Optimal randomized multilevel Monte Carlo for repeatedly nested expectations
Authors: Yasa Syed, Guanyang Wang
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We test our algorithm on three examples. Our comparison result is summarized in Figure 1. |
| Researcher Affiliation | Academia | 1Department of Statistics, Rutgers University, New Brunswick, United States. |
| Pseudocode | Yes | Algorithm 1 A recursive r MLMC algorithm for RNEs |
| Open Source Code | Yes | Our code is available at https://github. com/guanyangwang/r MLMC_RNE. |
| Open Datasets | No | The paper uses synthetic data generated from specified distributions and financial models (e.g., 'y(0) N(π/2, 1)', 'non-central t-distribution'), but does not utilize or provide access information for any publicly available datasets. |
| Dataset Splits | No | The paper does not provide details on specific train/validation/test dataset splits. Experiments are conducted on simulated processes or financial models rather than standard datasets with such splits. |
| Hardware Specification | No | The paper mentions running experiments on a '500-core cluster' but does not provide specific hardware details such as CPU/GPU models, memory, or exact cluster specifications. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers required to replicate the experiments. |
| Experiment Setup | Yes | For READ, since all assumptions in Theorem 2.2 are satisfied, therefore when r0 (1/2, 3/4) and r1 (1/2, 1 2 4/3), the READ estimator generated by Algorithm 1 is unbiased and of finite variance. Since the computational cost gets lower when each ri gets larger, we choose r0 = 0.74 and r1 = 0.6 (close to the upper-end of their respective ranges above) to facilitate the computational efficiency. We also adopt the standard parameters in (Jain & Oosterlee, 2012; Bender et al., 2006; Zhou et al., 2022): T = 3, M = 5, σ = 0.2, r = 0.05, K = y(0) i = 100 for every i. |