BoTorch: A Framework for Efficient Monte-Carlo Bayesian Optimization (1910.06403v3)

Abstract: Bayesian optimization provides sample-efficient global optimization for a broad range of applications, including automatic machine learning, engineering, physics, and experimental design. We introduce BoTorch, a modern programming framework for Bayesian optimization that combines Monte-Carlo (MC) acquisition functions, a novel sample average approximation optimization approach, auto-differentiation, and variance reduction techniques. BoTorch's modular design facilitates flexible specification and optimization of probabilistic models written in PyTorch, simplifying implementation of new acquisition functions. Our approach is backed by novel theoretical convergence results and made practical by a distinctive algorithmic foundation that leverages fast predictive distributions, hardware acceleration, and deterministic optimization. We also propose a novel "one-shot" formulation of the Knowledge Gradient, enabled by a combination of our theoretical and software contributions. In experiments, we demonstrate the improved sample efficiency of BoTorch relative to other popular libraries.

• The paper introduces BoTorch, which leverages Monte-Carlo acquisition functions and sample average approximation for efficient Bayesian optimization.
• The paper utilizes PyTorch’s auto-differentiation and GPU acceleration to streamline gradient-based optimization of complex models.
• The paper presents a novel one-shot knowledge gradient along with theoretical convergence guarantees that reduce computational overhead.

Overview of BoTorch: A Framework for Efficient Monte-Carlo Bayesian Optimization

The paper introduces BoTorch, a contemporary programming framework specifically designed for Bayesian optimization (BO). Bayesian optimization is a powerful technique employed for sample-efficient global optimization in various domains such as automatic machine learning, engineering, physics, and experimental design. BoTorch aims to streamline the process of implementing new acquisition functions and probabilistic models by leveraging modern computational approaches.

The framework is grounded in several innovative contributions:

1. Monte-Carlo Acquisition Functions: BoTorch utilizes Monte-Carlo (MC) acquisition functions to facilitate a flexible and model-agnostic approach to Bayesian optimization. These functions approximate the expectation over uncertain outcomes by sampling from posterior distributions, enabling better handling of complex model architectures that do not allow analytic computation of these expectations.
2. Sample Average Approximation (SAA) Approach: BoTorch introduces the use of sample average approximation for optimizing MC acquisition functions. This method fixes a set of base samples from the posterior distribution during optimization, allowing the use of deterministic optimization algorithms. This approach contrasts with stochastic methods that require continual resampling, offering consistency and more efficient computations.
3. Integration with Auto-Differentiation: The framework is implemented in PyTorch, benefiting from automatic differentiation and the ability to leverage GPU acceleration. This integration simplifies the computation of gradients necessary for gradient-based optimization methods, enhancing the efficiency of model training and acquisition function optimization.
4. Novel ``One-Shot'' Knowledge Gradient: A new formulation of the Knowledge Gradient acquisition function, termed ``One-Shot Knowledge Gradient'' (OKG), is developed within BoTorch. This formulation extends the knowledge gradient method to consider look-ahead acquisition strategies while maintaining scalability and flexibility. Unlike traditional KG methods, which require nested optimization and can be computationally expensive, the OKG solves the problem in a single optimization, reducing computational overhead.
5. Theoretical Convergence Results: The paper provides theoretical convergence guarantees for the SAA of MC acquisition functions, including conditions under which convergence of the sample-level optimizer to the true optimizer happens almost surely.

Implications and Future Work

The development and release of BoTorch have significant implications for researchers and practitioners engaged in Bayesian optimization. By providing a modular and scalable framework, BoTorch reduces the time and effort involved in developing and testing new methodologies. This reduction in development time can accelerate advancements in various fields that rely on efficient global optimization techniques.

Practically, BoTorch's design enables the exploration and testing of novel acquisition functions and models, making it a robust tool for both theoretical and applied research in optimization. The use of auto-differentiation and hardware acceleration ensures that large-scale and complex optimization problems can be tackled more efficiently than with previous methods.

Future developments may include extending BoTorch's capabilities to encompass more complex domains such as high-dimensional Bayesian optimization, multi-fidelity optimization, and applications involving hybrid models that combine deep learning with probabilistic inference. Additionally, the integration and testing of alternative MC sampling methods, such as Quasi-Monte Carlo, to further improve the convergence rates and computational efficiency of the framework's existing algorithms could be explored.

Overall, BoTorch represents a significant contribution to the landscape of Bayesian optimization tools, offering a modern computational paradigm that is both practically useful and theoretically robust. Researchers will find in BoTorch a flexible and powerful ally in the pursuit of solving intricate optimization challenges.