Summary
Reinforcement learning with verifiable rewards (RLVR) aims to learn reasoning skills through trial and error with clear feedback. The authors studied how RLVR behaves when learning to multiply elements repeatedly in certain structured ways. They found that the underlying landscape guiding learning doesn’t have many tricky local traps that would block learning. Instead, the real challenges are technical issues like how noisy the feedback is and how the learning process explores options. Their findings help explain why some tasks are hard yet not because of complicated landscapes, and they show that tuning certain parameters can ease these difficulties.
What this means in practice
- •For machine learning engineers: Design RL algorithms with better entropy tuning to avoid optimization traps on algorithmic tasks.
- •For ai system architects: Improve training strategies for transformer models handling symbolic reasoning by understanding landscape-related obstacles.
Tested on simulated data.
Abstract
Despite the importance of reinforcement learning with verifiable rewards (RLVR), the extent to which it can learn new reasoning capabilities remains debated. Here we study the optimization landscape of RLVR on algorithmic tasks, such as iterated group and quasigroup multiplication. To this end, we map entropy-regularized RLVR over myopic tabular policies onto an energy-based (spin-glass) model over deterministic policies. This mapping upper-bounds what RLVR can achieve, and lets us rigorously characterize the landscape in this tabular setting. We show, both theoretically and experimentally, that for a wide class of models and tasks with uncorrelated inputs, this landscape is benign, containing no local minima that could trap RLVR training. Rather, the practical difficulty of these tasks appears to stem, at least in part, from issues such as diffusive barriers and gradient-estimation error in traversing the landscape. These are genuine obstacles that can prevent a solution from being found, but they are distinct from the landscape itself being rugged. We show that these obstacles can often be mitigated through the choice of entropy regulator. Consistent with this theory, we find that a transformer trained from scratch, using only last-token rewards, successfully learns an algorithmic chain of thought for iterated non-Abelian group multiplications.