Efficient Projection-free Algorithms for Saddle Point Problems
Authors: Cheng Chen, Luo Luo, Weinan Zhang, Yong Yu
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental results demonstrate the effectiveness of our algorithms and verify our theoretical guarantees. We also conduct experiments on several real-world data sets for robust optimization problem to validate our theoretical analysis. The empirical results show that the proposed methods outperform previous projection-free and projection-based methods when the feasible set is complicated. In this section, we empirically evaluate the performance of our methods on the robust multiclass classification problem introduced in Section 2.3. |
| Researcher Affiliation | Academia | Cheng Chen1 Luo Luo2 Weinan Zhang1 Yong Yu1 1Shanghai Jiao Tong University 2The Hong Kong University of Science and Technology |
| Pseudocode | Yes | Algorithm 1 CGS Method for strongly convex functions, Algorithm 2 Procedure q+=Cnd G(r, q, β, η, Ω), Algorithm 3 Mirror-Prox Conditional Gradient Sliding, Algorithm 4 Procedure (x R, y R, v R)=Prox-step(f, x0, y0, z, v, γ, α, ζ, ϵ), Algorithm 5 Inexact STORC (i STORC), Algorithm 6 Mirror-Prox Stochastic Conditional Gradient Sliding, Algorithm 7 Procedure (x R, y R, v R)=Stochastic-Prox-step(f, x0, y0, z, v, γ, α, ζ, P, ϵ) |
| Open Source Code | No | The paper does not provide any concrete access to source code for the methodology described. |
| Open Datasets | Yes | We conduct experiments on three real-world data sets from the LIBSVM repository2: rcv1 (n = 15, 564, d = 47, 236, h = 53), sector (n = 6, 412, d = 55, 197, h = 105) and news20 (n = 15, 935, d = 62, 061, h = 20). 2https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/ |
| Dataset Splits | No | The paper mentions using 'real-world data sets' but does not specify the train/validation/test splits, percentages, or methodology for data partitioning. |
| Hardware Specification | No | The paper does not provide any specific hardware details (exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details, such as library or solver names with version numbers, needed to replicate the experiment. |
| Experiment Setup | Yes | We implement the mini-batch version of SVRE with batch size 100. The learning rate of SVRE is searched in {10 1, 10 2, . . . , 10 6}. On the other hand, the parameters of projection-free methods follows what the theory suggests. |