KV-Cache Persistence Issue with SSD Offloading

Description:
follow the SSD offload guide in :

https://docs.lmcache.ai/kv_cache/local_storage.html

experimentation with vLLM and LMCache, we observed that the KV-Cache offloading to SSD works partially but lacks persistence across server restarts.

Steps to Reproduce:

1. Configure vLLM server with SSD offloading for KV-Cache
2. Run inference scripts with a specific prompt
3. Observe 2.4GB .pt file generated in the SSD cache directory
4. Restart the vLLM server process
5. Query the same prompt again
6. the kv-cache regenerated in SSD

Expected Behavior:
The existing KV-Cache files should be reused, avoiding redundant computation and disk I/O.

Actual Behavior:
New identical KV-Cache files are regenerated instead of reusing the existing ones

This optimization would significantly improve latency for recurring queries in production scenarios. I would appreciate guidance on recommended methods to achieve proper KV-Cache persistence across server restarts in this workflow.