The field of "algorithms with predictions" studies how to use predictions/learning within traditional CS problem settings:
> We introduce algorithms that use predictions from machine learning applied to the input to circumvent worst-case analysis. We aim for algorithms that have near optimal performance when these predictions are good, but recover the prediction-less worst case behavior when the predictions have large errors.
An example is using learning to decide which variable to discretize next in a branch-and-bound integer linear programming solver. The algorithm might be extremely similar to the classic version, but the analysis is new.
> We introduce algorithms that use predictions from machine learning applied to the input to circumvent worst-case analysis. We aim for algorithms that have near optimal performance when these predictions are good, but recover the prediction-less worst case behavior when the predictions have large errors.
An example is using learning to decide which variable to discretize next in a branch-and-bound integer linear programming solver. The algorithm might be extremely similar to the classic version, but the analysis is new.
https://arxiv.org/abs/2006.09123
More broadly, I think there's a lot of work on applying more refined analysis to classic algorithms - online settings, smoothed analysis, etc.