Meta Subspace Optimization

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 efficient meta optimizer based on very low-dimensional subspace optimization coefficients, inducing a rule-based agent that can significantly improve performance. Finally, we design and analyze a reinforcement learning procedure based on the subspace optimization dynamics whose learnt policies outperform existing subspace optimization methods.