A Primal-Dual Approach to Solving Variational Inequalities with General Constraints
Authors: Tatjana Chavdarova, Tong Yang, Matteo Pagliardini, Michael Jordan
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In numerical experiments, we show that this technique can converge much faster than its exact counterpart. Furthermore, for the cases when the inequality constraints are simple, we introduce an alternative variant of ACVI and establish its convergence under the same conditions. Finally, we relax the smoothness assumptions in Yang et al., yielding, to our knowledge, the first convergence result for VIs with general constraints that does not rely on the assumption that the operator is L-Lipschitz. |
| Researcher Affiliation | Academia | Tatjana Chavdarova University of California, Berkeley tatjana.chavdarova@berkeley.edu Tong Yang Carnegie Mellon University tongyang@andrew.cmu.edu Matteo Pagliardini University of California, Berkeley & EPFL matteo.pagliardini@epfl.ch Michael I. Jordan University of California, Berkeley jordan@cs.berkeley.edu |
| Pseudocode | Yes | Algorithm 1 Inexact ACVI (I-ACVI) pseudocode. Algorithm 2 P-ACVI: ACVI with simple inequalities. Algorithm 3 (exact) ACVI pseudocode (Yang et al., 2023). Algorithm 4 Greedy projection method for the baseline. |
| Open Source Code | Yes | Source code: https://github.com/Chavdarova/I-ACVI. |
| Open Datasets | Yes | MNIST. We train GANs on the MNIST (Lecun & Cortes, 1998) dataset. |
| Dataset Splits | No | The paper does not explicitly provide training/validation/test dataset splits (e.g., percentages, sample counts, or references to predefined splits) for reproducibility. |
| Hardware Specification | Yes | We used the Colab platform (https://colab.research.google.com/) and Nvidia T4 GPUs. |
| Software Dependencies | No | The paper mentions 'Py Torch library (Paszke et al., 2017)' but does not provide a specific version number for PyTorch or any other software dependency used. |
| Experiment Setup | Yes | For I-ACVI, we set β = 0.5, µ 1 = 10 6, δ = 0.8, λ0 = 0, K = 10, ℓ= 10 and the step size is 0.05. For PI-ACVI, we set β = 0.5, and K = 5000, we use ℓ+ = 20 and ℓ0 {100, 500}. |