Provably Efficient Interactive-Grounded Learning with Personalized Reward

TL;DR

This paper introduces provably efficient algorithms for Interactive-Grounded Learning with personalized, context-dependent rewards, featuring a novel Lipschitz reward estimator that ensures sublinear regret and improved generalization.

Contribution

It provides the first theoretical guarantees for personalized IGL algorithms using a new Lipschitz reward estimator and explores practical applications with image and text feedback.

Findings

The Lipschitz reward estimator outperforms previous step-function estimators.

Algorithms achieve sublinear regret under realizability assumptions.

Experimental results confirm the effectiveness of the proposed methods.

Abstract

Interactive-Grounded Learning (IGL) [Xie et al., 2021] is a powerful framework in which a learner aims at maximizing unobservable rewards through interacting with an environment and observing reward-dependent feedback on the taken actions. To deal with personalized rewards that are ubiquitous in applications such as recommendation systems, Maghakian et al. [2022] study a version of IGL with context-dependent feedback, but their algorithm does not come with theoretical guarantees. In this work, we consider the same problem and provide the first provably efficient algorithms with sublinear regret under realizability. Our analysis reveals that the step-function estimator of prior work can deviate uncontrollably due to finite-sample effects. Our solution is a novel Lipschitz reward estimator which underestimates the true reward and enjoys favorable generalization performances. Building on this estimator, we propose two algorithms, one based on explore-then-exploit and the other based on inverse-gap weighting. We apply IGL to learning from image feedback and learning from text feedback, which are reward-free settings that arise in practice. Experimental results showcase the importance of using our Lipschitz reward estimator and the overall effectiveness of our algorithms.