A SMART Stochastic Algorithm for Nonconvex Optimization with Applications to Robust Machine Learning
This addresses robust model fitting for machine learning practitioners by improving efficiency in handling contaminated data, though it appears incremental as it builds on existing optimization techniques.
The paper tackles the problem of robust machine learning by transforming optimization to detect and remove contaminated data while fitting a trimmed model, achieving a gradient evaluation complexity of O(n^{2/3}/ε) that is n^{1/3} times better than full gradient methods.
In this paper, we show how to transform any optimization problem that arises from fitting a machine learning model into one that (1) detects and removes contaminated data from the training set while (2) simultaneously fitting the trimmed model on the uncontaminated data that remains. To solve the resulting nonconvex optimization problem, we introduce a fast stochastic proximal-gradient algorithm that incorporates prior knowledge through nonsmooth regularization. For datasets of size $n$, our approach requires $O(n^{2/3}/\varepsilon)$ gradient evaluations to reach $\varepsilon$-accuracy and, when a certain error bound holds, the complexity improves to $O(κn^{2/3}\log(1/\varepsilon))$. These rates are $n^{1/3}$ times better than those achieved by typical, full gradient methods.