Analysis of Kimi K3 Reinforcement Learning Loss Derivation
brianryhuang · x · 2026-07-31
Researcher Manan Tomar shared notes on the derivation of the reinforcement learning (RL) loss function used for the Kimi K3 model.
Starting from a Mirror Descent formulation and plugging in a softmax policy—standard for computing token probabilities—it naturally leads to a symmetric loss function. This function incorporates clipping to handle async train/inference mismatches and KL penalization to maintain trust region properties. The author appreciates that a frontier-level model adopts such a principled, clean recipe without needing unnecessary bells and whistles.
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