# Constraint Tree Exploration for Learning from Language Feedback

arXiv: https://arxiv.org/abs/2610.09107 · HTML: https://mlsanity.com/paper/2610.09107/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Builds on (most cited first, 4 of 4)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [LLF-Bench: Benchmark for Interactive Learning from Language Feedback](https://mlsanity.com/paper/2312.06853/) (2023)
- [Formalizing Learning from Language Feedback with Provable Guarantees](https://mlsanity.com/paper/2506.10341/) (2025)

## Abstract (arXiv)

Natural-language feedback in interactive learning often explains why an action failed by pointing to violated requirements. Misinterpreting this feedback can lead an agent to rule out valid solutions. We study this setting by modeling user intent as latent constraints over an action space and formulating learning from language feedback as pure exploration over feasible regions. We introduce TRACE, an algorithm that organizes candidate constraints in a tree and tests each proposed refinement by generating actions that satisfy it. TRACE commits to the refinement only if the resulting feedback does not contradict it over repeated tests. We distinguish two ways of using the same feedback: (i) falsification, which detects contradictions to the constraint set currently being tested, and (ii) identification, which may additionally name a violated constraint. We prove high-probability coverage bounds with dependence on the candidate class size H for TRACE-Falsification. With reliable identification, TRACE-Identification can replace this dependence by K/pext, where K is the number of latent constraints and pext lower-bounds the probability of extracting a missing true constraint from informative feedback. We evaluate TRACE across six language-feedback tasks. On RecMovie, TRACE-Identification achieves 73% and 86% final-output success under caps of 20 and 60 evaluated outputs, compared with at most 42% and 48% for the evaluated prompting baselines given the same feedback and output caps. Controlled identity-corruption experiments further show greater robustness than direct accumulation when the falsification detector remains reliable.