Information maximization for generalized multiarmed bandit games

Information and free-energy maximization are physics principles that provide general rules for an agent to optimize actions in line with specific goals and policies. These principles can serve as building blocks for designing decision-making policies capable of efficient performance with only partial information. Notably, the information-maximization principle has shown remarkable success in the classical bandit problem and has recently been shown to yield optimal algorithms for Gaussian and sub-Gaussian reward distributions. This article explores a broad extension of physics-based approaches to more complex and structured bandit problems. To this end, we cover three distinct types of bandit problems, where information maximization is adapted and leads to strong performance for Gaussian and Bernoulli reward distributions. Since the main challenge of information maximization lies in avoiding overexploration, we highlight how information is tailored at various levels to mitigate this issue, paving the way for more efficient and robust decision-making strategies.