A Bayesian Approach to Learning Bandit Structure in Markov Decision Processes

TL;DR

This paper introduces a Bayesian online algorithm that helps determine whether a decision-making environment is better modeled as a contextual bandit or an MDP, improving learning efficiency and robustness.

Contribution

It presents a Bayesian hypothesis testing approach that incorporates prior knowledge to adaptively distinguish between CB and MDP environments, interpolating between the two models.

Findings

Lower regret in CB settings compared to MDP algorithms

Effective learning of optimal policy in MDP settings

Robustness to environment misspecification

Abstract

In the reinforcement learning literature, there are many algorithms developed for either Contextual Bandit (CB) or Markov Decision Processes (MDP) environments. However, when deploying reinforcement learning algorithms in the real world, even with domain expertise, it is often difficult to know whether it is appropriate to treat a sequential decision making problem as a CB or an MDP. In other words, do actions affect future states, or only the immediate rewards? Making the wrong assumption regarding the nature of the environment can lead to inefficient learning, or even prevent the algorithm from ever learning an optimal policy, even with infinite data. In this work we develop an online algorithm that uses a Bayesian hypothesis testing approach to learn the nature of the environment. Our algorithm allows practitioners to incorporate prior knowledge about whether the environment is that of a CB or an MDP, and effectively interpolate between classical CB and MDP-based algorithms to mitigate against the effects of misspecifying the environment. We perform simulations and demonstrate that in CB settings our algorithm achieves lower regret than MDP-based algorithms, while in non-bandit MDP settings our algorithm is able to learn the optimal policy, often achieving comparable regret to MDP-based algorithms.