Policy gradients and GRPO-style training, on a problem you can run
Reinforcement learning with verifiable rewards from first principles: the policy-gradient identity, baselines and group-relative advantages (GRPO), a runnable toy that learns from 0.2 to 0.99 success, and how this maps to real LLM training including KL penalties, clipping and failure modes.
Supervised training teaches a model to imitate. Reinforcement learning (RL) teaches it to achieve: generate attempts, get a reward, make rewarded behaviour more likely. For reasoning with checkable answers (maths, code), the reward is the verifier's verdict (verifiers). This is the idea behind recent reasoning-model training such as the GRPO method.
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