Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Linear Lower Bounds and Conditioning of Differentiable Games
Authors: Adam Ibrahim, Waı̈ss Azizian, Gauthier Gidel, Ioannis Mitliagkas
ICML 2020 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we approach the question of fundamental iteration complexity by providing lower bounds to complement the linear (i.e. geometric) upper bounds observed in the literature on a wide class of problems. We cast saddle-point and min-max problems as 2-player games. We leverage tools from single-objective convex optimisation to propose new linear lower bounds for convex-concave games. Notably, we give a linear lower bound for n-player differentiable games, by using the spectral properties of the update operator. We then propose a new definition of the condition number arising from our lower bound analysis. |
| Researcher Affiliation | Academia | 1Mila, University of Montreal 2Ecole Normale Supérieure, Paris. |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide concrete access to source code for the methodology described. |
| Open Datasets | No | The paper is theoretical, focusing on mathematical lower bounds and condition numbers, and does not use or reference any publicly available datasets for training or empirical evaluation. |
| Dataset Splits | No | The paper is theoretical and does not describe experimental validation or dataset splits. |
| Hardware Specification | No | The paper is theoretical and does not mention any hardware specifications used for experiments. |
| Software Dependencies | No | The paper is theoretical and does not mention any specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe specific experimental setup details, hyperparameters, or training configurations. |