Asymmetric Prompt Weighting for Reinforcement Learning with Verifiable Rewards

TL;DR

This paper introduces asymmetric prompt weighting in reinforcement learning with verifiable rewards, improving training efficiency especially in low-success scenarios by emphasizing prompts with low or zero success probability.

Contribution

It proposes a novel asymmetric weighting scheme for prompts, supported by theoretical analysis, that accelerates learning in reinforcement learning with verifiable rewards.

Findings

Asymmetric weighting benefits from-scratch RL more than post-SFT RL.

Optimal weights upweight low success probability prompts in low-success regimes.

Theoretical characterization of prompt weights minimizes training time to reach target accuracy.

Abstract

Reinforcement learning with verifiable rewards has driven recent advances in LLM post-training, in particular for reasoning. Policy optimization algorithms generate a number of responses for a given prompt and then effectively weight the corresponding gradients depending on the rewards. The most popular algorithms including GRPO, DAPO, and RLOO focus on ambiguous prompts, i.e., prompts with intermediate success probability, while downgrading gradients with very easy and very hard prompts. In this paper, we consider asymmetric prompt weightings that assign higher weights to prompts with low, or even zero, empirical success probability. We find that asymmetric weighting particularly benefits from-scratch RL (as in R1-Zero), where training traverses a wide accuracy range, and less so in post-SFT RL where the model already starts at high accuracy. We also provide theory that characterizes prompt weights which minimize the time needed to raise success probability from an initial level to a target accuracy under a fixed update budget. In low-success regimes, where informative responses are rare and response cost dominates, these optimal weights become asymmetric, upweighting low success probabilities and thereby accelerating effective-time convergence.