[Feature Proposal] Cost-Senstive Querying

[KrisNguyen135]

Hello, I was wondering if accounting for situations where the costs of querying different points are not uniform is something we'd like to have, sometimes more broadly referred to as cost-sensitive active learning.

There are two main strategies:

1. Value of information (Kapoor et al., 2007), which queries the point that minimizes the sum of querying cost and some risk measure like, say, expected future loss, or
2. Return of investment, which queries the point that maximizes the ratio between querying utility like info gain and querying cost.

Both are natural but (2) is preferred to (1) if querying costs are not in the same unit as querying utility/risk.

Overall, I imagine the interface for this can extend existing acquisition functions for uncertainty sampling (for querying utility) and expected error reduction (for measuring risk). If querying costs are unknown, we can take in a predictor to get a point estimation for them as well.

Interestingly, these two strategies can be easily extended to Bayesian optimization for acquistion functions that are derived from specific utility functions too. I think (2) is applicable for all three acquisition functions that have been implemented (EI, PoI, UCB).

I'd be happy to start working on an implementation and create a PR if there's interest in this.