Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods

We introduce implicit Deep Adaptive Design (iDAD), a new method for performing adaptive experiments in real-time with implicit models. iDAD amortizes the cost of Bayesian optimal experimental design (BOED) by learning a design policy network upfront, which can then be deployed quickly at the time of the experiment. The iDAD network can be trained on any model which simulates differentiable samples, unlike previous design policy work that requires a closed form likelihood and conditionally independent experiments. At deployment, iDAD allows design decisions to be made in milliseconds, in contrast to traditional BOED approaches that require heavy computation during the experiment itself. We illustrate the applicability of iDAD on a number of experiments, and show that it provides a fast and effective mechanism for performing adaptive design with implicit models. Recently, Foster et al. [17] proposed an exciting alternative approach, called Deep Adaptive Design (DAD), that is based on learning design policies. DAD provides a way to avoid significant computation 35th Conference on Neural Information Processing Systems (NeurIPS 2021). We also relax DAD's requirement for experiments to be conditionally independent, allowing its application in complex settings like time series data, and, through innovative architecture adaptations, also provide improvements in the conditionally independent setting as well. This further expands the model space for policy-based BOED, and leads to additional performance improvements. Critically, iDAD forms the first method in the literature that can practically perform real-time adaptive BOED with implicit models: previous approaches are either not fast enough to run in real-time for non-trivial models, or require explicit likelihood models. We illustrate the applicability of iDAD on a range of experimental design problems, highlighting its benefits over existing baselines, even finding that it often outperforms costly non-amortized approaches. Code for iDAD is publicly available at https://github.com/desi-ivanova/idad . Background The BOED framework [32] begins by specifying a Bayesian model of the experimental process, consisting of a prior on the unknown parameters p(θ), a set of controllable designs ξ, and a data generating process that depends on them y|θ, ξ; as usual in BOED, we assume that p(θ) does not depend on ξ. In this paper, we consider the situation where y|θ, ξ is specified implicitly. This means