Training Neural Networks Without Gradients: A Scalable ADMM Approach (1605.02026v1)

Abstract: With the growing importance of large network models and enormous training datasets, GPUs have become increasingly necessary to train neural networks. This is largely because conventional optimization algorithms rely on stochastic gradient methods that don't scale well to large numbers of cores in a cluster setting. Furthermore, the convergence of all gradient methods, including batch methods, suffers from common problems like saturation effects, poor conditioning, and saddle points. This paper explores an unconventional training method that uses alternating direction methods and Bregman iteration to train networks without gradient descent steps. The proposed method reduces the network training problem to a sequence of minimization sub-steps that can each be solved globally in closed form. The proposed method is advantageous because it avoids many of the caveats that make gradient methods slow on highly non-convex problems. The method exhibits strong scaling in the distributed setting, yielding linear speedups even when split over thousands of cores.

• The paper introduces a gradient-free training method that reformulates neural network optimization into a series of solvable ADMM sub-problems.
• It demonstrates significant linear speedups in distributed environments with faster convergence than traditional gradient-based techniques.
• The approach reduces reliance on GPUs by effectively enabling CPU cluster training and opens new avenues for non-gradient optimization methods.

Training Neural Networks Without Gradients: A Scalable ADMM Approach

In the domain of neural network optimization, the reliance on gradient-based methods, such as stochastic gradient descent (SGD), has traditionally necessitated the usage of high-performance hardware resources, including GPUs. Within this context, the research paper titled "Training Neural Networks Without Gradients: A Scalable ADMM Approach" presents a novel method that eschews gradients and embraces the Alternating Direction Method of Multipliers (ADMM) and Bregman iteration to train neural networks. This novel approach signifies a departure from conventional methods, presenting both practical and theoretical implications.

Overview of Proposed Method

The paper introduces an innovative technique where neural network training is reframed as a series of minimization sub-problems. This strategy diverges significantly from traditional gradient-based approaches by avoiding direct computation of gradients. By decomposing the optimization problem into globally solvable sub-steps, the method purportedly mitigates several inherent challenges faced by gradient-based methods, including saturation effects, poor conditioning, and vanishing gradients.

The essence of this approach involves partitioning the neural network training task into a constrained optimization problem. The constraints are then relaxed using an $\ell_2$ penalty, and a Lagrange multiplier term is introduced to the objective. This results in an unconstrained problem solved through ADMM, wherein weight updates, activation updates, and output updates are sequentially executed.

Strong Numerical Results

One of the compelling aspects of this approach is its ability to achieve linear speedups in distributed computing environments. The paper provides experimental results on benchmark datasets, demonstrating significant performance gains when training is parallelized across thousands of cores. For example, in comparison to SGD and conjugate gradients executed on GPUs, the ADMM approach consistently exhibits faster convergence times across varying problem sizes, even achieving substantial improvements on extremely large datasets like the Higgs boson.

Analysis and Implications

This methodology offers several noteworthy advantages. By sidestepping gradient computation, it circumvents common bottlenecks and parallelization challenges associated with gradient-based optimization. In practical terms, this could potentially reduce the reliance on GPU-based training, enabling efficient networking training using CPU clusters. This characteristic holds significance for large-scale settings, where traditional methods struggle with scalability.

Theoretically, this research opens new avenues for neural network training by demonstrating the viability of non-gradient-based methods. It provides a framework potentially applicable to recurrent networks and convolutional networks, suggesting future exploration into these areas could yield further advancements.

Speculative Future Directions

Future developments may involve adapting and extending this method to handle diverse architectures, such as recurrent and convolutional networks. Explorations into integrating momentum terms and examining different initializations could enhance convergence rates further. Additionally, refining the penalty parameters could optimize performance across a broader spectrum of neural network configurations.

In conclusion, the proposed ADMM approach to neural network training represents a distinctive alternative to traditional gradient-based methods. By leveraging strong parallelization capabilities, it could offer substantial practical benefits in large-scale machine learning applications, while challenging established paradigms and expanding the theoretical landscape of neural network optimization methods.