Multidimensional Bayesian Estimation for Deep Brain Stimulation Using the SafeOpt Algorithm

Some symptoms treated with Deep Brain Stimulation (DBS) such as gait in Parkinson's disease (PD), are often poorly responsive to DBS. This may be because DBS settings are usually optimized to other symptoms. To test this, we require an efficient, safe optimization algorithm. To develop such a tool, we extend the BayesOpt algorithm whose successful application to DBS settings we previously published [Louie et al 2021 J Neuroeng Rehabil], using, as a test bed, a simulated cost function constructed for biological plausibility, with measurement noise based on experimental data. We found that the SafeOpt algorithm [Sui et al 2015 Proc Machine Learning Res] converged to the optimum as well, and as fast as the BayesOpt algorithm, while avoiding high-cost points much more effectively. In three dimensions, SafeOpt converged in about 30 iterations, which is a feasible number for physical (not simulated) experiments in real patients. Convergence was slower when measurement nose was greater, but this could be overcome by running it for more iterations. The algorithm was relatively robust to misspecification of hyperparameters, and considerably more robust when hyperparameter fitting was incorporated into the algorithm. The algorithm did not perform as well when the quantization of stimulation settings was coarser, suggesting that it will work better with neurostimulators capable of independent current control. Finally, the algorithm was able to cope with a cost function having multiple local minima.