As is well known, both sampling from the posterior and computing the mean of the posterior in Gaussian process regression reduces to solving a large linear system of equations. We study the use of stochastic gradient descent for solving this linear system, and show that when done right---by which we mean using specific insights from the optimisation and kernel communities---stochastic gradient descent is highly effective. To that end, we introduce a particularly simple stochastic dual descent algorithm, explain its design in an intuitive manner and illustrate the design choices through a series of ablation studies. Further experiments demonstrate that our new method is highly competitive. In particular, our evaluations on the UCI regression tasks and on Bayesian optimisation set our approach apart from preconditioned conjugate gradients and variational Gaussian process approximations. Moreover, our method places Gaussian process regression on par with state-of-the-art graph neural networks for molecular binding affinity prediction.

Retrosynthesis is the task of planning a series of chemical reactions to create a desired molecule from simpler, buyable molecules. While previous works have proposed algorithms to find optimal solutions for a range of metrics (e.g. shortest, lowest-cost), these works generally overlook the fact that we have imperfect knowledge of the space of possible reactions, meaning plans created by algorithms may not work in a laboratory. In this paper we propose a novel formulation of retrosynthesis in terms of stochastic processes to account for this uncertainty. We then propose a novel greedy algorithm called retro-fallback which maximizes the probability that at least one synthesis plan can be executed in the lab. Using in-silico benchmarks we demonstrate that retro-fallback generally produces better sets of synthesis plans than the popular MCTS and retro* algorithms.

Retrosynthesis, which aims to find a route to synthesize a target molecule from commercially available starting materials, is a critical task in drug discovery and materials design. Recently, the combination of ML-based single-step reaction predictors with multi-step planners has led to promising results. However, the single-step predictors are mostly trained offline to optimize the single-step accuracy, without considering complete routes. Here, we leverage reinforcement learning (RL) to improve the single-step predictor, by using a tree-shaped MDP to optimize complete routes. Specifically, we propose a novel online training algorithm, called Planning with Dual Value Networks (PDVN), which alternates between the planning phase and updating phase. In PDVN, we construct two separate value networks to predict the synthesizability and cost of molecules, respectively. To maintain the single-step accuracy, we design a two-branch network structure for the single-step predictor. On the widely-used USPTO dataset, our PDVN algorithm improves the search success rate of existing multi-step planners (e.g., increasing the success rate from 85.79% to 98.95% for Retro$^{\ast}$, and reducing the number of model calls by half while solving 99.47% molecules for RetroGraph). Additionally, PDVN helps find shorter synthesis routes (e.g., reducing the average route length from 5.76 to 4.83 for Retro$^{\ast}$, and from 5.63 to 4.78 for RetroGraph).

We introduce GAUCHE, an open-source library for GAUssian processes in CHEmistry. Gaussian processes have long been a cornerstone of probabilistic machine learning, affording particular advantages for uncertainty quantification and Bayesian optimisation. Extending Gaussian processes to molecular representations, however, necessitates kernels defined over structured inputs such as graphs, strings and bit vectors. By providing such kernels in a modular, robust and easy-to-use framework, we seek to enable expert chemists and materials scientists to make use of state-of-the-art black-box optimization techniques. Motivated by scenarios frequently encountered in practice, we showcase applications for GAUCHE in molecular discovery, chemical reaction optimisation and protein design. The codebase is made available at https://github.com/leojklarner/gauche.

The Tanimoto coefficient is commonly used to measure the similarity between molecules represented as discrete fingerprints, either as a distance metric or a positive definite kernel. While many kernel methods can be accelerated using random feature approximations, at present there is a lack of such approximations for the Tanimoto kernel. In this paper we propose two kinds of novel random features to allow this kernel to scale to large datasets, and in the process discover a novel extension of the kernel to real-valued vectors. We theoretically characterize these random features, and provide error bounds on the spectral norm of the Gram matrix. Experimentally, we show that these random features are effective at approximating the Tanimoto coefficient of real-world datasets and are useful for molecular property prediction and optimization tasks. Future updates to this work will be available at http://arxiv.org/abs/2306.14809.

Many important problems in science and engineering, such as drug design, involve optimizing an expensive black-box objective function over a complex, high-dimensional, and structured input space. Although machine learning techniques have shown promise in solving such problems, existing approaches substantially lack sample efficiency. We introduce an improved method for efficient black-box optimization, which performs the optimization in the low-dimensional, continuous latent manifold learned by a deep generative model. In contrast to previous approaches, we actively steer the generative model to maintain a latent manifold that is highly useful for efficiently optimizing the objective. We achieve this by periodically retraining the generative model on the data points queried along the optimization trajectory, as well as weighting those data points according to their objective function value. This weighted retraining can be easily implemented on top of existing methods, and is empirically shown to significantly improve their efficiency and performance on synthetic and real-world optimization problems.