The files are divided in the following way:

• The ipython notebooks contain the experiments to be run;
  
• The files *.py are the libraries with all the necessary functions.
  

Some general notes:

• The names of the ipynb files refer directly to the experiments in the cited work.
  
• The last cells of the notebooks produce the pictures of the pdf, except for plots_rules.ipynb.
  
• To reduce the running time the parameters can be easily changed, e.g. decreasing N, n or sample.
  

They contain the algorithms relative to the acceleration of the GD-based methods via the
Caratheodory's Theorem. The first is specialised in the logistic regression, while the second in
the least-squares case. The second contains also functions which replicate the behaviour of ADAM and SAG.
Only the functions in CaGD_ls.py are parallelized.
Requirement: recombination.py.

These are the files necessary for the experiments done using the rules of [Nutini et al.].

• Create_dataset_A.m creates the Dataset A of [Nutini et al.] using Matlab.
  
• Train.py contains the functions which are the skeleton of the optimization procedure.
  It corresponds to trainval.py in [Nutini URL]. We have :
  • removed dependencies not relevant for our experiments;
  • added the skeleton for the optimization procedure using the Caratheodory Sampling Procedure.
  
• src/losses.py follows the same logic as losses.py from [Nutini URL].
  We have kept only the least-squares object and we have modified it because the Cartheodory
  Sampling procedure requires the gradient for any sample.
  
• src/update_rules/update_rules.py the same structure of the same file from [Nutini URL].
  The function update_Caratheodory(…) is the same as update(…) in the cited repository. We added the functions:
  update_Caratheodory, recomb_step, Caratheodory_Acceleration.
  
• The rest of the files is the same as [Nutini URL].
  

[Nutini et al.] Julie Nutini, Issam Laradji, and Mark Schmidt - "Let’s make block coordinate
descent go fast: Faster greedy rules, message-passing, active-set complexity, and
superlinear convergence", arXiv preprint arXiv:1712.08859, 2017.
[Nutini URL] https://github.com/IssamLaradji/BlockCoordinateDescent

It contains the algorithms relative to the reduction of the measure presented in
COSENTINO, OBERHAUSER, ABATE - "A randomized algorithm to reduce the support of discrete measures",
NeurIPS 2020, Available at https://github.com/FraCose/Recombination_Random_Algos

The notebooks "CaGD_paths.ipynb" and "Comparison_GD_vs_CaGD.ipynb" contain multiple experiments.
You have to comment/uncomment the respective parts of the code as indicated to reproduce the
wanted experiments.

To run the experiments, the following dataset need to be donwloaded and saved in the /Datasets folder:

• 3D_spatial_network.txt -
  https://archive.ics.uci.edu/ml/machine-learning-databases/00246/3D_spatial_network.txt
  
• household_power_consumption.txt -
  https://archive.ics.uci.edu/ml/machine-learning-databases/00235/household_power_consumption.zip
  (extract the .txt file)
  
• NY_train.csv -
  https://www.kaggle.com/c/nyc-taxi-trip-duration/data?select=train.zip
  (extract the .csv file and rename it to NY_train.csv)
  

The authors want to thank The Alan Turing Institute and the University of Oxford
for the financial support given. FC is supported by The Alan Turing Institute, TU/C/000021,
under the EPSRC Grant No. EP/N510129/1. HO is supported by the EPSRC grant Datasig
[EP/S026347/1], The Alan Turing Institute, and the Oxford-Man Institute.