  This paper studies the problem of performing a sequence of optimal
interventions in a causal dynamical system where both the target variable of
interest and the inputs evolve over time. This problem arises in a variety of
domains e.g. system biology and operational research. Dynamic Causal Bayesian
Optimization (DCBO) brings together ideas from sequential decision making,
causal inference and Gaussian process (GP) emulation. DCBO is useful in
scenarios where all causal effects in a graph are changing over time. At every
time step DCBO identifies a local optimal intervention by integrating both
observational and past interventional data collected from the system. We give
theoretical results detailing how one can transfer interventional information
across time steps and define a dynamic causal GP model which can be used to
quantify uncertainty and find optimal interventions in practice. We demonstrate
how DCBO identifies optimal interventions faster than competing approaches in
multiple settings and applications.
