Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design (2103.02438v2)

Abstract: We introduce Deep Adaptive Design (DAD), a method for amortizing the cost of adaptive Bayesian experimental design that allows experiments to be run in real-time. Traditional sequential Bayesian optimal experimental design approaches require substantial computation at each stage of the experiment. This makes them unsuitable for most real-world applications, where decisions must typically be made quickly. DAD addresses this restriction by learning an amortized design network upfront and then using this to rapidly run (multiple) adaptive experiments at deployment time. This network represents a design policy which takes as input the data from previous steps, and outputs the next design using a single forward pass; these design decisions can be made in milliseconds during the live experiment. To train the network, we introduce contrastive information bounds that are suitable objectives for the sequential setting, and propose a customized network architecture that exploits key symmetries. We demonstrate that DAD successfully amortizes the process of experimental design, outperforming alternative strategies on a number of problems.

• The paper introduces Deep Adaptive Design (DAD) to amortize sequential Bayesian experimental design, reducing computational costs for adaptive experiments.
• The paper leverages a neural network trained on simulated data with contrastive information bounds to enable swift, near-optimal design decisions in real time.
• The paper validates DAD across diverse settings, demonstrating its superior performance and potential for real-time adaptive experimentation.

Overview of Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design

The paper "Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design" addresses the computational challenges inherent in traditional Bayesian optimal experimental design (BOED) methods when applied sequentially. The authors introduce a novel method, Deep Adaptive Design (DAD), which aims to amortize the cost of adaptive BOED, enabling it to be employed in real-time applications.

In conventional sequential BOED, the process involves iteratively updating posterior distributions and optimizing experimental designs, which poses significant computational challenges, making real-time implementation infeasible. DAD overcomes this by leveraging deep learning to pre-train a design network that can make swift design decisions during live experiments based on previous data, alleviating the computational bottleneck.

Methodology

DAD hinges on learning a design policy, represented as a neural network, which takes the history of past design-outcome pairs and outputs an optimal design for the next experiment. This contrasts with traditional approaches that require real-time inference and optimization. The network is trained using simulated experimental data trajectories, thereby enabling it to approximate near-optimal design decisions swiftly at deployment.

A significant innovation in the paper is the introduction of contrastive information bounds for training the network, allowing for end-to-end optimization without the need for posterior estimation at each step. These bounds help in constructing unbiased gradient estimates, thereby facilitating efficient training of the design network.

The proposed architecture exploits permutation invariance properties of the BOED problem, leading to a network capable of effectively generalizing across varying experiment lengths. The network architecture incorporates a pooling layer to create invariant representations of experiment histories, enhancing its learning efficiency and efficacy.

Experimental Validation and Findings

The authors validate DAD across several experimental settings, including locating hidden sources in a 2D space, a psychological model involving temporal discounting, and a biomedical infection modeling scenario. In all these cases, DAD demonstrates superior performance over fixed design strategies and non-adaptive methods, while also achieving faster deployment times compared to traditional adaptive approaches.

In the location finding task, DAD's network learns a sophisticated design strategy that significantly outperforms fixed baselines, underscoring the value of adaptive experimentation. The method exhibits robustness in generalizing to varying design horizons, highlighting its flexibility.

Crucially, DAD also challenges the hypothesis that amortizing BOED inherently leads to a loss in performance compared to non-amortized methods. The results reveal that DAD not only matches but often exceeds the efficacy of traditional methods, due in part to its ability to approximate non-myopic strategies that consider the sequences of future decisions.

Implications and Future Directions

The introduction of DAD signifies a notable advancement in the practical applicability of BOED in various fields, such as online surveys and clinical trials, where real-time adaptive experimentation is crucial. By significantly reducing the computational overhead associated with adaptive BOED, the method opens up the possibility for broader application across disciplines that require rapid decision-making.

The research indicates promising potential for further exploration in areas such as design for complex models, integration with reinforcement learning frameworks, and expansion into implicit likelihood models. Future work could also address the current constraints such as the need for explicit likelihoods and explore more sophisticated policy representations and inference strategies.

In summary, the paper presents a compelling approach to breaking the computation barrier in sequential BOED, providing both theoretical and practical contributions that could considerably impact experimental sciences and engineering disciplines.