Revisiting Inexact Fixed-Point Iterations for Min-Max Problems: Stochasticity and Structured Nonconvexity
Authors: Ahmet Alacaoglu, Donghwan Kim, Stephen Wright
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We obtain optimal or best-known complexity guarantees with cohypomonotonicity or weak MVI conditions for ρ < 1 L. First main insight for the improvements in the convergence analyses is to harness the recently proposed conic nonexpansiveness property of operators. Second, we provide a refined analysis for inexact Halpern iteration... Third, we analyze a stochastic inexact Krasnosel ski ı-Mann iteration... (from Abstract) and sections like 'A. Proofs for Section 2'. |
| Researcher Affiliation | Academia | 1University of Wisconsin Madison, USA 2University of British Columbia, Canada 3KAIST, Republic of Korea. |
| Pseudocode | Yes | Algorithm 1 Inexact Halpern iteration for problems with cohypomonotonicity (p. 4), Algorithm 2 FBF(z0, N, A, Bin, LB) from (Tseng, 2000) (p. 4), Algorithm 3 Inexact KM iteration for problems with weak MVI (p. 6), etc. |
| Open Source Code | No | The paper does not provide any explicit statement about releasing code or a link to a code repository. |
| Open Datasets | No | The paper is theoretical and focuses on mathematical analysis and algorithm design. It provides theoretical examples of problem classes (e.g., interaction dominant min-max problems, von Neumann’s ratio game) but does not describe the use of any specific dataset for training or evaluation. |
| Dataset Splits | No | The paper is theoretical and does not describe empirical experiments with training, validation, or test data splits. |
| Hardware Specification | No | The paper is theoretical and does not describe experimental procedures, therefore no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and focuses on mathematical analysis. It does not mention any software dependencies with specific version numbers needed for replication. |
| Experiment Setup | No | The paper is theoretical and discusses algorithm parameters (e.g., 'Input: Parameters βk = 1 k+2, η > 0, L, ρ, α = 1 ρ η, K 1, initial iterate x0 Rd') as part of its theoretical framework, not as settings for an empirical experimental setup. |