Latent Preference Bandits

Bandit algorithms are guaranteed to solve diverse sequential decision-making problems, provided that a sufficient exploration budget is available. However, learning from scratch is often too costly for personalization tasks where a single individual faces only a small number of decision points. Latent bandits offer substantially reduced exploration times for such problems, given that the joint distribution of a latent state and the rewards of actions is known and accurate. In practice, finding such a model is non-trivial, and there may not exist a small number of latent states that explain the responses of all individuals. For example, patients with similar latent conditions may have the same preference in treatments but rate their symptoms on different scales. With this in mind, we propose relaxing the assumptions of latent bandits to require only a model of the \emph{preference ordering} of actions in each latent state. This allows problem instances with the same latent state to vary in their reward distributions, as long as their preference orderings are equal. We give a posterior-sampling algorithm for this problem and demonstrate that its empirical performance is competitive with latent bandits that have full knowledge of the reward distribution when this is well-specified, and outperforms them when reward scales differ between instances with the same latent state.