Reinforcement Learning from Rich Feedback with Distributional DAgger

• URL: http://arxiv.org/abs/2606.05152v2
• Date: Fri, 05 Jun 2026 17:44:05 GMT
• Title: Reinforcement Learning from Rich Feedback with Distributional DAgger
• Abstract summary: Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow.<n>We study how to use such feedback through a distributional variant of the classic imitation learning algorithm DAgger.<n>This yields a simple forward cross-entropy objective that admits a blackbox expert and whose sequence-level gradient conduct rich credit assignment by propagating future expert-student disagreement.
• Score: 9.188497824291854
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow: sample many responses and reward each with a single bit indicating whether the final answer is correct. Yet many settings provide rich feedback, including execution traces, tool outputs, expert corrections, and model self-evaluations. We study how to use such feedback through a distributional variant of the classic imitation learning algorithm DAgger, where the learner has local access to an expert distribution on states visited by the current policy. This yields a simple forward cross-entropy objective that admits a blackbox expert and whose sequence-level gradient {conduct rich credit assignment by propagating} future expert-student disagreement back to earlier decisions. We show that prior RL with self-distillation objectives based on reverse KL or Jensen-Shannon fail to guarantee monotonic policy improvement: even when the expert has higher reward, their updates may increase probability on worse actions. In contrast, we show that forward cross-entropy admits monotonic policy improvement and enjoys guarantees on regret. We further show that our objective optimizes a lower bound on teacher-weighted likelihood of success, leading to improved Pass@N. Empirically, our approach, DistIL, improves over RLVR and RL with self-distillation baselines across a variety of domains: scientific reasoning, coding, and solving hard mathematical problems.

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