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..
Extragradient Method for $(L_0, L_1)$-Lipschitz Root-finding Problems
Authors: Sayantan Choudhury, Nicolas Loizou
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 4 Numerical Experiments In this section, we conduct experiments to validate the efficiency of our proposed step size strategy γk = 1 c0+c1 F (xk) α with α = 1. In the first experiment, we compare our step size choice with that of Vankov et al. [2024] on a strongly monotone problem, and in the second experiment, we make a comparison with the constant step size strategy for solving a monotone problem. Finally, we evaluate our scheme for solving the Global Forsaken problem from Pethick et al. [2022]. |
| Researcher Affiliation | Academia | Sayantan Choudhury AMS & MINDS Johns Hopkins University EMAIL Nicolas Loizou AMS & MINDS Johns Hopkins University EMAIL |
| Pseudocode | No | The paper describes the extragradient method algorithm in prose, 'The algorithm is defined as follows ˆxk = xk γk F(xk), xk+1 = xk ωk F(ˆxk) (3)', but does not provide a formally structured pseudocode or algorithm block. |
| Open Source Code | Yes | We provide the code for all of our experiments at https://github.com/isayantan/L0L1extragradient. |
| Open Datasets | No | The paper conducts experiments on problem formulations and mathematical operators (e.g., 'the operator F(x) = (sign (u1) |u1| + u2, sign (u2) |u2| u1)', 'min-max optimization problem... (20)', 'Global Forsaken problem... (21)') rather than traditional, publicly available datasets. |
| Dataset Splits | No | The paper conducts experiments on mathematical problem formulations rather than traditional datasets. Therefore, no dataset splits are applicable or mentioned. |
| Hardware Specification | Yes | All experiments in this work were conducted using a personal Mac Book with an Apple M3 chip and 16GB of RAM. |
| Software Dependencies | No | The paper does not explicitly mention any specific software dependencies or their version numbers, such as programming languages, libraries, or frameworks used for implementation. |
| Experiment Setup | Yes | For our method, we use γk = ωk = ν L0+L1 F (xk) while for EG [Vankov et al., 2024] we use stepsize γk = ωk = min n 1 4µ, 1 2 2e L0 , 1 2 2e L1 F (xk) o . For the constant step size EG, we perform a grid search over c {102, 103, 104, 105, 106, 107}. We find that c = 105 yields the best performance: larger values lead to slower convergence, while smaller values cause divergence. For our adaptive EG method, we perform a grid search over c0 {10, 100, 1000} and c1 {0.1, 1, 10}, evaluating all 9 possible combinations. For our method, we set the step size parameters as (c0, c1) = (1, 1). In Figure 5, we present the trajectory plots of these algorithms, all initialized at (w1, w2) = (1, 1). |