Model Calibration with Hierarchically Structured Bayesian Learning Automata

Abstract

When using a hydrological model to estimate the amount of available resources, the accuracy of the estimates depends on the calibration of the model. That is, one needs to nd appropriate values for the model parameters. Calibration of hydrological models requires the exploration of a signi cant search space, rendering traditional gradient descent techniques sub-optimal. The Bayesian learning automaton has emerged as a simple and computationally e cient addition to current, largely evolutionary, calibration techniques. Although particularly well suited for learning in stochastic environments, the automaton struggles with navigating huge action spaces. To alleviate this limitation, we introduce a hierarchically structured variant of the Bayesian learning automaton, applying it to the eld of model calibration and function optimization. Several variants of the automaton is implemented and empirically tested, as well as compared to competing calibration techniques from the literature. The new hierarchically structured automaton shows great promise, improving on action space handling compared to earlier, non-hierarchical structures. Indeed, the computational complexity now grows logarithmically rather than linearly with the size of the action space. Our experiments show that this approach is a viable alternative to competing calibration techniques.