Sequential Bayesian optimal experimental design via approximate dynamic programming
This work addresses the challenge of efficient experimental design for researchers in fields like parameter inference, offering a more optimal approach than existing methods, though it is incremental in advancing numerical techniques for dynamic programming.
The paper tackles the problem of designing sequential experiments optimally, moving beyond suboptimal batch or greedy strategies, by formulating it as a dynamic program and developing numerical methods for nonlinear settings, demonstrating advantages in a nonlinear source inversion problem.
The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new strategies for the optimal design of sequential experiments. First, we rigorously formulate the general sequential optimal experimental design (sOED) problem as a dynamic program. Batch and greedy designs are shown to result from special cases of this formulation. We then focus on sOED for parameter inference, adopting a Bayesian formulation with an information theoretic design objective. To make the problem tractable, we develop new numerical approaches for nonlinear design with continuous parameter, design, and observation spaces. We approximate the optimal policy by using backward induction with regression to construct and refine value function approximations in the dynamic program. The proposed algorithm iteratively generates trajectories via exploration and exploitation to improve approximation accuracy in frequently visited regions of the state space. Numerical results are verified against analytical solutions in a linear-Gaussian setting. Advantages over batch and greedy design are then demonstrated on a nonlinear source inversion problem where we seek an optimal policy for sequential sensing.