arxiv:2605.15113

Learning from Language Feedback via Variational Policy Distillation

Published on May 18

· Submitted by

Yang Li on May 21

Salesforce AI Research

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Abstract

Variational Policy Distillation enables reinforcement learning from language feedback by co-evolving teacher and student policies through variational expectation-maximization, overcoming limitations of passive distillation in complex reasoning tasks.

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Reinforcement learning from verifiable rewards (RLVR) suffers from sparse outcome signals, creating severe exploration bottlenecks on complex reasoning tasks. Recent on-policy self-distillation methods attempt to address this by utilizing language feedback to generate dense, token-level supervision. However, these approaches rely on a fixed, passive teacher to interpret the feedback. As the student policy improves, the teacher's zero-shot assessment capabilities plateau, ultimately halting further learning. To overcome this, we propose Variational Policy Distillation (VPD), a framework that formalizes learning from language feedback as a Variational Expectation-Maximization (EM) problem. VPD co-evolves both policies: in the E-step, the teacher is actively refined on trajectory outcomes via an adaptive trust-region update, translating textual feedback into a dynamically improved target token distribution. In the M-step, the student internalizes this dense distributional guidance on its own on-policy rollouts. By continuously improving the teacher's ability to extract actionable signals from textual critique, VPD overcomes the limitations of passive distillation. Evaluated across diverse sources of diagnostic feedback on scientific reasoning and code generation tasks, VPD consistently outperforms both standard RLVR and existing self-distillation baselines. Finally, by stress-testing our framework on rigid mathematical reasoning and cold-start regimes, we illuminate the fundamental bounds of feedback-driven self-distillation compared to pure environment-driven RL.

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yli-ml

Paper submitter about 15 hours ago

Variational Policy Distillation (VPD) addresses a key limitation of reinforcement learning from verifiable rewards (RLVR): the binary reward signal discards all information from near-miss failures. A coding solution that fails 1 test out of 50 gets the same reward as random noise, even though the compiler error tells you exactly what went wrong.

VPD formalizes learning from language feedback (compiler errors, LLM critiques, self-corrections) as a variational EM problem. Unlike prior self-distillation methods that treat the feedback-conditioned teacher as a frozen function, VPD co-trains the teacher and student in an alternating loop:

E-step: refine the teacher's ability to interpret feedback via preference optimization
M-step: distill the improved teacher into the student on its own rollouts

Both share a single network, so there's zero additional memory overhead.

We evaluate on 3 model families (Qwen3-4B, Qwen3-8B, Llama-3.1-8B) across code generation (LiveCodeBench) and scientific reasoning (SciKnowEval). VPD consistently improves over GRPO and self-distillation baselines, with notably more stable training dynamics. We also characterize where the approach has limitations — on strict mathematical reasoning where error feedback is less informative, standard RL remains stronger.

Happy to discuss — feedback welcome!