IHT dies hard: Provable accelerated Iterative Hard Thresholding
This work addresses the challenge of improving convergence speed in sparse optimization problems, which is incremental as it modifies an existing method rather than introducing a new paradigm.
The paper tackles the problem of accelerating iterative hard thresholding (IHT) methods for convex optimization with non-convex constraints by incorporating momentum, resulting in significant improvements over state-of-the-art methods like projected gradient descent and Frank-Wolfe variants in diverse scenarios.
We study --both in theory and practice-- the use of momentum motions in classic iterative hard thresholding (IHT) methods. By simply modifying plain IHT, we investigate its convergence behavior on convex optimization criteria with non-convex constraints, under standard assumptions. In diverse scenaria, we observe that acceleration in IHT leads to significant improvements, compared to state of the art projected gradient descent and Frank-Wolfe variants. As a byproduct of our inspection, we study the impact of selecting the momentum parameter: similar to convex settings, two modes of behavior are observed --"rippling" and linear-- depending on the level of momentum.