[Misc] add litellm integration (#18320)

Signed-off-by: reidliu41 <reid201711@gmail.com>
Co-authored-by: reidliu41 <reid201711@gmail.com>

docs/source/deployment/frameworks/index.md

@@ -10,6 +10,7 @@ chatbox
 dify
 dstack
 helm
+litellm
 lobe-chat
 lws
 modal

docs/source/deployment/frameworks/litellm.md

+(deployment-litellm)=
+
+# LiteLLM
+
+[LiteLLM](https://github.com/BerriAI/litellm) call all LLM APIs using the OpenAI format [Bedrock, Huggingface, VertexAI, TogetherAI, Azure, OpenAI, Groq etc.]
+
+LiteLLM manages:
+
+- Translate inputs to provider's `completion`, `embedding`, and `image_generation` endpoints
+- [Consistent output](https://docs.litellm.ai/docs/completion/output), text responses will always be available at `['choices'][0]['message']['content']`
+- Retry/fallback logic across multiple deployments (e.g. Azure/OpenAI) - [Router](https://docs.litellm.ai/docs/routing)
+- Set Budgets & Rate limits per project, api key, model [LiteLLM Proxy Server (LLM Gateway)](https://docs.litellm.ai/docs/simple_proxy)
+
+And LiteLLM supports all models on VLLM.
+
+## Prerequisites
+
+- Setup vLLM and litellm environment
+
+```console
+pip install vllm litellm
+```
+
+## Deploy
+
+### Chat completion
+
+- Start the vLLM server with the supported chat completion model, e.g.
+
+```console
+vllm serve qwen/Qwen1.5-0.5B-Chat
+```
+
+- Call it with litellm:
+
+```python
+import litellm 
+
+messages = [{ "content": "Hello, how are you?","role": "user"}]
+
+# hosted_vllm is prefix key word and necessary
+response = litellm.completion(
+            model="hosted_vllm/qwen/Qwen1.5-0.5B-Chat", # pass the vllm model name
+            messages=messages,
+            api_base="http://{your-vllm-server-host}:{your-vllm-server-port}/v1",
+            temperature=0.2,
+            max_tokens=80)
+
+print(response)
+```
+
+### Embeddings
+
+- Start the vLLM server with the supported embedding model, e.g.
+
+```console
+vllm serve BAAI/bge-base-en-v1.5
+```
+
+- Call it with litellm:
+
+```python
+from litellm import embedding   
+import os
+
+os.environ["HOSTED_VLLM_API_BASE"] = "http://{your-vllm-server-host}:{your-vllm-server-port}/v1"
+
+# hosted_vllm is prefix key word and necessary
+# pass the vllm model name
+embedding = embedding(model="hosted_vllm/BAAI/bge-base-en-v1.5", input=["Hello world"])
+
+print(embedding)
+```
+
+For details, see the tutorial [Using vLLM in LiteLLM](https://docs.litellm.ai/docs/providers/vllm).