Group Distributionally Robust Optimization-Driven RL for LLM Reasoning

Abstract

Reasoning post-training with GRPO is typically built on *static uniformity*: uniform prompt sampling and a fixed number of rollouts per prompt. For heterogeneous, heavy-tailed reasoning data, this wastes compute on already-solved patterns while under-training the long tail of hard problems. We cast GRPO post-training as *two independent GDRO games* (not coupled) over *dynamic difficulty groups* defined online by pass@8: a *data adversary* that reshapes prompt sampling and a *compute adversary* that redistributes rollouts. **Prompt-GDRO** applies multiplicative-weights reweighting over bins (with an EMA-debiased difficulty score) to upweight persistently hard groups without frequency bias. **Rollout-GDRO** allocates rollouts across bins under a fixed *mean* budget via a shadow-price controller, improving gradient information efficiency on high-uncertainty groups while remaining compute-neutral. Our approach is principled and theory-driven: we provide no-regret guarantees for the Prompt-GDRO game (via an entropy-regularized GDRO surrogate) and a variance-proxy analysis that yields a square-root optimal compute allocation for Rollout-GDRO. On DAPO 14.1k with Qwen3-Base (1.7B/4B/8B), each controller improves pass@8 by 9-13\% over GRPO, and diagnostics reveal an emergent curriculum that tracks the evolving reasoning frontier.