Multiple Adaptive Bayesian Linear Regression for Scalable Bayesian Optimization with Warm Start

arXiv.org Machine Learning

Bayesian optimization (BO) is a model-based approach for gradient-free black-box function optimization. Typically, BO is powered by a Gaussian process (GP), whose algorithmic complexity is cubic in the number of evaluations. Hence, GP-based BO cannot leverage large amounts of past or related function evaluations, for example, to warm start the BO procedure. We develop a multiple adaptive Bayesian linear regression model as a scalable alternative whose complexity is linear in the number of observations. The multiple Bayesian linear regression models are coupled through a shared feedforward neural network, which learns a joint representation and transfers knowledge across machine learning problems.


Multi-Task Learning as Multi-Objective Optimization

Neural Information Processing Systems

In multi-task learning, multiple tasks are solved jointly, sharing inductive bias between them. Multi-task learning is inherently a multi-objective problem because different tasks may conflict, necessitating a trade-off. A common compromise is to optimize a proxy objective that minimizes a weighted linear combination of per-task losses. However, this workaround is only valid when the tasks do not compete, which is rarely the case. To this end, we use algorithms developed in the gradient-based multi-objective optimization literature.


ZOOpt: Toolbox for Derivative-Free Optimization

arXiv.org Machine Learning

Recent advances of derivative-free optimization allow efficient approximating the global optimal solutions of sophisticated functions, such as functions with many local optima, non-differentiable and non-continuous functions. This article describes the ZOOpt (https://github.com/eyounx/ZOOpt) toolbox that provides efficient derivative-free solvers and are designed easy to use. ZOOpt provides a Python package for single-thread optimization, and a light-weighted distributed version with the help of the Julia language for Python described functions. ZOOpt toolbox particularly focuses on optimization problems in machine learning, addressing high-dimensional, noisy, and large-scale problems. The toolbox is being maintained toward ready-to-use tool in real-world machine learning tasks.


Automatic Configuration of Deep Neural Networks with EGO

arXiv.org Machine Learning

Designing the architecture for an artificial neural network is a cumbersome task because of the numerous parameters to configure, including activation functions, layer types, and hyper-parameters. With the large number of parameters for most networks nowadays, it is intractable to find a good configuration for a given task by hand. In this paper an Efficient Global Optimization (EGO) algorithm is adapted to automatically optimize and configure convolutional neural network architectures. A configurable neural network architecture based solely on convolutional layers is proposed for the optimization. Without using any knowledge on the target problem and not using any data augmentation techniques, it is shown that on several image classification tasks this approach is able to find competitive network architectures in terms of prediction accuracy, compared to the best hand-crafted ones in literature. In addition, a very small training budget (200 evaluations and 10 epochs in training) is spent on each optimized architectures in contrast to the usual long training time of hand-crafted networks. Moreover, instead of the standard sequential evaluation in EGO, several candidate architectures are proposed and evaluated in parallel, which saves the execution overheads significantly and leads to an efficient automation for deep neural network design.


Learning to Optimize in Swarms

Neural Information Processing Systems

Learning to optimize has emerged as a powerful framework for various optimization and machine learning tasks. Current such "meta-optimizers" often learn in the space of continuous optimization algorithms that are point-based and uncertainty-unaware. To overcome the limitations, we propose a meta-optimizer that learns in the algorithmic space of both point-based and population-based optimization algorithms. Specifically, we learn and interpret the update formula through a population of LSTMs embedded with sample- and feature-level attentions. Meanwhile, we estimate the posterior directly over the global optimum and use an uncertainty measure to help guide the learning process.