Semi-Proximal Mirror-Prox for Nonsmooth Composite Minimization
Authors: Niao He, Zaid Harchaoui
NeurIPS 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We report the experimental results obtained with the proposed Semi-Proximal Mirror-Prox, denoted Semi-MP here, and competing algorithms. We consider two different applications: i) robust collaborative filtering for movie recommendation; ii) link prediction for social network analysis. For i), we compare to two competing approaches: a) smoothing conditional gradient proposed in [24] (denoted Smooth-CG); b) smoothing proximal gradient [20, 5] equipped with semi-proximal setup (Semi-SPG). For ii), we compare to Semi-LPADMM, using [22] equipped with semi-proximal setup. Additional experiments and implementation details are given in Appendix E. In Fig. 1, we can see that Semi-MP clearly outperforms Smooth-CG, while it is competitive with Semi-SPG. |
| Researcher Affiliation | Academia | Niao He Georgia Institute of Technology nhe6@gatech.edu Zaid Harchaoui NYU, Inria firstname.lastname@nyu.edu |
| Pseudocode | Yes | Algorithm 1 Composite Mirror Prox Algorithm (CMP) for VI(X, F) ... Algorithm 2 Composite Conditional Gradient Algorithm CCG(X, φ( ), θ; ǫ) ... Algorithm 3 Semi-Proximal Mirror-Prox Algorithm for Semi-VI(X, F) |
| Open Source Code | No | The paper does not provide any explicit statements or links for open-source code for the methodology described. |
| Open Datasets | Yes | We consider two different applications: i) robust collaborative filtering for movie recommendation; ii) link prediction for social network analysis. ... The small-size dataset consists of 943 users and 1682 movies with about 100K ratings, while the medium-size dataset consists of 3952 users and 6040 movies with about 1M ratings. We conduct experiments on a binary social graph data set called Wikivote, which consists of 7118 nodes and 103747 edges. |
| Dataset Splits | No | The paper mentions using specific datasets (MovieLens, Wikivote) and referring to prior work for regularization parameters, but it does not explicitly specify the training/validation/test splits (e.g., percentages or sample counts) for their experiments. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., GPU/CPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers (e.g., programming languages, libraries, or solvers). |
| Experiment Setup | Yes | Input: stepsizes γt > 0, accuracies ǫt 0, t = 1, 2, . . . ... Proposition 3.2. Under the assumption (A.1) (A.4) and (S.1) (S.4) with M = 0, and choice of stepsize γt = L 1, t = 1, . . . , T, for the outlined algorithm to return an ǫ-solution to the variational inequality V I(X, F), the total number of Mirror Prox steps required does not exceed ... We follow [24] to set the regularization parameters. ... with different strategies for the inner LMO calls. |