Transition Constrained Bayesian Optimization via Markov Decision
  Processes
Jose Pablo Folch Calvin Tsay Robert M Lee Behrang Shafei Weronika Ormaniec Andreas Krause Mark van der Wilk Ruth Misener Mojmír Mutný
Bayesian optimization is a methodology to optimize black-box functions.
Traditionally, it focuses on the setting where you can arbitrarily query the
search space. However, many real-life problems do not offer this flexibility;
in particular, the search space of the next query may depend on previous ones.
Example challenges arise in the physical sciences in the form of local movement
constraints, required monotonicity in certain variables, and transitions
influencing the accuracy of measurements. Altogether, such transition
constraints necessitate a form of planning. This work extends Bayesian
optimization via the framework of Markov Decision Processes, iteratively
solving a tractable linearization of our objective using reinforcement learning
to obtain a policy that plans ahead over long horizons. The resulting policy is
potentially history-dependent and non-Markovian. We showcase applications in
chemical reactor optimization, informative path planning, machine calibration,
and other synthetic examples.