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].
Stochastic Halpern Iteration with Variance Reduction for Stochastic Monotone Inclusions
Authors: Xufeng Cai, Chaobing Song, Cristóbal Guzmán, Jelena Diakonikolas
NeurIPS 2022 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We now illustrate the empirical performance of stochastic Halpern iteration on robust least square problems. Specifically, given data matrix A ∈ R n×d and noisy observation vector b ∈ R n subject to bounded deterministic perturbation δ with ‖δ‖ ∞, robust least square (RLS) minimizes the worst-case residue as minx∈R d maxδ:‖δ‖∞≤ε ‖Ax − y‖ 2 2 with y = b + δ [16]. We consider solving MI induced from RLS with Lagrangian relaxation where u = (x, y)T and F(u) = |
| Researcher Affiliation | Academia | Xufeng Cai Department of Computer Sciences University of Wisconsin-Madison EMAIL Chaobing Song Department of Computer Sciences University of Wisconsin-Madison EMAIL Cristóbal Guzmán Institute for Mathematical and Computational Eng. Facultad de Matemáticas and Escuela de Ingeniería Pontificia Universidad Católica de Chile EMAIL Jelena Diakonikolas Department of Computer Sciences University of Wisconsin-Madison EMAIL |
| Pseudocode | Yes | Algorithm 1: Stochastic Halpern-Cocoercive (Halpern) Algorithm 2: Extrapolated Stochastic Halpern-Monotone (E-Halpern) Algorithm 3: Restarted Extrapolated Stochastic Halpern-Sharp (Restarted E-Halpern) |
| Open Source Code | Yes | 2Code is available at https://github.com/zephyr-cai/Halpern. |
| Open Datasets | Yes | We use a real-world superconductivity dataset [22] from UCI Machine Learning Repository [15] for our experiment, which is of size 21263 × 81. To ensure the problem is concave in y, we need that λ > 1; in the experiments, we set λ = 1.5. For the experiment, we compare Halpern, E-Halpern, and Restarted E-Halpern algorithms with gradient descent-ascent (GDA), extragradient (EG) [28], and Popov’s method [42] in stochastic settings. |
| Dataset Splits | No | The main text describes the dataset but does not provide specific training/test/validation split percentages, sample counts, or detailed splitting methodology. |
| Hardware Specification | Yes | We implement all the algorithms in Python and run each algorithm using one CPU core on a mac OS machine with Intel 2.3GHz Dual Core i5 Processor and 8GB RAM. |
| Software Dependencies | No | The paper mentions implementation in 'Python' but does not specify its version or any other software dependencies with version numbers. |
| Experiment Setup | Yes | We use constant batch sizes and constant step sizes for GDA, EG, and Popov. We also choose the batch sizes of PAGE estimator to ensure E[‖F(uk) − e F(uk)‖^2] = O(1/k), which handles error accumulation [29] and early stagnation of stochastic Halpern iteration. We implement all the algorithms in Python and run each algorithm using one CPU core on a mac OS machine with Intel 2.3GHz Dual Core i5 Processor and 8GB RAM.2 |