We proposed Relative Sparsity in 2023, and I wrote this post, focusing on the idea of a new policy that has a sparse difference from the standard of care. I wanted to emphasize another use of Relative Sparsity, in which I have become increasingly interested.

Relative Sparsity can be viewed as a window into the development of a treatment policy. In particular, relative sparsity shows (in a succinct way) how individual weights placed on covariates might change when we attempt to move toward maximizing expected reward by incorporating observational data and the associated assumptions. It’s possible that sometimes a succinct description is not possible, which is challenging. However, either way, this insight, to me, is a helpful deliverable.

Here is a video of a presentation based on my presentation at the Medical Scientist Research Symposium in April of 2025 (it is longer than the original presentation). It is pretty close to my thesis slides, but I try to emphasize the “window” perspective.

In general, I think Policy search is an interesting approach (for example, see e.g., Thomas or Wager). I summarize it more formally here. Observational data is plentiful, and these methods could therefore be quite useful.

It is in our best interest to have techniques, like Relative Sparsity, that can show us the changes policy search might suggest, and therefore serve as another layer of assessment.