  We propose a new procedure named PASOA, for Bayesian experimental design,
that performs sequential design optimization by simultaneously providing
accurate estimates of successive posterior distributions for parameter
inference. The sequential design process is carried out via a contrastive
estimation principle, using stochastic optimization and Sequential Monte Carlo
(SMC) samplers to maximise the Expected Information Gain (EIG). As larger
information gains are obtained for larger distances between successive
posterior distributions, this EIG objective may worsen classical SMC
performance. To handle this issue, tempering is proposed to have both a large
information gain and an accurate SMC sampling, that we show is crucial for
performance. This novel combination of stochastic optimization and tempered SMC
allows to jointly handle design optimization and parameter inference. We
provide a proof that the obtained optimal design estimators benefit from some
consistency property. Numerical experiments confirm the potential of the
approach, which outperforms other recent existing procedures.
