Wrong the Same Way: Cross-Prompt Sharing Both Suppresses and Amplifies Reward Hacking in RLVR

arXiv:2611.13218v1 Announce Type: new Abstract: Two accounts of how reinforcement learning with verifiable rewards (RLVR) interacts with an imperfect verifier coexist: in one, reward hacking is inherited from the base model; in the other, RL amplifies it. We study both in a controlled environment small enough to compute the entire response distribution exactly. We vary the universality of a leak, or the fraction of prompts that accept the same wrong response, and the verifier's static false-positive rate. At its KL-regularized optimum, RLVR acts as a filter that reweights the accepted set without altering its composition, so the hack rate is inherited exactly.