# When Gradient Descent Meets Derivative-Free Optimization: A Match Made in Black-Box Scenario

arXiv: https://arxiv.org/abs/2305.10013 · HTML: https://mlsanity.com/paper/2305.10013/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 52 references that are in the map.
- First posted on arXiv 17 May 2023.

## Builds on (most cited first, 30 of 41)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Making Pre-trained Language Models Better Few-shot Learners](https://mlsanity.com/paper/2012.15723/) (2020)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [How Can We Know What Language Models Know?](https://mlsanity.com/paper/1911.12543/) (2019)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [GPT Understands, Too](https://mlsanity.com/paper/2103.10385/) (2021)
- [P-Tuning v2: Prompt Tuning Can Be Comparable to Fine-tuning Universally Across Scales and Tasks](https://mlsanity.com/paper/2110.07602/) (2021)
- [RLPrompt: Optimizing Discrete Text Prompts with Reinforcement Learning](https://mlsanity.com/paper/2205.12548/) (2022)
- [ERNIE 3.0: Large-scale Knowledge Enhanced Pre-training for Language Understanding and Generation](https://mlsanity.com/paper/2107.02137/) (2021)
- [Black-Box Tuning for Language-Model-as-a-Service](https://mlsanity.com/paper/2201.03514/) (2022)
- [Revisiting Few-sample BERT Fine-tuning](https://mlsanity.com/paper/2006.05987/) (2020)
- [PPT: Pre-trained Prompt Tuning for Few-shot Learning](https://mlsanity.com/paper/2109.04332/) (2021)
- [Delta Tuning: A Comprehensive Study of Parameter Efficient Methods for Pre-trained Language Models](https://mlsanity.com/paper/2203.06904/) (2022)
- [Constrained Language Models Yield Few-Shot Semantic Parsers](https://mlsanity.com/paper/2104.08768/) (2021)
- [GrIPS: Gradient-free, Edit-based Instruction Search for Prompting Large Language Models](https://mlsanity.com/paper/2203.07281/) (2022)

## Built on by (most cited first, 5 of 5)

- [Feedback Descent: Open-Ended Text Optimization via Pairwise Comparison](https://mlsanity.com/paper/2511.07919/) (2025)
- [Prompting Techniques for Secure Code Generation: A Systematic Investigation](https://mlsanity.com/paper/2407.07064/) (2024)
- [When Large Language Models Meet Evolutionary Algorithms: Potential Enhancements and Challenges](https://mlsanity.com/paper/2401.10510/) (2024)
- [Multi-Prompting Decoder Helps Better Language Understanding](https://mlsanity.com/paper/2406.06279/) (2024)
- [Derivative Free Weight-space Ensembling](https://mlsanity.com/paper/2307.03506/) (2023)

## Abstract (arXiv)

Large pre-trained language models (PLMs) have garnered significant attention for their versatility and potential for solving a wide spectrum of natural language processing (NLP) tasks. However, the cost of running these PLMs may be prohibitive. Furthermore, PLMs may not be open-sourced due to commercial considerations and potential risks of misuse, such as GPT-3. The parameters and gradients of PLMs are unavailable in this scenario. To solve the issue, black-box tuning has been proposed, which utilizes derivative-free optimization (DFO), instead of gradient descent, for training task-specific continuous prompts. However, these gradient-free methods still exhibit a significant gap compared to gradient-based methods. In this paper, we introduce gradient descent into black-box tuning scenario through knowledge distillation. Furthermore, we propose a novel method GDFO, which integrates gradient descent and derivative-free optimization to optimize task-specific continuous prompts in a harmonized manner. Experimental results show that GDFO can achieve significant performance gains over previous state-of-the-art methods.