  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.
