Sensitivity-Free Gradient Descent Algorithms

We introduce two block coordinate descent algorithms for solving optimization problems with ordinary differential equations (ODEs) as dynamical constraints. In contrast to prior algorithms, ours do not need to implement sensitivity analysis methods to evaluate loss function gradients. They result from the reformulation of the original problem as an equivalent optimization problem with equality constraints. In our first algorithm we avoid explicitly solving the ODE by integrating the ODE solver as a sequence of implicit constraints. In our second algorithm, …

algorithms analysis constraints contrast differential equality free function gradient loss optimization ordinary prior sensitivity