Provably Learning from Language Feedback
Authors: name: Wanqiao Xu, name: Allen Nie, name: Ruijie Zheng, name: Aditya Modi, name: Adith Swaminathan, name: Ching-An Cheng

Interactively learning from observation and language feedback is an
increasingly studied area driven by the emergence of large language model (LLM)
agents. While impressive empirical demonstrations have been shown, so far a
principled framing of these decision problems remains lacking. In this paper,
we formalize the Learning from Language Feedback (LLF) problem, assert
sufficient assumptions to enable learning despite latent rewards, and introduce
transfer eluder dimension as a complexity measure to characterize
the hardness of LLF problems. We show that transfer eluder dimension captures
the intuition that information in the feedback changes the learning complexity
of the LLF problem. We demonstrate cases where learning from rich language
feedback can be exponentially faster than learning from reward. We develop a
no-regret algorithm, called HELiX, that provably solves LLF problems
through sequential interactions, with performance guarantees that scale with
the transfer eluder dimension of the problem. Across several empirical domains,
we show that HELiX performs well even when repeatedly prompting LLMs
does not work reliably. Our contributions mark a first step towards designing
principled interactive learning algorithms from generic language feedback.