Bayesian Experimental Design

While adaptive experimental design has outgrown one-dimensional, staircase-based adaptations, most cognitive experiments still control a single factor and summarize performance with a scalar. In contrast, we validate here a Bayesian, two-axis, active-classification approach in an immersive virtual testing environment, using a 5-by-5 spatial working-memory reconstruction task as an application domain. Two variables are controlled: spatial load L (number of occupied tiles) and feature-binding load K (number of distinct colors) of items. Stimulus acquisition is guided by posterior uncertainty of a nonparametric Gaussian Process (GP) probabilistic classifier, which outputs a surface over (L, K) rather than a single threshold or maximum span value. In a young adult population, we compare GP-driven Adaptive Mode (AM) with a traditional adaptive staircase Classic Mode (CM), which varies L only at K = 3. Parity between the methods is achieved for this cohort, with an intraclass correlation coefficient of 0.755 at K = 3. As a secondary exploratory result, AM reveals individual differences in interactions between spatial load and feature binding. AM estimates converge more quickly than other sampling strategies, demonstrating that only about 30 samples are required for accurate fitting of the full model.

General chemical reaction conditions that achieve consistently high performance across multiple substrates are important for practical applications such as library synthesis and high-throughput experimentation. However, identifying such conditions efficiently has been a longstanding challenge, as it requires decision making under uncertainty with respect to both conditions and substrates, while minimizing the number of required experiments. Here, we introduce CurryBO, a high-level framework for generality-oriented optimization. By formalizing the problem as Bayesian optimization over curried functions, CurryBO provides a unified framework that accommodates different generality definitions (e.g., mean yield across substrates), and supports a range of substrate and condition selection strategies. We evaluate this framework on four benchmark tasks in experimental reaction optimization, and systematically analyze key algorithmic components. Our results show that efficient experiment planning can be achieved by emphasizing exploration when selecting reaction conditions, followed by the uncertainty-guided prioritization of substrates in a sequential decison-making scheme. Based on these insights, we design and validate an optimization policy that substantially improves sample efficiency relative to previously reported approaches across all benchmarks. Overall, the flexibility and modularity of CurryBO facilitate the integration of generality-oriented optimization into experimental settings, enabling more efficient identification of solutions that perform robustly across diverse tasks.

This paper presents a fully probabilistic approach for solving optimal experimental design problems under budget constraints. The experimental design is viewed as a random variable and is associated with a parametric conditional distribution that inherently models the budget constraints. The original optimization problem is replaced with an optimization over the expected value of the original objective, which is then optimized over the distribution parameters. The resulting optimal parameter (policy) is used to sample the feasible region of binary space to produce estimates of the optimal solution(s) of the original optimization problem. In this work we extend the family of conditional Bernoulli models to model the random variable conditioned by the total number of nonzero entries, that is, the budget constraint. This approach (a) is generally applicable to binary optimization problems with nonstochastic black-box objective functions and budget constraints; (b) employs conditional probabilities to model and sample only the feasible region and thus considerably reduces the computational cost compared with employing soft constraints; and (c) does not employ soft constraints and thus does not require tuning of a regularization parameter, for example to promote sparsity, which is generally challenging. The proposed approach is verified numerically using an optimal sensor placement experiment based on an advection-diffusion forward model in a parameter identification setup.