Weaker MVI Condition: Extragradient Methods with Multi-Step Exploration
Authors: Yifeng Fan, Yongqiang Li, Bo Chen
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 6 EXAMPLES AND EXPERIMENTS. We consider three classic examples corresponding to ρ > 1/e L , ρ ∈ (0, 1/e L ), ρ < 1/L respectively. ... Tested algorithms include (n-step EG), (MDEG) in this paper, (Adaptive EG+), (Curvature EG+) from (Pethick et al., 2022) and (EG+ Adaptive) from (Bohm, 2022). All experiments are implemented without the knowledge of ρ. In Example 1 we choose the parameters to make ρL ∈ (0.6, 0.5) and verify the convergence result of (n-step EG) in Theorem 4.4(i). Example 2 exhibits two limit cycles, one attracting and one repellent. (Algorithm 1) excels at handling such cyclic problems and evades the limit cycle in the first iteration. Example 3 further exceeds the manageable threshold of ρ > 1/L, posing challenges for the algorithms. |
| Researcher Affiliation | Academia | Yifeng Fan Yongqiang Li Bo Chen Zhejiang University of Technology {yifengfan,yqli,bchen}@zjut.edu.cn |
| Pseudocode | Yes | Algorithm 1 Max Distance Extragradient |
| Open Source Code | No | The paper does not include any statement about making the source code available or provide a link to a code repository. |
| Open Datasets | No | The paper uses examples defined by mathematical functions (e.g., 'Example 1. (bilinear) min x R max y R f(x, y) := axy + b/2(x2 y2)', 'Example 2. (Polar Game)', 'Example 3. (Forsaken)'). These are synthetic problems defined within the paper, not publicly available datasets with links or formal citations for access. |
| Dataset Splits | No | The paper tests algorithms on synthetic mathematical functions (Example 1, 2, 3) which do not have traditional training, validation, or test dataset splits. Therefore, no specific details about such splits are provided. |
| Hardware Specification | No | The paper does not specify any particular hardware used for running the experiments, such as GPU or CPU models, or any cloud computing specifics. |
| Software Dependencies | No | The paper mentions that some calculations were performed in 'Mathematica' in the appendix, but it does not provide specific version numbers for any software dependencies or libraries used for the main experiments. |
| Experiment Setup | Yes | D.1 EXPERIMENT PARAMETERS: For Example 1, two experiments are conducted. In the first experiment, a = 3/2, b = 1. γk,i = 1/2L, σk = 10/9 γi 0.99 is used in 2-step EG. In the second experiment, a = 2, b = 1. γk,i = 1/4L, σk = 1476/625 γi 0.99 is used in 4-step EG. For Example 2 and Example 3, in both experiment γk,i = 1/L and σk = 1/2L is used in (MDEG). Recommended tolerance for (MDEG) is ε1 = 10^-3, ε2 = 10^-3. |