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.