Multi-armed Bandits with Missing Outcome
This addresses a practical challenge in online decision-making for applications where data is incomplete, offering a rigorous methodology to prevent biased outcomes, though it is incremental as it builds on existing bandit frameworks.
The paper tackles the problem of missing outcomes in multi-armed bandits, which can cause biased reward estimates and linear regret, by introducing algorithms that handle missingness under MAR and MNAR models, showing drastic improvements in decision-making through analysis and simulations.
While significant progress has been made in designing algorithms that minimize regret in online decision-making, real-world scenarios often introduce additional complexities, perhaps the most challenging of which is missing outcomes. Overlooking this aspect or simply assuming random missingness invariably leads to biased estimates of the rewards and may result in linear regret. Despite the practical relevance of this challenge, no rigorous methodology currently exists for systematically handling missingness, especially when the missingness mechanism is not random. In this paper, we address this gap in the context of multi-armed bandits (MAB) with missing outcomes by analyzing the impact of different missingness mechanisms on achievable regret bounds. We introduce algorithms that account for missingness under both missing at random (MAR) and missing not at random (MNAR) models. Through both analytical and simulation studies, we demonstrate the drastic improvements in decision-making by accounting for missingness in these settings.