Multilevel Monte Carlo Allocation

Allocate costly multilevel samples by variance while distinguishing real lower bounds from executable counts. The Multilevel Monte Carlo (MLMC) method relies on a finite telescoping estimator to approximate the expected value of a computationally expensive quantity. By distributing samples across multiple levels with different costs and variances, we can significantly reduce the overall computational cost required to achieve a target accuracy compared to standard Monte Carlo simulation.

Interactive Experiment

You can interactively explore the allocation algorithm using the real controls:

1. Adjust the Levels native select to choose between variance and cost profiles (Fast variance, Slow variance, or Expensive fine).
2. Modify the Level count native select to use between 1 and 3 levels. Observe how dropping levels affects the optimal counts for the remaining levels.
3. Change the Cost budget native select to observe how a restricted budget forces smaller sample allocations or creates large gaps between the continuous approximation and best valid integer strategy.

Open the Interactive Module to modify the controls and see the optimal allocations update in real-time.