Nataša Djurdjevac Conrad, Max von Kleist, Martin Weiser, Sarah Wolf
01.01.2021 − 31.12.2021
Infection spreading and the impact of counteracting policies is today modeled using detailed and complex agent-based models (ABMs). Mathematical optimization methods for these models are lacking. The project develops multilevel methods, exploiting different coarsening options, in support of policy design.
Policy optimization subject to ABMs is computationally challenging due to (i) missing differentiability of single trajectories, i.e. realizations because of inherently discrete decisions of the agents and (ii) the high-dimensional integration required for computing objective expectations. Thus, computing gradients of the objective expectation with respect to policy parameters is extremely expensive.
We will construct multilevel optimization algorithms for ABMs based on deterministic ODE coarse models (and later on SDEs, spatially coarsened, or hierarchical MC approximations) that are fitted to the ABM in order to reproduce its outcome well. Optimizing the coarse models is relatively cheap, and is expected to provide much better trial steps than the gradient direction in nonlinear or ill-conditioned problems.