Efficient Meta Subspace Optimization

TL;DR

This paper introduces a Meta Subspace Optimization framework that dynamically determines subspaces during large-scale optimization, utilizing a low-dimensional meta optimizer and reinforcement learning to outperform existing methods.

Contribution

The paper proposes a novel MSO framework with a dynamic subspace selection mechanism and an RL-based policy learning approach, improving optimization efficiency.

Findings

Reinforcement learning policies outperform existing subspace methods.

The meta optimizer effectively adapts subspaces at each iteration.

The approach remains invariant to problem dimension.

Abstract

Subspace optimization methods have the attractive property of reducing large-scale optimization problems to a sequence of low-dimensional subspace optimization problems. However, existing subspace optimization frameworks adopt a fixed update policy of the subspace and therefore appear to be sub-optimal. In this paper, we propose a new \emph{Meta Subspace Optimization} (MSO) framework for large-scale optimization problems, which allows to determine the subspace matrix at each optimization iteration. In order to remain invariant to the optimization problem's dimension, we design an \emph{efficient} meta optimizer based on very low-dimensional subspace optimization coefficients, inducing a rule-based method that can significantly improve performance. Finally, we design and analyze a reinforcement learning (RL) procedure based on the subspace optimization dynamics whose learnt policies outperform existing subspace optimization methods.