The Limits of Min-Max Optimization Algorithms: Convergence to Spurious Non-Critical Sets
Authors: Ya-Ping Hsieh, Panayotis Mertikopoulos, Volkan Cevher
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | On the surface, this provides a highly optimistic outlook for min-max algorithms; however, we show that there exist spurious attractors that do not contain any stationary points of the problem under study. In this regard, our work suggests that existing min-max algorithms may be subject to inescapable convergence failures. We complement our theoretical analysis by illustrating such attractors in simple, two-dimensional, almost bilinear problems. |
| Researcher Affiliation | Collaboration | Ya-Ping Hsieh 1 Panayotis Mertikopoulos 2 3 Volkan Cevher 4 1Department of Computer Science, ETH Zurich, Zurich, Switzerland. 2Univ. Grenoble Alpes, CNRS, Inria, LIG, Grenoble, France. 3Criteo AI Lab. 4Ecole Polytechnique Fédérale de Lausanne, Switzerland. Correspondence to: Ya-Ping Hsieh <yaping.hsieh@inf.ethz.ch>. |
| Pseudocode | No | The paper describes algorithms (e.g., Algorithm 1: SGDA) using mathematical formulas for update rules (e.g., 'Zn+1 = Zn + γn V(Zn; ωn), (SGDA)') but does not include structured pseudocode blocks or clearly labeled algorithm sections. |
| Open Source Code | No | The paper does not contain any explicit statement about releasing source code for the methodology or provide a link to a code repository. |
| Open Datasets | No | The paper uses 'simple, two-dimensional, almost bilinear problems' and mathematical functions for illustration purposes (e.g., equations 10 and 11). It does not use or refer to any publicly available datasets for training. |
| Dataset Splits | No | The paper does not provide specific details on training, validation, or test dataset splits. The illustrations use synthetic functions, not datasets with defined splits. |
| Hardware Specification | No | The paper does not explicitly describe the specific hardware (e.g., GPU/CPU models, memory, or cloud instance types) used to run its numerical illustrations or simulations. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers (e.g., Python, PyTorch, specific solvers) that would be needed to replicate the numerical illustrations. |
| Experiment Setup | No | While the paper presents illustrations with specific mathematical parameters (e.g., 'ε = 0.01' in Example 5.1), it does not provide comprehensive 'experimental setup' details such as concrete hyperparameter values (learning rate, batch size, number of epochs) or system-level training settings typically found in machine learning experiments. |