Residual-Controlled Douglas--Rachford Splitting for Differentiable Solver Layers

What the math gives to ML

The paper turns a fixed-parameter unrolled Douglas–Rachford solver into a feedback-controlled dynamical system: intermediate splitting residuals determine relaxation and objective-drive parameters rather than fixing them for every instance. The transferable asset is the combination of projection-based feasibility preservation, residual feedback, and averaged-operator safeguards, which gives a principled way to spend a limited unrolling budget where convergence is currently slow. A strong neural-network use is an adaptive differentiable optimization layer whose iteration hyperparameters are selected online from primal, dual, and fixed-point residuals, while clipping and summable parameter changes retain stable rollout behavior.