BLADE is a novel framework that enhances black-box large language models (LLMs) with small domain-specific models to improve performance in specialized domains. The framework combines a general black-box LLM with a small domain-specific LM, which provides domain-specific knowledge and specialized insights. The small LM is pre-trained on domain-specific data, then fine-tuned using knowledge instruction data, and finally, the two models are jointly optimized using Bayesian optimization. This approach significantly outperforms existing methods in legal and medical benchmarks, demonstrating its effectiveness and cost-efficiency in adapting general LLMs for vertical domains. The framework consists of three main components: Domain-specific Pre-training (DP), Knowledge Instruction Tuning (KIT), and Bayesian Prompted Optimization (BPO). DP involves pre-training the small LM on domain-specific data to encode domain knowledge. KIT enhances the small LM's ability to follow instructions and generate question-specific knowledge. BPO aligns the small LM's output with the general LLM's understanding through derivative-free optimization on soft embeddings. Extensive experiments on legal and medical datasets show that BLADE significantly improves performance across various models. For example, Baichuan-7B achieves a 28.4% performance improvement, while ChatGPT achieves a 31.3% improvement. BLADE also outperforms retrieval-augmented LLMs in both legal and medical domains, demonstrating its effectiveness in providing domain-specific, contextually appropriate responses. The framework is effective in various scenarios, including legal and medical question-answering tasks. It is particularly effective in cases where the general LLM lacks sufficient domain knowledge. BLADE's approach of combining a general LLM with a small domain-specific LM allows for more accurate and contextually appropriate responses. The framework is also cost-effective, as it does not require extensive pre-training or additional annotations. Overall, BLADE provides a promising solution for adapting general LLMs to specialized domains. It is effective in improving performance across various models and domains, and it is cost-efficient. The framework's approach of combining a general LLM with a small domain-specific LM allows for more accurate and contextually appropriate responses. The framework is particularly effective in cases where the general LLM lacks sufficient domain knowledge.BLADE is a novel framework that enhances black-box large language models (LLMs) with small domain-specific models to improve performance in specialized domains. The framework combines a general black-box LLM with a small domain-specific LM, which provides domain-specific knowledge and specialized insights. The small LM is pre-trained on domain-specific data, then fine-tuned using knowledge instruction data, and finally, the two models are jointly optimized using Bayesian optimization. This approach significantly outperforms existing methods in legal and medical benchmarks, demonstrating its effectiveness and cost-efficiency in adapting general LLMs for vertical domains. The framework consists of three main components: Domain-specific Pre-training (DP), Knowledge Instruction Tuning (KIT), and Bayesian Prompted Optimization (BPO). DP involves pre-training the small LM on domain-specific data to encode domain knowledge. KIT enhances the small LM's ability to follow instructions and generate question-specific knowledge. BPO aligns the small LM's output with the general LLM's understanding through derivative-free optimization on soft embeddings. Extensive experiments on legal and medical datasets show that BLADE significantly improves performance across various models. For example, Baichuan-7B achieves a 28.4% performance improvement, while ChatGPT achieves a 31.3% improvement. BLADE also outperforms retrieval-augmented LLMs in both legal and medical domains, demonstrating its effectiveness in providing domain-specific, contextually appropriate responses. The framework is effective in various scenarios, including legal and medical question-answering tasks. It is particularly effective in cases where the general LLM lacks sufficient domain knowledge. BLADE's approach of combining a general LLM with a small domain-specific LM allows for more accurate and contextually appropriate responses. The framework is also cost-effective, as it does not require extensive pre-training or additional annotations. Overall, BLADE provides a promising solution for adapting general LLMs to specialized domains. It is effective in improving performance across various models and domains, and it is cost-efficient. The framework's approach of combining a general LLM with a small domain-specific LM allows for more accurate and contextually appropriate responses. The framework is particularly effective in cases where the general LLM lacks sufficient domain knowledge.