CoachA surrogate model is a fast approximation of a slow function, here a pricer, fitted to its outputs on sampled inputs. Differential machine learning trains the surrogate on the derivatives of the labels with respect to the inputs as well as on the labels, the network’s own derivatives being computed by automatic differentiation (Book 4, chapter 28); with Monte Carlo labels the derivative labels are pathwise (Huge and Savine, 2020).
| price RMSE | delta RMSE | |||
| training samples | standard | differential | standard | differential |
| 256 | 0.927 | 0.679 | 0.066 | 0.057 |
| 1 024 | 0.436 | 0.218 | 0.059 | 0.021 |
| 4 096 | 0.297 | 0.279 | 0.042 | 0.020 |
ml_hedge.surrogates.