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].
Handling Hard Affine SDP Shape Constraints in RKHSs
Authors: Pierre-Cyril Aubin-Frankowski, Zoltan Szabo
JMLR 2022 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section we demonstrate the efficiency of the proposed tightened schemes. Particularly, we designed the following experiments: Experiment-1: We show that the soap bubble algorithm (Section 5) can be more efficient both in terms of accuracy and of computation time when compared to non-adaptive techniques (Section 4). We illustrate this result on a 1D-shape optimization problem... Experiment-2: In our second application we tackle a linear-quadratic optimal control problem... Experiment-3: The third experiment is about estimating the end pose of a robotic arm... Experiment-4: Our fourth example pertains to econometrics... |
| Researcher Affiliation | Academia | Pierre-Cyril Aubin-Frankowski EMAIL INRIA D epartement d Informatique de l Ecole Normale Sup erieure, PSL Research University, 2 rue Simone Iff, 75012, Paris, France, Zolt an Szab o EMAIL Department of Statistics, London School of Economics Houghton Street, London, WC2A 2AE, UK |
| Pseudocode | Yes | Algorithm 1 Ball covering in X (shortly Cover), Algorithm 2 Ω-covering in FK (shortly Ω-Cover), Algorithm 3 Soap Bubble Algorithm with Ω-covering (I = P = 1), Algorithm 4 Soap Bubble Algorithm with ball coverings I ≥ 1, Pi ≥ 1 |
| Open Source Code | Yes | The code replicating our numerical experiments is available at https://github.com/PCAubin/Handling-Hard-Affine-SDP-Shape-Constraints-in-RKHSs. |
| Open Datasets | Yes | For our experiment, we considered a benchmark dataset containing the production data of 569 Belgian firms.18 The dataset is available at https://vincentarelbundock.github.io/Rdatasets/doc/Ecdat/Labour. html. |
| Dataset Splits | Yes | In our experiments, we partitioned randomly the dataset (xn, yn)n [Ntot] into a validation set Dval and a test set Dtest of approximately equal size (#Dval = 271, #Dtest = 272) corresponding each to 50% of the total dataset. 20-fold cross-validation was performed on Dval to estimate the optimal value of λ on a logarithmic grid. We then selected randomly 10% of Dval (referred to as D val) to optimize L over this small training set using one of the four constraint settings detailed above for the estimated λ.21 |
| Hardware Specification | Yes | In our experiments we used an i5-CPU 16GB-RAM computer and the YALMIP solver (Lofberg, 2004) to solve the optimization problem (35) with each of the constraints (37)-(40). |
| Software Dependencies | No | In our experiments we used an i5-CPU 16GB-RAM computer and the YALMIP solver (Lofberg, 2004) to solve the optimization problem (35) with each of the constraints (37)-(40). While YALMIP is a specific solver, its version number is not explicitly stated in the text. The year 2004 refers to the publication of the paper describing YALMIP, not necessarily the version used. |
| Experiment Setup | Yes | In our experiments we chose the bandwidth parameter to be λ = 5. This initial covering is then iteratively refined in our experiments using a rate γ = 0.8. The shape constraint were considered to be saturated when the condition |ηm f k + 0.5 f( xm)| ≤ 10−8 held, determining the bursting condition of the balls in Alg. 4. The hyperparameters (σi)i [d] and the regularization λ > 0 were optimized using 5-fold cross-validation. λk So S = 10−8 was chosen. |