Neural Network Training via Stochastic Alternating Minimization with Trainable Step Sizes

The training of deep neural networks is inherently a nonconvex optimization problem, yet standard approaches such as stochastic gradient descent (SGD) require simultaneous updates to all parameters, often leading to unstable convergence and high computational cost. To address these issues, we propose a novel method, Stochastic Alternating Minimization with Trainable Step Sizes (SAMT), which updates network parameters in an alternating manner by treating the weights of each layer as a block. By decomposing the overall optimization into sub-problems corresponding to different blocks, this block-wise alternating strategy reduces per-step computational overhead and enhances training stability in nonconvex settings. To fully leverage these benefits, inspired by meta-learning, we proposed a novel adaptive step size strategy to incorporate into the sub-problem solving steps of alternating updates. It supports different types of trainable step sizes, including but not limited to scalar, element-wise, row-wise, and column-wise, enabling adaptive step size selection tailored to each block via meta-learning. We further provide a theoretical convergence guarantee for the proposed algorithm, establishing its optimization soundness. Extensive experiments for multiple benchmarks demonstrate that SAMT achieves better generalization performance with fewer parameter updates compared to state-of-the-art methods, highlighting its effectiveness and potential in neural network optimization.

A Triple-Inertial Accelerated Alternating Optimization Method for Deep Learning Training

The stochastic gradient descent (SGD) algorithm has achieved remarkable success in training deep learning models. However, it has several limitations, including susceptibility to vanishing gradients, sensitivity to input data, and a lack of robust theoretical guarantees. In recent years, alternating minimization (AM) methods have emerged as a promising alternative for model training by employing gradient-free approaches to iteratively update model parameters. Despite their potential, these methods often exhibit slow convergence rates. To address this challenge, we propose a novel Triple-Inertial Accelerated Alternating Minimization (TIAM) framework for neural network training. The TIAM approach incorporates a triple-inertial acceleration strategy with a specialized approximation method, facilitating targeted acceleration of different terms in each sub-problem optimization. This integration improves the efficiency of convergence, achieving superior performance with fewer iterations. Additionally, we provide a convergence analysis of the TIAM algorithm, including its global convergence properties and convergence rate. Extensive experiments validate the effectiveness of the TIAM method, showing significant improvements in generalization capability and computational efficiency compared to existing approaches, particularly when applied to the rectified linear unit (ReLU) and its variants.