# Dual gradient ascent vs Primal Interior Point methods

When solving problems, particularly constrained optimization in the field of reinforcement learning, I have noticed the use of dual gradient descent. An example of this is in model-based reinforcement learning, where we constrain the KL-divergence between 2 policies.

When would dual gradient descent be preferred over methods like interior-point methods? A example of paper for which the authors go with dual gradient descent, is here - Learning Contact-Rich Manipulation Skills with Guided Policy Search

However, for very large sized problems it eventually becomes impossible to store and factor the $$n$$ by $$n$$ matrices that arise in second-order methods. For example, if your problem has one million variables, then you'll end up having to deal with matrices of size one million rows by one million columns. The storage requirements for such a matrix and its factorization may be impractical, even though the matrix is typically sparse.
For very large scale problems, first-order methods, which require only $$O(n)$$ storage, are often preferable, even though the theoretical convergence rate may be slower. First-order methods have become the focus of much of the research in optimization in the last decade as researchers have focused on very large scale optimization problems, particularly those arising in machine learning on sets of "big data" and in the training of deep neural networks.