The Stochastic Proximal Distance Algorithm
This work provides a scalable solution for constrained estimation problems in machine learning, though it is incremental as it builds on existing proximal methods.
The authors tackled the problem of scaling constrained optimization by proposing a stochastic version of the proximal distance algorithm, establishing its convergence guarantees and finite error bounds, and showing it outperforms batch versions on learning tasks.
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and analyze a stochastic version of the recently proposed proximal distance algorithm, a class of iterative optimization methods that recover a desired constrained estimation problem as a penalty parameter $ρ\rightarrow \infty$. By uncovering connections to related stochastic proximal methods and interpreting the penalty parameter as the learning rate, we justify heuristics used in practical manifestations of the proximal distance method, establishing their convergence guarantees for the first time. Moreover, we extend recent theoretical devices to establish finite error bounds and a complete characterization of convergence rates regimes. We validate our analysis via a thorough empirical study, also showing that unsurprisingly, the proposed method outpaces batch versions on popular learning tasks.