Accelerated searches, made possible by machine learning techniques, are of growing interest in materials discovery. A suitable case involves the solution processing of components that ultimately form thin films of solar cell materials known as hybrid organic-inorganic perovskites (HOIPs). The number of molecular species that combine in solution to form these films constitutes an overwhelmingly large "compositional" space (at times, exceeding 500,000 possible combinations). Selecting a HOIP with desirable characteristics involves choosing different cations, halides, and solvent blends from a diverse palette of options. An unguided search by experimental investigations or molecular simulations is prohibitively expensive. In this work, we propose a Bayesian optimization method that uses an application-specific kernel to overcome challenges where data is scarce, and in which the search space is given by binary variables indicating whether a constituent is present or not. We demonstrate that the proposed approach identifies HOIPs with the targeted maximum intermolecular binding energy between HOIP salt and solvent at considerably lower cost than previous state-of-the-art Bayesian optimization methodology and at a fraction of the time (less than 10%) needed to complete an exhaustive search. We find an optimal composition within 15 ± 10 iterations in a HOIP compositional space containing 72 combinations, and within 31 ± 9 iterations when considering mixed halides (240 combinations). Exhaustive quantum mechanical simulations of all possible combinations were used to validate the optimal prediction from a Bayesian optimization approach. This paper demonstrates the potential of the Bayesian optimization methodology reported here for new materials discovery.

We consider restless multi-armed bandit (RMAB) with a finite horizon and multiple pulls per period. Leveraging the Lagrangian relaxation, we approximate the problem with a collection of single arm problems. We then propose an index-based policy that uses optimal solutions of the single arm problems to index individual arms, and offer a proof that it is asymptotically optimal as the number of arms tends to infinity. We also use simulation to show that this index-based policy performs better than the state-of-art heuristics in various problem settings.

We consider the problem of multiple comparisons with a known standard, in which we wish to allocate simulation effort efficiently across a finite number of simulated systems, to determine which systems have mean performance exceeding a known threshold. We suppose that parallel computing resources are available, and that we are given a fixed simulation budget. We consider this problem in a Bayesian setting, and formulate it as a stochastic dynamic program. For simplicity, we focus on Bernoulli sampling, with a linear loss function. Using links to restless multi-armed bandits, we provide a computationally tractable upper bound on the value of the Bayes-optimal policy, and an index policy motivated by these upper bounds.