We have a new preprint out looking at how to apply shrinkage estimation to estimating large sets of causal parameters: Asymptotically Efficient Data-adaptive Penalized Shrinkage Estimation with Application to Causal Inference. The main idea is to define a new causal parameter of interest that is the solution of an optimization problem that balances fidelity to the parameter of interest and a penalty term. This structure allows us to apply standard techniques to analyze the penalized parameter, while choosing the strength of the penalization in such a way that the variance of an estimator is lower in finite samples.