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What does this PR do?

In Async rollout, AsyncOpenAI has a default 600-second timeout, which can lead to timeouts during longer inference. See details at #1138 (comment).

High-Level Design

See details at #1138 (comment).

Specific Changes

See details at #1138 (comment).

API

Demonstrate how the API changes if any.

Usage Example

Provide usage example(s) for easier usage.

# Add code snippet or script demonstrating how to use this 

Test

For changes that can not be tested by CI (e.g., algorithm implementation, new model support), validate by experiment(s) and show results like training curve plots, evaluatuion results, etc.

Additional Info.

• Issue Number: Fixes issue # or discussion # if any.
• Training: [Note which backend this PR will affect: FSDP, Megatron, both, or none]
• Inference: [Note which backend this PR will affect: vLLM, SGLang, both, or none]

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