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Bayesian Experimental Design (BED), which aims to find the optimalexperimental conditions for Bayesian inference, is usually posed as to optimizethe expected information gain (EIG). The gradient information is often neededfor efficient EIG optimization, and as a result the ability to estimate thegradient of EIG is essential for BED problems. The primary goal of this work isto develop methods for estimating the gradient of EIG, which, combined with thestochastic gradient descent algorithms, result in efficient optimization ofEIG. Specifically, we first introduce a posterior expected representation ofthe EIG gradient with respect to the design variables. Based on this, wepropose two methods for estimating the EIG gradient, UEEG-MCMC that leveragesposterior samples generated through Markov Chain Monte Carlo (MCMC) to estimatethe EIG gradient, and BEEG-AP that focuses on achieving high simulationefficiency by repeatedly using parameter samples. Theoretical analysis andnumerical studies illustrate that UEEG-MCMC is robust agains the actual EIGvalue, while BEEG-AP is more efficient when the EIG value to be optimized issmall. Moreover, both methods show superior performance compared to severalpopular benchmarks in our numerical experiments.

On Estimating the Gradient of the Expected Information Gain in Bayesian Experimental Design