Follow-the-Regularized-Leader Routes to Chaos in Routing Games
Authors: Jakub Bielawski, Thiparat Chotibut, Fryderyk Falniowski, Grzegorz Kosiorowski, Michał Misiurewicz, Georgios Piliouras
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Firstly, we numerically show that for Fo Re L dynamics a locally attracting Nash equilibrium and chaos can coexist, see Figure 2. In this section we report complex behaviors in bifurcation diagrams of Fo Re L dynamics. |
| Researcher Affiliation | Academia | 1Department of Mathematics, Cracow University of Economics, Rakowicka 27, 31-510 Krak ow, Poland. 2Chula Intelligent and Complex Systems, and Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand. 3Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202, USA. 4Engineering Systems and Design, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372. |
| Pseudocode | No | The paper provides mathematical equations for the dynamics (e.g., equation 6), but it does not contain a clearly labeled 'Pseudocode' or 'Algorithm' block, nor a structured, code-like procedure. |
| Open Source Code | No | The paper does not contain any statement about releasing source code or a link to a code repository for the methodology described. |
| Open Datasets | No | The paper analyzes theoretical models ('simple linear non-atomic congestion games'), not datasets that would typically be made publicly available with specific access information like links or citations. |
| Dataset Splits | No | The paper focuses on theoretical analysis and numerical simulation of game dynamics rather than empirical evaluation on a dataset, and therefore does not specify training, validation, or test dataset splits. |
| Hardware Specification | No | The paper discusses theoretical analysis and numerical simulations of game dynamics without providing any specific details about the hardware (e.g., GPU/CPU models, memory, cloud resources) used for these computations. |
| Software Dependencies | No | The paper describes mathematical models and numerical observations but does not list any specific software dependencies with version numbers (e.g., Python 3.8, PyTorch 1.9). |
| Experiment Setup | Yes | The bifurcation diagrams for fa,b where the dynamics is induced by the regularizer r(x) = (1 x) log(1 x) + x log x 0.4167 log( x2 + x + 0.11) for b = 0.61. On the horizontal axis the parameter a is between 2.6 and 3.4, and on the vertical axis values of fa,b are shown. As starting points for bifurcation diagrams two critical points of fa,b are taken red refers to the critical point in (0, 0.5) and blue the critical point in (0.5, 1). Each critical point is iterated 4000 times, visualizing the last 200 iterates. |