
This folder contains the numerical example implemented for our paper "Controlling the Flow: Stability and Convergence for Stochastic Gradient Descent with Decaying Regularization". The code has been developed in MATLAB.

- The directory "Radon" contains the implementations of our Radon transform example presented in Section A.1. The file "radon_forward.m" contains a function that generates the approximation of the radon transform resulting in a matrix. The file "magma.m" selects the colorbar used for our image visualization. The MATLAB script "main_radon.m" is the execution for the comparison of SGD and reg-SGD. To run the code the user may select an increased final iterate.

- The directory "Toy_example" contains the implementations of our toy example presented in Section A.2. The MATLAB script "main_L2rates.m" generates a comparison of the derived L^2 convergence rates presented in Figure 6. The MATLAB script "main_asrates.m" generates a comparison of the derived a.s. convergence rates presented in Figure 7. The MATLAB script "main_comparison.m" generates a comparison for different choices of (p,q) presented in Figure 8. To run the code the user may select an increased final iterate.

- The directory "ODE_example" contains the implementations of our ODE-based inverse problem example presented in Section A.3. The file "A_ellipticPDE.m" contains a function that generates the approximation of the ODE resulting in a matrix. The file "observation_matrix.m" maps the discretized ODE solution to the finite observation points. The file "m_ref.mat" contains the reference random function used in our paper submission for the rhs. The MATLAB script "main_ODE.m" is the execution for the comparison of SGD and reg-SGD. To run the code the user may select an increased final iterate. Note that own examples of linear inverse problems can easily be implemented by changing the function "A_ellipticPDE.m" in the subfolder "Functions".

- Note that the user may parallelize over the MC runs by replacing the for loop over "m=1:MC_runs" with "parfor".





