Nearly Optimal Catoni’s M-estimator for Infinite Variance
Authors: Sujay Bhatt, Guanhua Fang, Ping Li, Gennady Samorodnitsky
ICML 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We empirically validate the performance improvement in using our proposed algorithm based on Catoni’s estimator for ε ∈ (0, 1] by comparing it with the state of the art best arm identification algorithms proposed in Yu et al. (2018). (...) A significant improvement in performance using our algorithms is observed in Figure 1, more so in case of smaller ε, indicating the tightness for smaller ε. Table 1 shows the performance of Algorithm 3 for K from 10 to 1000. |
| Researcher Affiliation | Collaboration | Sujay Bhatt, Guanhua Fang, Ping Li Gennady Samorodnitsky Cognitive Computing Lab School of ORIE Baidu Research Cornell University 10900 NE 8th St. Bellevue, WA 98004, USA 220 Frank T Rhodes Hall, Ithaca, NY 14853, USA {sujaybhatt.hr, fanggh2018, pingli98}@gmail.com gs18@cornell.edu |
| Pseudocode | Yes | Algorithm 1 Lepskii Moment Adaptation (LMA) (...) Algorithm 2 Iterative Elimination with Catoni (...) Algorithm 3 Phase-based Iterative Elimination with Catoni (...) Algorithm 4 Adaptive Elimination with Catoni (...) Algorithm 5 Restricted Differential Privacy for Heavy-tailed Data |
| Open Source Code | No | The paper does not contain an explicit statement or link indicating that the source code for the described methodology is publicly available. |
| Open Datasets | No | The experimental setup is as follows: the rewards for all arms in all experiments are generated from the heavy tailed Student’s-t distribution. The shifted mean of each arm is given using the following rule: µ(i) = 2 − (i − 1/K)0.6 for i = 2, ..., K and µ(1) = 2. The number of degrees of freedom for the first two figures from the left is ν = 3 which corresponds to ε = 1 and υε = 3. The third figure uses ν = 2 which has infinite variance and for ε = 0.85, an upper bound is υε = 50. |
| Dataset Splits | No | The paper describes experiments in a multi-armed bandit setting with sequentially generated data, rather than using predefined training/validation/test splits from a fixed dataset. |
| Hardware Specification | No | The paper does not explicitly describe the specific hardware (e.g., CPU, GPU models, memory) used to run the experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers (e.g., Python 3.8, PyTorch 1.9) required to replicate the experiments. |
| Experiment Setup | Yes | The experimental setup is as follows: the rewards for all arms in all experiments are generated from the heavy tailed Student’s-t distribution. The shifted mean of each arm is given using the following rule: µ(i) = 2 − (i − 1/K)0.6 for i = 2, ..., K and µ(1) = 2. The number of degrees of freedom for the first two figures from the left is ν = 3 which corresponds to ε = 1 and υε = 3. The third figure uses ν = 2 which has infinite variance and for ε = 0.85, an upper bound is υε = 50. Smaller values for τ and larger values for h will have sharper bounds, and can be chosen depending on the tolerance to the cost of initial exploration. One choice parameters used is τ = 0.05 and h = 0.7. Further, γ(> 1) in Algorithm 3 is set to 1.1; this can be tuned further to improve performance. |