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].
Optimal Feedback Law Recovery by Gradient-Augmented Sparse Polynomial Regression
Authors: Behzad Azmi, Dante Kalise, Karl Kunisch
JMLR 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | An extended set of low and high-dimensional numerical tests in nonlinear optimal control reveal that enriching the dataset with gradient information reduces the number of training samples, and that the sparse polynomial regression consistently yields a feedback law of lower complexity. |
| Researcher Affiliation | Academia | Behzad Azmi EMAIL Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences AltenbergerstraĆe 69, A-4040 Linz, Austria Dante Kalise EMAIL School of Mathematical Sciences University of Nottingham University Park, Nottingham NG7 2QL, United Kingdom Karl Kunisch EMAIL Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences and Institute of Mathematics and Scientiļ¬c Computing University of Graz HeinrichstraĆe 36, A-8010 Graz, Austria |
| Pseudocode | Yes | Algorithm 1 Barzilai-Borwein two-point step-size gradient method |
| Open Source Code | No | The paper states: "Both sampling and regression algorithms were implemented in MATLAB R2014b, and the numerical tests were run in a Mac Book Pro with 2.9 GHz Dual-Core Intel Core i5 and memory 16 GB 1867 MHz DDR3." This describes their implementation environment but does not explicitly state that the code for their methodology is open-source or provide a link to a repository. |
| Open Datasets | No | Generating the samples. For each test we ļ¬xed an n dimensional hyperrectangle as the domain for sampling initial condition vectors {xj}N j=1 Rn. These initial vectors were generated using Halton quasi-random sequences2 in dimension n. |
| Dataset Splits | Yes | We split the sampling dataset {xj, V j, V j x }N j=1 into two sets: a set of training indices Itr which is used for regression, and a set of validation indices Ival, with Ival Itr = {1, . . . , N}. Without loss of generality, we assume that Itr = {1, . . . , Nd} and Ival = {Nd + 1, . . . , N} for N N with Nd < N. |
| Hardware Specification | Yes | Both sampling and regression algorithms were implemented in MATLAB R2014b, and the numerical tests were run in a Mac Book Pro with 2.9 GHz Dual-Core Intel Core i5 and memory 16 GB 1867 MHz DDR3. |
| Software Dependencies | Yes | Both sampling and regression algorithms were implemented in MATLAB R2014b, and the numerical tests were run in a Mac Book Pro with 2.9 GHz Dual-Core Intel Core i5 and memory 16 GB 1867 MHz DDR3. |
| Experiment Setup | Yes | Every optimal control problem was solved in the reduced form by using Algorithm 1 with tol = 10 5 as discussed in Section 2.1. For problem (Pā1) and (APā1) we chose the sparse penalty parameter Ī» = 0.002 and Ī» = {0.01, 0.02}, respectively. The linear least square problems (Pā2) and (APā2) were solved using a preconditioned conjugate gradient method, and the algorithm was terminated when the norm of residual was less than 10 8. For the LASSO regressions (Pā1) and (APā1), we employed Algorithm 2 with tol = 10 5. |