### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### The Feature

Introduce an optional routing strategy based on a Markov decision process that continuously adjusts provider selection according to real-time operational metrics.

Instead of relying solely on static priorities or reactive fallbacks, the router would dynamically adapt transition probabilities between providers using signals such as:

- token cost - latency - error rate - provider health - quota or rate-limit utilization - optional quality metrics

As provider conditions evolve, traffic would naturally shift toward providers delivering the best overall cost-performance-reliability balance.

The strategy would remain entirely opt-in and disabled by default, preserving full backward compatibility with LiteLLM's existing routing behavior.

### Motivation, pitch

LiteLLM already provides excellent retry, fallback, and load-balancing capabilities. These mechanisms are highly effective once a provider has failed or become unavailable.

However, many production issues arise before a provider actually fails.

For example, a provider may gradually become mo…