Title: ADMM SLIM: Sparse Recommendations for Many Users

Authors: Harald Steck,Maria Dimakopoulou,Nickolai Riabov,Tony Jebara

Abstract: The Sparse Linear Method (Slim) is a well-established approach for top-N recommendations. This article proposes several improvements that are enabled by the Alternating Directions Method of Multipliers (ADMM), a well-known optimization method with many application areas. First, we show that optimizing the original Slim-objective by ADMM results in an approach where the training time is independent of the number of users in the training data, and hence trivially scales to large numbers of users. Second, the flexibility of ADMM allows us to switch on and off the various constraints and regularization terms in the original Slim-objective, in order to empirically assess their contributions to ranking accuracy on given data. Third, we also propose two extensions to the original Slim training-objective in order to improve recommendation accuracy further without increasing the computational cost. In our experiments on three well-known data-sets, we first compare to the original Slim-implementation and find that not only ADMM reduces training time considerably, but also achieves an improvement in recommendation accuracy due to better optimization. We then compare to various state-of-the-art approaches and observe up to 25% improvement in recommendation accuracy in our experiments. Finally, we evaluate the importance of sparsity and the non-negativity constraint in the original Slim-objective with subsampling experiments that simulate scenarios of cold-starting and large catalog sizes compared to relatively small user base, which often occur in practice.

Running with RecBole

Model Hyper-Parameters:

  • lambda1 (float) : L1-norm regularization parameter. Defaults to 3.0.

  • lambda2 (float) : L2-norm regularization parameter. Defaults to 200.0.

  • alpha (float) : The exponents to control the power-law in the regularization terms. Defaults to 0.5.

  • rho (float) : The penalty parameter that applies to the squared difference between primal variables. Defaults to 4000.0.

  • k (int) : The number of running iterations. Defaults to 100.

  • positive_only (bool) : Whether or not to preserve all positive values only. Defaults to True.

  • center_columns (bool) : Whether or not to use additional item-bias terms. Defaults to False.

A Running Example:

Write the following code to a python file, such as

from recbole.quick_start import run_recbole

run_recbole(model='ADMMSLIM', dataset='ml-100k')

And then:


Tuning Hyper Parameters

If you want to use HyperTuning to tune hyper parameters of this model, you can copy the following settings and name it as hyper.test.

lambda1 choice [0.1 , 0.5 , 5 , 10]
lambda2 choice [5 , 50 , 1000 , 5000]
alpha choice [0.25 , 0.5 , 0.75 , 1]

Note that we just provide these hyper parameter ranges for reference only, and we can not guarantee that they are the optimal range of this model.

Then, with the source code of RecBole (you can download it from GitHub), you can run the to tuning:

python --model=[model_name] --dataset=[dataset_name] --config_files=[config_files_path] --params_file=hyper.test

For more details about Parameter Tuning, refer to Parameter Tuning.

If you want to change parameters, dataset or evaluation settings, take a look at