[doc] explain common errors around torch.compile (#12340)

Signed-off-by: youkaichao <youkaichao@gmail.com>

docs/source/getting_started/troubleshooting.md

@@ -197,6 +197,27 @@ if __name__ == '__main__':
     llm = vllm.LLM(...)
 ```
 
+## `torch.compile` Error
+
+vLLM heavily depends on `torch.compile` to optimize the model for better performance, which introduces the dependency on the `torch.compile` functionality and the `triton` library. By default, we use `torch.compile` to [optimize some functions](https://github.com/vllm-project/vllm/pull/10406) in the model. Before running vLLM, you can check if `torch.compile` is working as expected by running the following script:
+
+```python
+import torch
+
+@torch.compile
+def f(x):
+    # a simple function to test torch.compile
+    x = x + 1
+    x = x * 2
+    x = x.sin()
+    return x
+
+x = torch.randn(4, 4).cuda()
+print(f(x))
+```
+
+If it raises errors from `torch/_inductor` directory, usually it means you have a custom `triton` library that is not compatible with the version of PyTorch you are using. See [this issue](https://github.com/vllm-project/vllm/issues/12219) for example.
+
 ## Known Issues
 
 - In `v0.5.2`, `v0.5.3`, and `v0.5.3.post1`, there is a bug caused by [zmq](https://github.com/zeromq/pyzmq/issues/2000) , which can occasionally cause vLLM to hang depending on the machine configuration. The solution is to upgrade to the latest version of `vllm` to include the [fix](gh-pr:6759).