  Living organisms exhibit remarkable adaptations across all scales, from
molecules to ecosystems. We believe that many of these adaptations correspond
to optimal solutions driven by evolution, training, and underlying physical and
chemical laws and constraints. While some argue against such optimality
principles due to their potential ambiguity, we propose generalized inverse
optimal control to infer them directly from data. This novel approach
incorporates multi-criteria optimality, nestedness of objective functions on
different scales, the presence of active constraints, the possibility of
switches of optimality principles during the observed time horizon,
maximization of robustness, and minimization of time as important special
cases, as well as uncertainties involved with the mathematical modeling of
biological systems. This data-driven approach ensures that optimality
principles are not merely theoretical constructs but are firmly rooted in
experimental observations. Furthermore, the inferred principles can be used in
forward optimal control to predict and manipulate biological systems, with
possible applications in bio-medicine, biotechnology, and agriculture. As
discussed and illustrated, the well-posed problem formulation and the inference
are challenging and require a substantial interdisciplinary effort in the
development of theory and robust numerical methods.
