Identifiable Latent Bandits: Leveraging observational data for personalized decision-making (2407.16239v4)

Abstract: For many decision-making tasks, such as precision medicine, historical data alone are insufficient to determine the right choice for a new problem instance or patient. Online algorithms like multi-armed bandits can find optimal personalized decisions but are notoriously sample-hungry. In practice, training a bandit for a new individual from scratch is often infeasible, as the number of trials required is larger than the practical number of decision points. Latent bandits offer rapid exploration and personalization beyond what context variables can reveal, provided that a latent variable model can be learned consistently. In this work, we propose an identifiable latent bandit framework that leads to optimal decision-making with a shorter exploration time than classical bandits by learning from historical records of decisions and outcomes. Our method is based on nonlinear independent component analysis that provably identifies representations from observational data sufficient to infer the optimal action in new bandit instances. We verify this strategy in simulated and semi-synthetic environments, showing substantial improvement over online and offline learning baselines when identifying conditions are satisfied.