Bayesian Optimisation vs. Input Uncertainty Reduction

Simulators often require calibration inputs estimated from real-world data, and the estimate can significantly affect simulation output. Particularly when performing optimisation to find an optimal solution, uncertainty in affects quality of found solution. One remedy is search for solution that has best performance on average over uncertain range yielding compromise We consider more general setting where a user may choose between either running simulations or querying external data source, improving input enabling targeted, less compromised explicitly examine trade-off real collection simulator with true inputs. Using value information procedure, we propose novel unified procedure called Bayesian Information Collection Optimisation that, each iteration, automatically determines which two actions (running collection) beneficial. theoretically prove convergence infinite budget limit perform numerical experiments demonstrating proposed algorithm able determine appropriate balance collection.