General Proximal Incremental Aggregated Gradient Algorithms: Better and Novel Results under General Scheme
This work addresses optimization challenges in network and machine learning applications, offering incremental improvements to existing algorithms.
The paper tackles the limitations of incremental aggregated gradient algorithms, which previously required strong convexity and had restricted stepsizes, by proposing a general proximal version that achieves better convergence results, including sublinear rates and larger stepsizes, even in nonconvex settings.
The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence rates are also limited to linear convergence. Due to the mathematical techniques, the stepsize in the algorithm is restricted by the strongly convex constant, which may make the stepsize be very small (the strongly convex constant may be small). In this paper, we propose a general proximal incremental aggregated gradient algorithm, which contains various existing algorithms including the basic incremental aggregated gradient method. Better and new convergence results are proved even with the general scheme. The novel results presented in this paper, which have not appeared in previous literature, include: a general scheme, nonconvex analysis, the sublinear convergence rates of the function values, much larger stepsizes that guarantee the convergence, the convergence when noise exists, the line search strategy of the proximal incremental aggregated gradient algorithm and its convergence.