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Policy Gradients for LLMs Explained Visually
This visual derivation of the policy gradient shows that RL training for LLMs is essentially supervised fine-tuning on self-sampled completions, weighted by reward.
What: Tyler Romero provides a step-by-step mathematical derivation of the REINFORCE algorithm for LLMs. It explains how to convert expected reward into a differentiable gradient using the log-derivative trick, and highlights how baselines reduce variance.
Why it matters: This offers a clear mental model for how PPO and GRPO work, stripping away the complexity to reveal the core mechanism used to train models on reasoning and coding tasks.
Deep dive
- Derives the policy gradient starting from the objective of maximizing expected reward J(θ).
- Uses the log-derivative trick to compute gradients despite the non-differentiable sampling process.
- Demonstrates that the REINFORCE estimator is essentially supervised learning weighted by reward.
- Explains the 'credit assignment' problem in LLMs where all tokens share a single completion reward.
- Discusses group-based normalization (GRPO) as a standard way to implement a reward baseline.
Decoder
- Policy Gradient: An RL optimization method that directly adjusts the model's output probabilities to increase expected reward.
- REINFORCE: A Monte Carlo policy gradient algorithm that updates model parameters based on completed sampled sequences.
- Log-derivative trick: A mathematical identity (∇log p = ∇p/p) used to turn an expectation of a function of a probability into an expectation of a gradient, making it differentiable.
- Baseline: A reference value (like a mean reward) subtracted from the reward to reduce the variance of the gradient estimate.
Original article
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