Adaptive and Optimal Second-order Optimistic Methods for Minimax Optimization
Authors: Ruichen Jiang, Ali Kavis, Qiujiang Jin, Sujay Sanghavi, Aryan Mokhtari
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 7 Numerical experiments |
| Researcher Affiliation | Academia | Ruichen Jiang ECE department, UT Austin rjiang@utexas.edu Ali Kavis ECE department, UT Austin kavis@austin.utexas.edu Qiujiang Jin ECE department, UT Austin qiujiangjin0@gmail.com Sujay Sanghavi ECE department, UT Austin sanghavi@mail.utexas.edu Aryan Mokhtari ECE department, UT Austin mokhtari@austin.utexas.edu |
| Pseudocode | Yes | Algorithm 1 Adaptive Second-order Optimistic Method |
| Open Source Code | Yes | We have uploaded our Matlab codes which generate all the empirical results in the numerical experiments. We have also included the instructions to reproduce all the experimental results Section 7 which could be found in Appendix D. |
| Open Datasets | No | Synthetic min-max problem: We first consider the min-max problem in [21, 30], given by minx Rn maxy Rn f(x, y) = (Ax b) y + (L2/6) x 3, which satisfies Assumptions 2.1 and 2.2. ... we generate the matrix A Rd d to ensure a condition number of 20. The vector b Rd is generated randomly according to N(0, I). |
| Dataset Splits | No | The paper does not explicitly specify training/validation/test dataset splits. It describes how data is generated for synthetic problems and problem formulations, but not how these are split for training, validation, and testing. |
| Hardware Specification | No | The paper mentions running experiments 'on our personal computer with normal CPU' but does not provide specific hardware details such as CPU model, GPU model, or memory specifications. |
| Software Dependencies | No | The paper mentions using 'MATLAB linear equation solver' and 'Matlab codes' but does not provide specific version numbers for MATLAB or any other software dependencies. |
| Experiment Setup | Yes | The hyper-parameters for methods in the prior work are tuned to achieve the best performance per method. Specifically, for the HIPNEX method in [30], it has a hyper-parameter σ (0, 0.5), which we choose in the interval [0.05, 0.1, 0.15, . . . , 0.45] for the best performance. Other hyper-parameters are determined by the formulas from [30]. For the Optimal SOM, the initial step size is set to be 1 as prescribed. Their algorithm has two line-search hyperparameters α and β. Note that their α is the same as ours, and we search for the best choice of α and β for their algorithm from the interval [0.1, 0.2, . . . , 0.9]. We use the combination that achieves the best empirical result. Finally, we initialize all the algorithms at the same point z0 = (x0, y0) Rd, drawn from the multivariate normal distribution. |