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 [1].
Generalized Smooth Stochastic Variational Inequalities: Almost Sure Convergence and Convergence Rates
Authors: Daniil Vankov, Angelia Nedich, Lalitha Sankar
TMLR 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We also provide the first in-expectation unbiased convergence rate results for these methods under a relaxed smoothness assumption for α 1. Finally, we present numerical experiments where we compare the performance of the methods with proposed stochastic clipping for different stepsize parameter q > 1/2 and quasi-sharpness parameter p. |
| Researcher Affiliation | Academia | Daniil Vankov EMAIL Arizona State University Angelia Nedić EMAIL Arizona State University Lalitha Sankar EMAIL Arizona State University |
| Pseudocode | No | The paper describes the methods using mathematical equations: "Stochastic projection method: uk+1 = PU(uk γkΦ(uk, ξk)), (7)" and "Stochastic Korpelevich method: uk = PU(hk γkΦ(hk, ξ1 k)), hk+1 = PU(hk γkΦ(uk, ξ2 k)), (8)". These are not formatted as pseudocode blocks or algorithms. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code or provide a link to a code repository for the methodology described. |
| Open Datasets | No | We consider an unconstrained minmax game: min u1 max u2 1 p u1 p + u1, u2 1 with p > 1, and u1 Rd, u2 Rd. Then, the corresponding operator F : R2d R2d is defined by F(u) = u1 p 2u1 + u2 u2 p 2u2 u1 We assume that we have an access only to a noise evaluation of the corresponding operator and aim to solve unconstrained SVI(R2d, F) with the following stochastic operator Φ(u, ξ) = F(u) + ξ, where ξ is a random vector with independent zero-mean Gaussian entries and with variance σ2 = 1. Then, F(u) = E[Φ(u, ξ)] is an α-symmetric and p-quasi sharp operator due to Vankov et al. (2024). We set these parameters to be {(α 0.33, p = 2.5), (α 0.5, p = 3.0), (α 0.8, p = 6.0)}. |
| Dataset Splits | No | The paper describes numerical experiments on a synthetically generated minmax game. This type of experiment does not typically involve training/test/validation dataset splits, and no such splits are mentioned in the text. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to run the experiments, such as GPU or CPU models. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers, such as programming languages, libraries, or frameworks used for implementation. |
| Experiment Setup | Yes | In Figure 1, we plot an average distance to solution from the current iterate over twenty runs to the solution set as a function of the number of iterations. In particular, the stepsizes for clipped stochastic projection and Korpelevich methods are chosen according to Theorems 3.4 and 4.4, respectively, with βk = 100/(100 + k1/2+ϵ) for q = 1/2 + ϵ with ϵ > 0. We also set βk = 100/(100 + k1 ϵ) for stochastic clipped Popov method and the stochastic clipped projection method using the same sample Φ(uk, ξk) for clipping. We set these parameters to be {(α 0.33, p = 2.5), (α 0.5, p = 3.0), (α 0.8, p = 6.0)}. We assume that we have an access only to a noise evaluation of the corresponding operator and aim to solve unconstrained SVI(R2d, F) with the following stochastic operator Φ(u, ξ) = F(u) + ξ, where ξ is a random vector with independent zero-mean Gaussian entries and with variance σ2 = 1. |