Formalizing Learning from Language Feedback with Provable Guarantees

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 measure to characterize the hardness of LLF problems. We formalize the intuition that information in the feedback governs the learning complexity of LLF problems. 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 an important step towards designing principled interactive learning algorithms from generic language feedback.