  This paper addresses the exploration-exploitation dilemma inherent in
decision-making, focusing on multi-armed bandit problems. The problems involve
an agent deciding whether to exploit current knowledge for immediate gains or
explore new avenues for potential long-term rewards. We here introduce a novel
algorithm, approximate information maximization (AIM), which employs an
analytical approximation of the entropy gradient to choose which arm to pull at
each point in time. AIM matches the performance of Infomax and Thompson
sampling while also offering enhanced computational speed, determinism, and
tractability. Empirical evaluation of AIM indicates its compliance with the
Lai-Robbins asymptotic bound and demonstrates its robustness for a range of
priors. Its expression is tunable, which allows for specific optimization in
various settings.
