Escaping Saddle Point Efficiently in Minimax and Bilevel Optimizations
Authors: Wenhan Xian, Feihu Huang, Heng Huang
IJCAI 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we conduct two numerical experiments to validate the performance of our new method. In this section we conduct the matrix sensing [Bhojanapalli et al., 2016; Park et al., 2017] experiment to validate the performance of out PRGDA algorithm for solving both minimax and bilevel problem. The experimental results of these two quantities versus the number of gradient oracles are shown in Figure 1. |
| Researcher Affiliation | Academia | 1University of Maryland, College Park 2University of Pittsburgh EMAIL, EMAIL, EMAIL |
| Pseudocode | Yes | Algorithm 1 Perturbed Recursive Gradient Descent Ascent Input: initial value x0, y0 Parameter: stepsize η and ηH, perturbation radius r, escaping phase threshold tthres, average movement D, tolerance ϵ, maximum iteration T. 1: Set escape = false, s = 0, esc = 0. 2: for t = 0, 1, . . . , T 1 do 3: Minimax: Update yt+1, vt, ut from Algorithm 2. 4: Bilevel: Update yt+1, vt, ut from Algorithm 3. |
| Open Source Code | No | The paper does not provide concrete access to source code. It only mentions: "The code is implemented on matlab." (Section 7.1). |
| Open Datasets | No | The paper describes generating synthetic data for its experiments: "The ground truth low-rank matrix M is generated by M = U (U )T where each entry of U is drawn from Gaussian distribution N(0, 1/d) independently. We randomly generate n = 20d samples of sensing matrices {Ai}n i=1, Ai Rd d from standard Gaussian distribution and calculate the corresponding labels bi = Ai, M hence there is no noise in the synthetic data." No publicly available dataset is directly accessed or provided. |
| Dataset Splits | Yes | We split all samples into two dataset: a train dataset D1 with 70% data and a validation dataset D2 with 30% data. |
| Hardware Specification | No | The paper does not provide specific hardware details. It only mentions that "The code is implemented on matlab." |
| Software Dependencies | No | The paper mentions "matlab" but does not specify a version number or any other software dependencies with version information. |
| Experiment Setup | Yes | We choose η = 0.001, ηH = 0.1, λ = 0.01, D = r = 0.01, tthres = 20, K = 5, S2 = 40 and q = 25. |