Towards optimization of a human-inspired heuristic for solving explore-exploit problems

Motivated by models of human decision making, we consider a heuristic solution for explore-exploit problems. In a numerical example we show that, with appropriate parameter values, the algorithm performs well. However, the parameters of the algorithm trade off exploration against exploitation in a complicated way so that finding the optimal parameter values is not obvious. We show that the optimal parameter values can be analytically computed in some cases and prove that suboptimal parameter tunings can provide robustness to modeling error. The analytic results suggest a feedback control law for dynamically optimizing parameters.