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

arXiv: https://arxiv.org/abs/2111.02329 · HTML: https://mlsanity.com/paper/2111.02329/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 62 references that are in the map.
- First posted on arXiv 3 Nov 2021.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Stand-Alone Self-Attention in Vision Models](https://mlsanity.com/paper/1906.05909/) (2019)
- [Quantifying the Carbon Emissions of Machine Learning](https://mlsanity.com/paper/1910.09700/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Stabilizing Transformers for Reinforcement Learning](https://mlsanity.com/paper/1910.06764/) (2019)
- [Music Transformer](https://mlsanity.com/paper/1809.04281/) (2018)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [Understanding the Limitations of Variational Mutual Information Estimators](https://mlsanity.com/paper/1910.06222/) (2019)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments](https://mlsanity.com/paper/1911.00294/) (2019)
- [Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimation](https://mlsanity.com/paper/2002.08129/) (2020)
- [Efficient Bayesian Experimental Design for Implicit Models](https://mlsanity.com/paper/1810.09912/) (2018)
- [Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Bounds](https://mlsanity.com/paper/2105.04379/) (2021)
- [Sequential Bayesian Experimental Design for Implicit Models via Mutual Information](https://mlsanity.com/paper/2003.09379/) (2020)

## Built on by (most cited first, 30 of 61)

- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [Optimizing Sequential Experimental Design with Deep Reinforcement Learning](https://mlsanity.com/paper/2202.00821/) (2022)
- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [BED-LLM: Intelligent Information Gathering with LLMs and Bayesian Experimental Design](https://mlsanity.com/paper/2508.21184/) (2025)
- [Amortized Bayesian Experimental Design for Decision-Making](https://mlsanity.com/paper/2411.02064/) (2024)
- [Policy-Based Bayesian Experimental Design for Non-Differentiable Implicit Models](https://mlsanity.com/paper/2203.04272/) (2022)
- [Differentiable Multi-Target Causal Bayesian Experimental Design](https://mlsanity.com/paper/2302.10607/) (2023)
- [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024)
- [Nesting Particle Filters for Experimental Design in Dynamical Systems](https://mlsanity.com/paper/2402.07868/) (2024)
- [Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design](https://mlsanity.com/paper/2507.14057/) (2025)
- [Bayesian Experimental Design via Contrastive Diffusions](https://mlsanity.com/paper/2410.11826/) (2024)
- [Amortized Active Causal Induction with Deep Reinforcement Learning](https://mlsanity.com/paper/2405.16718/) (2024)
- [Variational Sequential Optimal Experimental Design using Reinforcement Learning](https://mlsanity.com/paper/2306.10430/) (2023)
- [PABBO: Preferential Amortized Black-Box Optimization](https://mlsanity.com/paper/2503.00924/) (2025)
- [ALINE: Joint Amortization for Bayesian Inference and Active Data Acquisition](https://mlsanity.com/paper/2506.07259/) (2025)
- [Statistically Efficient Bayesian Sequential Experiment Design via Reinforcement Learning with Cross-Entropy Estimators](https://mlsanity.com/paper/2305.18435/) (2023)
- [Bayesian Active Learning in the Presence of Nuisance Parameters](https://mlsanity.com/paper/2310.14968/) (2023)
- [Statistical applications of contrastive learning](https://mlsanity.com/paper/2204.13999/) (2022)
- [PASOA- PArticle baSed Bayesian Optimal Adaptive design](https://mlsanity.com/paper/2402.07160/) (2024)
- [Active Learning of Model Discrepancy with Bayesian Experimental Design](https://mlsanity.com/paper/2502.05372/) (2025)
- [Bayesian Active Learning for Discrete Latent Variable Models](https://mlsanity.com/paper/2202.13426/) (2022)
- [CO-BED: Information-Theoretic Contextual Optimization via Bayesian Experimental Design](https://mlsanity.com/paper/2302.14015/) (2023)
- [JADAI: Jointly Amortizing Adaptive Design and Bayesian Inference](https://mlsanity.com/paper/2512.22999/) (2025)
- [Efficient Real-world Testing of Causal Decision Making via Bayesian Experimental Design for Contextual Optimisation](https://mlsanity.com/paper/2207.05250/) (2022)
- [Online simulator-based experimental design for cognitive model selection](https://mlsanity.com/paper/2303.02227/) (2023)
- [Experimentation Platforms Meet Reinforcement Learning: Bayesian Sequential Decision-Making for Continuous Monitoring](https://mlsanity.com/paper/2304.00420/) (2023)
- [Designing Optimal Behavioral Experiments Using Machine Learning](https://mlsanity.com/paper/2305.07721/) (2023)
- [Recursive Nested Filtering for Efficient Amortized Bayesian Experimental Design](https://mlsanity.com/paper/2409.05354/) (2024)

## Abstract (arXiv)

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.