Definition
Plain language
A basic math inequality that puts a ceiling on how big a certain combination of two things can get.
As stated in the literature
The Cauchy-Schwarz inequality bounding inner products by the product of norms; used in this corpus to prove that low reward variance caps the magnitude of policy gradients.
Why it matters: It's a foundational inequality that recurs across math and ML proofs, including in arguments about when RL training has enough signal to learn anything.
For example, applying Cauchy-Schwarz, you can show that if a model's reward signal has almost no variance across samples, the resulting policy gradient must be small.
Heard on the show
“… Using a Cauchy-Schwarz argument — which is just a couple of lines — they show that the size of the task gradient on …”Episode 010 — When Reward Climbs But Reasoning Goes Generic: Diagnosing Template Collapse in Agentic RL