Bayesian Experimental Design (BED) provides a principled framework for informative data collection, and is applied across domains as varied as adaptive clinical trials, ecological monitoring, hyperparameter optimization, and robotic search. Despite this broad applicability, BED methods remain difficult to deploy in practice: high-quality decision-making is computationally expensive, calibrated uncertainty estimation in sequential decision problems is challenging, and classical BED methods lack the mechanisms to leverage the rich, unstructured prior knowledge available in real-world problems. This thesis develops methods that make BED more efficient along each of these axes.

We first present a case study in multi-robot active search, casting the problem as a decentralized batch BED task. Our proposed algorithm, based on myopic posterior sampling, performs robustly across communication and robot failures, validated through field tests with heterogeneous teams of UGVs and UAVs in a 75,000 m2 forested environment. This case study makes a recurring tension in BED concrete: practitioners are routinely forced to trade off decision-making quality to stay within real-time computational budgets. To close this gap, we learn amortized BED policies by leveraging the domain-permutation equivariance inherent in BED problems, which yields markedly more sample-efficient policy and Q-value architectures. We field-test these amortized policies, achieving wall-clock speed-ups of up to 2.86× over our previous baselines to reach the same recall performance. 
Beyond active search, we make two further contributions. First, we introduce Epistemic Bellman equations: a model-based framework for Q-value uncertainty quantification that produces well-calibrated estimates in the bootstrapped Q-learning setting. Our estimates make value uncertainty usable as a primitive in downstream tasks such as robust policy optimization and efficient exploration. Second, we develop methods for incorporating LLM-elicited priors into Bayesian Optimization, leveraging the rich auxiliary information — expert knowledge, scientific literature, intermediate diagnostics, training curves — that is abundant in real-world optimization problems but discarded by standard BO algorithms. Across HPOBench and a real-world nuclear-fusion tokamak stabilization task, our methods consistently outperform both standard BO and prior LLM-based BO approaches.

Together, these contributions broaden the scope of the BED toolkit in the real world.