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.

Chain-of-Thought (CoT) prompting has successfully enhanced the reasoning capabilities of Large Language Models (LLMs) with at least 100 billion parameters. However, it is ineffective, or even detrimental, to the performance on reasoning tasks in Smaller Language Models (SLMs) with less than 10 billion parameters. In this paper, we propose Dialogue-guided Chain-of-Thought (DialCoT) to improve the reasoning capabilities of SLMs, with the aim of generating intermediate reasoning steps in a dialogue format to guide the model to the final answer. Furthermore, we optimize the model to choose the optimal reasoning path through the Proximal Policy Optimization (PPO) algorithm, further enhancing its reasoning capabilities. Compared to previous methods, our advantages lie in: 1) We transform the process of solving complex reasoning problems into decomposing problems and solving a series of simpler sub-questions, significantly reducing task difficulty and making it more suitable for SLMs. 2) We optimize the model to choose the optimal reasoning path through the PPO algorithm. Comprehensive experiments on four arithmetic reasoning datasets show that our method can achieve significant performance gains over state-of-the-art competitors.