Entropy balancing---how do we assess overlap? I am familiar with propensity score weighting. I set up the propensity score model, and then generally check for balance and overlap in propensity score to ensure that assumptions are met. However, I'm a little confused about how entropy balancing works.
As I understand it, entropy balancing directly optimizes the weights themselves and guarantees balance on the specified moments. That's easy enough to check. But, how do we diagnose limited overlap? (I may be missing something obvious here)

Entropy balancing enforces exact mean balance on all covariates included in the estimation of the weights and requires that the resulting weights are positive. If it is not possible to achieve mean balance with positive weights, entropy balancing will fail; the optimization will not be able to find a solution that balances the means.
When there is a lack of overlap in the covariates, it is impossible to exactly mean balance them. Personally, I don't believe lack of overlap is anything more than an extreme form of imbalance. If you have lack of overlap, then entropy balancing will fail. That is the diagnostic.
