Adaptive Three Operator Splitting
This work provides an incremental improvement for researchers and practitioners in optimization by enhancing an existing method with adaptive step-sizes for better efficiency.
The paper tackles the problem of solving composite optimization problems with smooth and non-smooth terms by proposing an adaptive step-size variant of the Davis-Yin three operator splitting method, which allows for larger step-sizes without hyperparameter tuning and achieves computational advantages in empirical tests on 6 problems.
We propose and analyze an adaptive step-size variant of the Davis-Yin three operator splitting. This method can solve optimization problems composed by a sum of a smooth term for which we have access to its gradient and an arbitrary number of potentially non-smooth terms for which we have access to their proximal operator. The proposed method sets the step-size based on local information of the objective --hence allowing for larger step-sizes--, only requires two extra function evaluations per iteration and does not depend on any step-size hyperparameter besides an initial estimate. We provide an iteration complexity analysis that matches the best known results for the non-adaptive variant: sublinear convergence for general convex functions and linear convergence under strong convexity of the smooth term and smoothness of one of the proximal terms. Finally, an empirical comparison with related methods on 6 different problems illustrates the computational advantage of the proposed method.