Beyond local optimality: An improved approach to hybrid model learning

Local convergence is a limitation of many optimization approaches for multimodal functions. For hybrid model learning, this can mean a compromise in accuracy. We develop an approach for learning the model parameters of hybrid discrete-continuous systems that avoids getting stuck in locally optimal solutions. We present an algorithm that implements this approach that 1) iteratively learns the locations and shapes of explored local maxima of the likelihood function, and 2) focuses the search away from these areas of the solution space, toward undiscovered maxima that are a priori likely to be optimal solutions. We evaluate the algorithm on autonomous underwater vehicle (AUV) data. Our aggregate results show reduction in distance to the global maximum by 16% in 10 iterations, averaged over 100 trials, and iterative increase in log-likelihood value of learned model parameters, demonstrating the ability of the algorithm to guide the search toward increasingly better optima of the likelihood function, avoiding local convergence.