Derive KL Divergence from First Principles
Author: @dejavucoder | Date: 2026-05-02
Challenge/reminder that anyone working in RL should be able to derive KL divergence from first principles. KL divergence is fundamental to RLHF, PPO constraints, and policy optimization — understanding it deeply matters.
Key Claims
- KL divergence derivation from first principles is essential knowledge for RL practitioners
- Underpins RLHF penalty terms, PPO clipping motivation, and policy trust regions
- Many practitioners use KL without understanding its information-theoretic origins
- Foundation: measures information lost when approximating one distribution with another
Takeaways
- Theoretical foundations matter for RL engineering decisions
- KL asymmetry (forward vs reverse) has practical implications for mode-seeking vs mode-covering behavior
- Understanding the derivation helps debug reward hacking and collapse issues in RLHF