Inverse Contextual Bandits without Rewards: Learning from a Non-Stationary Learner via Suffix Imitation

TL;DR

This paper introduces a two-phase imitation framework for inverse contextual bandits that enables a passive observer to recover optimal policies from non-stationary action data without access to rewards, matching the efficiency of reward-aware learners.

Contribution

The paper proposes a novel Two-Phase Suffix Imitation method that effectively learns from non-stationary data in inverse bandit problems without reward information, providing theoretical guarantees.

Findings

Passive observer achieves $ ilde O(1/ oot N)$ convergence rate.

Framework handles non-stationary exploration-exploitation data.

Performance matches reward-aware learner asymptotically.

Abstract

We study the Inverse Contextual Bandit (ICB) problem, in which a learner seeks to optimize a policy while an observer, who cannot access the learner's rewards and only observes actions, aims to recover the underlying problem parameters. During the learning process, the learner's behavior naturally transitions from exploration to exploitation, resulting in non-stationary action data that poses significant challenges for the observer. To address this issue, we propose a simple and effective framework called Two-Phase Suffix Imitation. The framework discards data from an initial burn-in phase and performs empirical risk minimization using only data from a subsequent imitation phase. We derive a predictive decision loss bound that explicitly characterizes the bias-variance trade-off induced by the choice of burn-in length. Despite the severe information deficit, we show that a reward-free observer can achieve a convergence rate of $\tilde O(1/\sqrt{N})$, matching the asymptotic efficiency of a fully reward-aware learner. This result demonstrates that a passive observer can effectively uncover the optimal policy from actions alone, attaining performance comparable to that of the learner itself.