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We present a mathematical framework and computational methods to optimallydesign a finite number of sequential experiments. We formulate this sequentialoptimal experimental design (sOED) problem as a finite-horizon partiallyobservable Markov decision process (POMDP) in a Bayesian setting and withinformation-theoretic utilities. It is built to accommodate continuous randomvariables, general non-Gaussian posteriors, and expensive nonlinear forwardmodels. sOED then seeks an optimal design policy that incorporates elements ofboth feedback and lookahead, generalizing the suboptimal batch and greedydesigns. We solve for the sOED policy numerically via policy gradient (PG)methods from reinforcement learning, and derive and prove the PG expression forsOED. Adopting an actor-critic approach, we parameterize the policy and valuefunctions using deep neural networks and improve them using gradient estimatesproduced from simulated episodes of designs and observations. The overallPG-sOED method is validated on a linear-Gaussian benchmark, and its advantagesover batch and greedy designs are demonstrated through a contaminant sourceinversion problem in a convection-diffusion field.

Bayesian Sequential Optimal Experimental Design for Nonlinear Models Using Policy Gradient Reinforcement Learning