Screening Rules and its Complexity for Active Set Identification
This work provides a theoretical foundation for accelerating machine learning optimization methods through dimension reduction, but it is incremental as it builds on existing screening rule techniques.
The paper tackles the problem of identifying active structures like sparsity in optimization problems by analyzing screening rules, showing that the number of iterations needed to identify the optimal active set depends only on the convergence rate of the algorithm.
Screening rules were recently introduced as a technique for explicitly identifying active structures such as sparsity, in optimization problem arising in machine learning. This has led to new methods of acceleration based on a substantial dimension reduction. We show that screening rules stem from a combination of natural properties of subdifferential sets and optimality conditions, and can hence be understood in a unified way. Under mild assumptions, we analyze the number of iterations needed to identify the optimal active set for any converging algorithm. We show that it only depends on its convergence rate.