Provably learning from language feedback

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