BoTorch (pronounced like "blow-torch") is a library for Bayesian Optimization research built on top of PyTorch, and is part of the PyTorch ecosystem. Read the BoTorch paper  for a detailed exposition.
Bayesian Optimization (BayesOpt) is an established technique for sequential optimization of costly-to-evaluate black-box functions. It can be applied to a wide variety of problems, including hyperparameter optimization for machine learning algorithms, A/B testing, as well as many scientific and engineering problems.
BoTorch is best used in tandem with Ax, Facebook's open-source adaptive experimentation platform, which provides an easy-to-use interface for defining, managing and running sequential experiments, while handling (meta-)data management, transformations, and systems integration. Users who just want an easy-to-use suite for Bayesian Optimization should start with Ax.
Improved Developer Efficiency
BoTorch provides a modular and easily extensible interface for composing Bayesian Optimization primitives, including probabilistic models, acquisition functions, and optimizers.
It significantly improves developer efficiency by utilizing quasi-Monte-Carlo acquisition functions (by way of the "re-parameterization trick" , ), which makes it straightforward to implement new ideas without having to impose restrictive assumptions about the underlying model. Specifically, it avoids pen and paper math to derive analytic expressions for acquisition functions and their gradients. More importantly, it opens the door for novel approaches that do not admit analytic solutions, including batch acquisition functions and proper handling of rich multi-output models with multiple correlated outcomes.
BoTorch follows the same modular design philosophy as PyTorch, which makes it very easy for users to swap out or rearrange individual components in order to customize all aspects of their algorithm, thereby empowering researchers to do state-of-the art research on modern Bayesian Optimization methods.
Bayesian Optimization traditionally relies heavily on Gaussian Process (GP) models, which provide well-calibrated uncertainty estimates. BoTorch provides first-class support for state-of-the art probabilistic models in GPyTorch, a library for efficient and scalable GPs implemented in PyTorch (and to which the BoTorch authors have significantly contributed). This includes support for multi-task GPs, deep kernel learning, deep GPs, and approximate inference. This enables using GP models for problems that have traditionally not been amenable to Bayesian Optimization techniques.
In addition, BoTorch's lightweight APIs are model-agnostic (they can for example work with Pyro models), and support optimization of acquisition functions over any kind of posterior distribution, as long as it can be sampled from.
Harnessing the Features of PyTorch
Built on PyTorch, BoTorch takes advantage of auto-differentiation, native support for highly parallelized modern hardware (such as GPUs) using device-agnostic code, and a dynamic computation graph that facilitates interactive development.
BoTorch's modular design allows for a great deal of modeling flexibility for including deep and/or convolutional architectures through seamless integration with generic PyTorch modules. Importantly, working full-stack in python allows back-propagating gradients through the full composite model, in turn enabling joint training of GP and Neural Network modules, and end-to-end gradient-based optimization of acquisition functions operating on differentiable models.
Bridging the Gap Between Research and Production
BoTorch implements modular building blocks for modern Bayesian Optimization. It bridges the gap between research and production by being a very flexible research framework, but at the same time, a reliable, production-grade implementation that integrates well with other higher-level platforms, specifically Ax.
The primary audience for hands-on use of BoTorch are researchers and sophisticated practitioners in Bayesian Optimization and AI.
We recommend using BoTorch as a low-level API for implementing new algorithms for Ax. Ax has been designed to be an easy-to-use platform for end-users, which at the same time is flexible enough for Bayesian Optimization researchers to plug into for handling of feature transformations, (meta-)data management, storage, etc. See Using BoTorch with Ax for more details.
We recommend that end-users who are not actively doing research on Bayesian Optimization simply use Ax.