# Stochastic Two Points Method for Deep Model Zeroth-order Optimization

arXiv: https://arxiv.org/abs/2402.01621 · HTML: https://mlsanity.com/paper/2402.01621/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 61 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Black-box Adversarial Attacks with Limited Queries and Information](https://mlsanity.com/paper/1804.08598/) (2018)
- [RLPrompt: Optimizing Discrete Text Prompts with Reinforcement Learning](https://mlsanity.com/paper/2205.12548/) (2022)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Why gradient clipping accelerates training: A theoretical justification for adaptivity](https://mlsanity.com/paper/1905.11881/) (2019)
- [Simple Black-box Adversarial Attacks](https://mlsanity.com/paper/1905.07121/) (2019)
- [ReCoRD: Bridging the Gap between Human and Machine Commonsense Reading Comprehension](https://mlsanity.com/paper/1810.12885/) (2018)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [On Hyperparameter Optimization of Machine Learning Algorithms: Theory and Practice](https://mlsanity.com/paper/2007.15745/) (2020)
- [GrIPS: Gradient-free, Edit-based Instruction Search for Prompting Large Language Models](https://mlsanity.com/paper/2203.07281/) (2022)
- [Noise Is Not the Main Factor Behind the Gap Between SGD and Adam on Transformers, but Sign Descent Might Be](https://mlsanity.com/paper/2304.13960/) (2023)
- [An Optimal Algorithm for Bandit and Zero-Order Convex Optimization with Two-Point Feedback](https://mlsanity.com/paper/1507.08752/) (2015)
- [Convergence of Adam Under Relaxed Assumptions](https://mlsanity.com/paper/2304.13972/) (2023)
- [Improved Analysis of Clipping Algorithms for Non-convex Optimization](https://mlsanity.com/paper/2010.02519/) (2020)
- [Stochastic Zeroth-order Optimization in High Dimensions](https://mlsanity.com/paper/1710.10551/) (2017)
- [Convergence of AdaGrad for Non-convex Objectives: Simple Proofs and Relaxed Assumptions](https://mlsanity.com/paper/2305.18471/) (2023)
- [Structured Evolution with Compact Architectures for Scalable Policy Optimization](https://mlsanity.com/paper/1804.02395/) (2018)
- [Zeroth-Order Regularized Optimization (ZORO): Approximately Sparse Gradients and Adaptive Sampling](https://mlsanity.com/paper/2003.13001/) (2020)

## Built on by (most cited first, 1 of 1)

- [Guiding the Recommender: Information-Aware Auto-Bidding for Content Promotion](https://mlsanity.com/paper/2601.20422/) (2026)

## Abstract (arXiv)

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, and the derived results help understand and inherently connect the two popular types of zeroth-order methods, basic random search and stochastic three-point method. The theoretical properties also shed light on a Variant of S2P (VS2P), through exploiting our new convergence properties that better represent the dynamics of deep models in training. Our comprehensive empirical results show that VS2P is highly effective in optimizing objectives for deep models. It outperforms or achieves competitive performance compared to standard methods across various model types and scales.