteration through an online learning algorithm and provably accelerates gradient-based methods asymptotically. In contrast with previous literature, where convergence is established based on worst-case analysis, our framework provides a strong convergence guarantee with respect to the optimal scaling matrix for the iteration trajectory. For smooth strongly convex optimization, our results provide an O(κ^⋆ log(1/ε)) complexity result, where κ^⋆ is the condition number achievable by the optimal preconditioner, improving on the previous O(√(n)κ^⋆ log(1/ε)) result. In particular, a variant of our method achieves superlinear convergence on convex quadratics. For smooth convex optimization, we show for the first time that the widely-used hypergradient descent heuristic improves on the convergence of gradient descent.
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