Fast adaptation to changes in the environment requires both natural and artificial agents to be able to dynamically tune an exploration-exploitation trade-off during learning. This trade-off usually determines a fixed proportion of exploitative choices (i.e. choice of the action that subjectively appears as best at a given moment) relative to exploratory choices (i.e. testing other actions that now appear worst but may turn out promising later). The problem of finding an efficient exploration-exploitation trade-off has been well studied both in the Machine Learning and Computational Neuroscience fields. Rather than using a fixed proportion, non-stationary multi-armed bandit methods in the former have proven that principles such as exploring actions that have not been tested for a long time can lead to performance closer to optimal - bounded regret. In parallel, researches in the latter have investigated solutions such as progressively increasing exploita- tion in response to improvements of performance, transiently increasing exploration in response to drops in average performance, or attributing exploration bonuses specifically to actions associated with high uncertainty in order to gain information when performing these actions. In this work, we first try to bridge some of these different methods from the two research fields by rewriting their decision process with a common formalism. We then show numerical simulations of a hybrid algorithm combining bio-inspired meta-learning, kalman filter and exploration bonuses compared to several state-of-the-art alternatives on a set of non-stationary stochastic multi-armed bandit tasks. While we find that different methods are appropriate in different scenarios, the hybrid algorithm displays a good combination of advantages from different methods and outperforms these methods in the studied scenarios.