MAST: Model-Agnostic Sparsified Training
Yury Demidovich, Grigory Malinovsky, Egor Shulgin, Peter Richtárik
TL;DR
MAST reframes training as sparsified optimization around a pre-trained center $v$ using random sketches $\mathbf{S}$, formulating $\min_x f_{\mathcal{D}}(x)=\mathbb{E}[f_{\mathbf{S}}(x)]$ with $f_{\mathbf{S}}(x)=f(v+\mathbf{S}(x-v))$. The gradient estimator $\nabla f_{\mathbf{S}}(x)=\mathbf{S}^{\top}\nabla f(v+\mathbf{S}(x-v))$ is unbiased when $\mathbb{E}[\mathbf{S}]=\mathbf{I}$, enabling SGD and VR-style algorithms that come with convergence guarantees in convex, strongly convex, and nonconvex regimes; the analysis ties performance to sketch properties via $L_{\mathbf{S}},\mu_{\mathbf{S}},L_{\mathcal{D}},\mu_{\mathcal{D}}$. The framework naturally subsumes Dropout and sparse training and extends to distributed/IST/FL contexts, deriving explicit rates and interpolation behavior under various assumptions. Empirical results on logistic regression and deep networks show MAST yields greater robustness to pruning and guidance for learning-rate tuning under sparsity, validating the theory and suggesting practical deployment benefits.
Abstract
We introduce a novel optimization problem formulation that departs from the conventional way of minimizing machine learning model loss as a black-box function. Unlike traditional formulations, the proposed approach explicitly incorporates an initially pre-trained model and random sketch operators, allowing for sparsification of both the model and gradient during training. We establish the insightful properties of the proposed objective function and highlight its connections to the standard formulation. Furthermore, we present several variants of the Stochastic Gradient Descent (SGD) method adapted to the new problem formulation, including SGD with general sampling, a distributed version, and SGD with variance reduction techniques. We achieve tighter convergence rates and relax assumptions, bridging the gap between theoretical principles and practical applications, covering several important techniques such as Dropout and Sparse training. This work presents promising opportunities to enhance the theoretical understanding of model training through a sparsification-aware optimization approach.