Stochastic Two Points Method for Deep Model Zeroth-order Optimization

Large foundation models, such as large language models, have performed exceptionally well in various application scenarios. Building or fully fine-tuning such large models is usually prohibitive due to either hardware budget or lack of access to backpropagation. The zeroth-order methods offer a promising direction for tackling this challenge, where only forward passes are needed to update the model. This paper introduces an efficient Stochastic Two-Point (S2P) approach within the gradient-free regime. We present the theoretical convergence properties of S2P under the general and relaxed smoothness assumptions. The theoretical properties also shed light on a faster and more stable S2P variant, Accelerated S2P (AS2P), through exploiting our new convergence properties that better represent the dynamics of deep models in training. Our comprehensive empirical results show that AS2P is highly effective in optimizing objectives for large deep models, including language models, and outperforms standard methods across various model types and scales, with 2 $\times$ speed-up in training over most conducted tasks.