First-Order Algorithms for Min-Max Optimization in Geodesic Metric Spaces
Authors: Michael Jordan, Tianyi Lin, Emmanouil-Vasileios Vlatakis-Gkaragkounis
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We present numerical experiments on the task of robust principal component analysis (RPCA) for symmetric positive definite (SPD) matrices. In particular, we compare the performance of Algorithm 1 and 2 with different outputs, i.e., the last iterate (x T , y T ) versus the time-average iterate ( x T , y T ) (see the precise definition in Theorem 3.3). |
| Researcher Affiliation | Academia | Michael I. Jordan Tianyi Lin Emmanouil V. Vlatakis-Gkaragkounis University of California, Berkeley {jordan@cs,darren_lin@,emvlatakis@}.berkeley.edu |
| Pseudocode | Yes | Algorithm 1 RCEG |
| Open Source Code | No | Note that our implementations of both algorithms are based on the MANOPT package [87]. The paper's checklist indicates code is available in supplemental material or via URL, but the main text does not provide a direct link or explicit statement of their code's open-source availability for the described methodology. |
| Open Datasets | No | Following the previous works of Zhang et al. [1] and Han et al. [78], we generate a sequence of data matrices Mi satisfying that their eigenvalues are in the range of [0.2, 4.5]. |
| Dataset Splits | No | The paper describes generating synthetic data for the RPCA problem but does not specify any training, validation, or test splits for this data, as it is an optimization problem rather than a standard supervised learning task. |
| Hardware Specification | Yes | All the experiments were implemented in MATLAB R2021b on a workstation with a 2.6 GHz Intel Core i7 and 16GB of memory. |
| Software Dependencies | Yes | All the experiments were implemented in MATLAB R2021b on a workstation with a 2.6 GHz Intel Core i7 and 16GB of memory. Note that our implementations of both algorithms are based on the MANOPT package [87]. |
| Experiment Setup | Yes | In our experiment, we fix α = 1.0 and also vary the problem dimension d {25, 50, 100}. The evaluation metric is set as gradient norm. We set n = 40 and n = 200 in Figure 1 and 2. For RCEG, we set η = 1 2ℓwhere ℓ> 0 is selected via grid search. For SRCEG, we set ηt = min{ 1 t } where ℓ, a > 0 are selected via grid search. |