Learning to Accelerate by the Methods of Step-size Planning
release_bzqaueek45cwzi6fhij7cj2yp4
by
Hengshuai Yao
2022
Abstract
Gradient descent is slow to converge for ill-conditioned problems and
non-convex problems. An important technique for acceleration is step-size
adaptation. The first part of this paper contains a detailed review of
step-size adaptation methods, including Polyak step-size, L4, LossGrad, Adam,
IDBD, and Hypergradient descent, and the relation of step-size adaptation to
meta-gradient methods. In the second part of this paper, we propose a new class
of methods of accelerating gradient descent that have some distinctiveness from
existing techniques. The new methods, which we call step-size planning,
use the update experience to learn an improved way of updating the
parameters. The methods organize the experience into K steps away from each
other to facilitate planning. From the past experience, our planning algorithm,
Csawg, learns a step-size model which is a form of multi-step machine that
predicts future updates. We extends Csawg to applying step-size planning
multiple steps, which leads to further speedup. We discuss and highlight the
projection power of the diagonal-matrix step-size for future large scale
applications. We show for a convex problem, our methods can surpass the
convergence rate of Nesterov's accelerated gradient, 1 - √(μ/L), where
μ, L are the strongly convex factor of the loss function F and the
Lipschitz constant of F', which is the theoretical limit for the convergence
rate of first-order methods. On the well-known non-convex Rosenbrock function,
our planning methods achieve zero error below 500 gradient evaluations, while
gradient descent takes about 10000 gradient evaluations to reach a 10^-3
accuracy. We discuss the connection of step-size planing to planning in
reinforcement learning, in particular, Dyna architectures.
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