RL for Reasoning by Adaptively Revealing Rationales

Abstract

Learning in the combinatorially large output space of sequence generation problems is challenging as providing expert demonstrations scales poorly with sequence length, and RL struggles with sparse rewards. Between dense demonstrations in supervised training and no demonstrations in reinforcement learning lies an underexplored regime: partial supervision. We ask whether some classes of sequence learning problems become efficiently learnable by exploiting this gap. We address this by introducing adaptive backtracking (AdaBack), a per-sample curriculum learning algorithm that reveals a partial prefix of the target output. The supervision length is adjusted dynamically for each sample based on the model's past reward signal, allowing it to incrementally learn to complete reasoning chains by conditioning on correct partial solutions. We investigate this intermediate regime between SFT and RL and argue that per-sample curriculum learning is more than a trade-off between efficiency and generality--it can succeed in tasks with long sequences of latent dependencies where SFT and RL both fail to generalize. Using a synthetic task with latent parity constraints, we show that AdaBack reliably solves problems that are otherwise intractable. On three mathematical reasoning benchmarks, DeepScaleR, MATH, and GSM8k, we find that AdaBack enables models to solve problems that RL alone cannot, acquiring new reasoning capabilities through incremental exposure to partial solutions.