Feature Subset Optimization I: Search Space Modeling and Feasibility Checks

Case setup:
A classifier has n candidate features. Each feature can be included or excluded, so the exact subset-search space is 2^n.

Why modeling comes first:
- estimate combinatorial cost before training,
- identify when brute force is impossible,
- decide between exact, heuristic, or hybrid search.

Examples:
- n=12 -> 4096 subsets,
- n=25 -> 33,554,432 subsets.

Practical constraints to include in model:
- max training time,
- max number of selected features,
- fairness and interpretability constraints,
- minimum acceptable validation score.

Edge cases:
- objective computed on unstable split,
- data leakage during feature selection,
- compute budget underestimated by per-subset CV cost.