The Multiple Ticket Hypothesis: Random Sparse Subnetworks Suffice for RLVR
This work addresses efficiency in RLVR for AI practitioners by demonstrating that extreme sparsity is viable, though it is incremental as it builds on the Lottery Ticket Hypothesis.
The paper tackles the problem of parameter redundancy in pretrained models for Reinforcement Learning with Verifiable Rewards (RLVR) by showing that training only 1% of randomly selected parameters matches or exceeds full-parameter finetuning across 3 models and 2 task domains, with minimal overlap between successful sparse masks.
The Lottery Ticket Hypothesis demonstrated that sparse subnetworks can match full-model performance, suggesting parameter redundancy. Meanwhile, in Reinforcement Learning with Verifiable Rewards (RLVR), recent work has shown that updates concentrate on a sparse subset of parameters, which further lends evidence to this underlying redundancy. We study the simplest possible way to exploit this redundancy: training only a randomly selected subset of parameters at extreme sparsities. Empirically, we find that training just 1\% of parameters matches or exceeds full-parameter RLVR finetuning across 3 models and 2 task domains. Moreover, different random masks show minimal overlap ($\leq 0.005$ Jaccard similarity) and yet all succeed, suggesting pretrained models contain many viable sparse subnetworks rather than one privileged set. We term this the Multiple Ticket Hypothesis. We explain this phenomenon through the implicit per-step KL constraint in RLVR, which restricts updates to a low-dimensional subspace, enabling arbitrary sparse masks to succeed.