Constrained BO to Solve Minimization Problem

[jan-99]

Hi,

My problem is similar to this #719 where I'm trying to maximize -f(x) in order to minimize f(x) (where f(x) > 0 for all x). I've tried setting the infeasible_cost argument of ConstrainedMCObjective as per #719 (comment).

I set up my optimization problem similar to this tutorial (Closed-loop batch, constrained BO in BoTorch with qEI and qNEI) and with the infeasible_cost arg, but I am getting -0.0 for my optimized objective values. I think it is due to the way the best_observed_value is determined:

best_observed_value = weighted_obj(train_x).max().item()

def weighted_obj(X):
    """Feasibility weighted objective; zero if not feasible."""
    feasible = (outcome_constraint_1(X) <= 0)     
    return objective_function(X) * feasible.type_as(X)

The infeasible points that are set to 0 end up being chosen as the best observed value instead. May I know how best_observed_value should be determined for such a minimization problem?

Also, would it be possible to perform constrained BO for a minimization function where the known minima is 0.0? Since the infeasible points are set to 0, it seems that the BO would think that the true minima is an infeasible point.

[Balandat]

The approach we use for feasibility-weighting essentially assumes that the function you're optimizing is positive, which doesn't seem to hold in your case (you're optimizing -f with f positive). Have you tried the strategy discussed here?