Data Driven ADMM Model And Its Applications In Decoding Problems

In this paper,a novel data driven framework for alternating direction method of multipliers(ADMM)is proposed.The framework is constructed based on some modifications of the objective function.The commonly adopted penalty term with a constant parameter is replaced by a vector parameter in the proposed ADMM framework,which endues the model more flexibility and nonlinearity.The vector based penalization parameter can allow the different elements within the penalized vector receive different penalization,which can improve system performance in many scenarios.The replacement makes the parameters in the model hard to determine by some heuristic methods.In a traditional way,one can try different value of the constant penalty parameter and choose a good one.In this case,since the penalization parameter is a vector,the combination of the elements in the penalization parameter can be infinite and we cannot determine which kind of penalization parameter can be good.In order to obtain proper parameters for the model,a data driven framework is devised to let the model learn the parameters from data automatically.This framework absorbs some vital ideas from machine learning algorithms and is adaptive and robust in multiple scenarios.The overall algorithm can solve constrained optimization problem in a machine learning way.The structure of the proposed framework has some similarities with the neural network except it uses specific calculation layers which make the model analyzable.We also compare the structure of the proposed model and the neural networks.The data driven ADMM framework can be considered as an elaborately designed neural network but it is easy to construct.We first implement this method on the decoding problem and uses the error correcting code adopted in 5G.The decoding problem is reformulated into a constrained optimization problem by a universal modeling method introduced in this paper.The simulation results reveal that the data driven ADMM framework significantly improves the performance of the classical ADMM algorithm.This model is not the only way to learn the penalization parameter from data,some other potential models are mentioned at the end of the paper.