Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the back-propagation of computational graphs. In order to expand the scope of learning problems that can be solved in an end-to-end fashion, we propose a systematic method to transform optimizers into operations that are differentiable and never locally constant. Our approach relies on stochastically perturbed optimizers, and can be used readily together with existing solvers. Their derivatives can be evaluated efficiently, and smoothness tuned via the chosen noise amplitude. We also show how this framework can be connected to a family of losses developed in structured prediction, and give theoretical guarantees for their use in learning tasks. We demonstrate experimentally the performance of our approach on various tasks.
Conventional optimization methods in machine learning and controls rely heavily on first-order update rules. Selecting the right method and hyperparameters for a particular task often involves trial-and-error or practitioner intuition, motivating the field of meta-learning. We generalize a broad family of preexisting update rules by proposing a meta-learning framework in which the inner loop optimization step involves solving a differentiable convex optimization (DCO). We illustrate the theoretical appeal of this approach by showing that it enables one-step optimization of a family of linear l…
Reasoning about 3D scenes from their 2D image projections is one of the core problems in computer vision. Solutions to this inverse and ill-posed problem typically involve a search for models that best explain observed image data. Notably, images depend both on the properties of observed scenes and on the process of image formation. Hence, if optimization techniques should be used to explain images, it is crucial to design differentiable functions for the projection of 3D scenes into images, also known as differentiable rendering. Previous approaches to differentiable rendering typically repla…
TU Darmstadt（达姆施塔特工业大学）；Fraunhofer IAIS（弗劳恩霍夫智能分析与信息系统研究所）
The move from hand-designed to learned optimizers in machine learning has been quite successful for gradient-based and -free optimizers. When facing a constrained problem, however, maintaining feasibility typically requires a projection step, which might be computationally expensive and not differentiable. We show how the design of projection-free convex optimization algorithms can be cast as a learning problem based on Frank-Wolfe Networks: recurrent networks implementing the Frank-Wolfe algorithm aka. conditional gradients. This allows them to learn to exploit structure when, e.g., optimizin…
We propose random hinge forests, a simple, efficient, and novel variant of decision forests. Importantly, random hinge forests can be readily incorporated as a general component within arbitrary computation graphs that are optimized end-to-end with stochastic gradient descent or variants thereof. We derive random hinge forest and ferns, focusing on their sparse and efficient nature, their min-max margin property, strategies to initialize them for arbitrary network architectures, and the class of optimizers most suitable for optimizing random hinge forest. The performance and versatility of ran…
Australian Artificial Intelligence Institute（澳大利亚人工智能研究院）；University of Technology Sydney（悉尼科技大学）
Black-box optimization is primarily important for many compute-intensive applications, including reinforcement learning (RL), robot control, etc. This paper presents a novel theoretical framework for black-box optimization, in which our method performs stochastic update with the implicit natural gradient of an exponential-family distribution. Theoretically, we prove the convergence rate of our framework with full matrix update for convex functions. Our theoretical results also hold for continuous non-differentiable black-box functions. Our methods are very simple and contain less hyper-paramet…
We present Theseus, an efficient application-agnostic open source library for differentiable nonlinear least squares (DNLS) optimization built on PyTorch, providing a common framework for end-to-end structured learning in robotics and vision. Existing DNLS implementations are application specific and do not always incorporate many ingredients important for efficiency. Theseus is application-agnostic, as we illustrate with several example applications that are built using the same underlying differentiable components, such as second-order optimizers, standard costs functions, and Lie groups. Fo…
Google Research, Brain Team（谷歌研究院大脑团队）；Radboud University（拉德堡德大学）；Donders Institute for Brain, Cognition and Behaviour（唐德斯脑、认知与行为研究所）
Differentiable programming techniques are widely used in the community and are responsible for the machine learning renaissance of the past several decades. While these methods are powerful, they have limits. In this short report, we discuss a common chaos based failure mode which appears in a variety of differentiable circumstances, ranging from recurrent neural networks and numerical physics simulation to training learned optimizers. We trace this failure to the spectrum of the Jacobian of the system under study, and provide criteria for when a practitioner might expect this failure to spoil…
Delhi Technological University（德里理工大学）；RelationalAI（RelationalAI公司）；Free University of Berlin（柏林自由大学）；Data61, CSIRO（澳大利亚联邦科学与工业研究组织数据61研究所）；University of Queensland（昆士兰大学）
We present ensmallen, a fast and flexible C++ library for mathematical optimization of arbitrary user-supplied functions, which can be applied to many machine learning problems. Several types of optimizations are supported, including differentiable, separable, constrained, and categorical objective functions. The library provides many pre-built optimizers (including numerous variants of SGD and Quasi-Newton optimizers) as well as a flexible framework for implementing new optimizers and objective functions. Implementation of a new optimizer requires only one method and a new objective function …
Recently, neural networks trained as optimizers under the "learning to learn" or meta-learning framework have been shown to be effective for a broad range of optimization tasks including derivative-free black-box function optimization. Recurrent neural networks (RNNs) trained to optimize a diverse set of synthetic non-convex differentiable functions via gradient descent have been effective at optimizing derivative-free black-box functions. In this work, we propose RNN-Opt: an approach for learning RNN-based optimizers for optimizing real-parameter single-objective continuous functions under li…
University of Minnesota（明尼苏达大学）；Queens College, City University of New York（纽约城市大学皇后学院）
Empirical robustness evaluation (RE) of deep learning models against adversarial perturbations entails solving nontrivial constrained optimization problems. Existing numerical algorithms that are commonly used to solve them in practice predominantly rely on projected gradient, and mostly handle perturbations modeled by the $\ell_1$, $\ell_2$ and $\ell_\infty$ distances. In this paper, we introduce a novel algorithmic framework that blends a general-purpose constrained-optimization solver PyGRANSO with Constraint Folding (PWCF), which can add more reliability and generality to the state-of-the-…
Recent works in deep learning have shown that integrating differentiable physics simulators into the training process can greatly improve the quality of results. Although this combination represents a more complex optimization task than supervised neural network training, the same gradient-based optimizers are typically employed to minimize the loss function. However, the integrated physics solvers have a profound effect on the gradient flow as manipulating scales in magnitude and direction is an inherent property of many physical processes. Consequently, the gradient flow is often highly unba…
RelationalAI；Free University of Berlin（柏林自由大学）；Collabora；Birla Institute of Technology and Science, Pilani（比拉理工学院）；The University of Texas at Arlington（德克萨斯大学阿灵顿分校）；Epsilon；Data61 / CSIRO（Data61 / 澳大利亚联邦科学与工业研究组织）；Griffith University（格里菲斯大学）
本文介绍 ensmallen 数值优化库，其提供快速灵活的 C++ 框架，支持多种优化器和目标函数，通过模板元编程实现零开销回调与自动推断，性能优于 Julia 和 SciPy。
We study online convex optimization with switching costs, a practically important but also extremely challenging problem due to the lack of complete offline information. By tapping into the power of machine learning (ML) based optimizers, ML-augmented online algorithms (also referred to as expert calibration in this paper) have been emerging as state of the art, with provable worst-case performance guarantees. Nonetheless, by using the standard practice of training an ML model as a standalone optimizer and plugging it into an ML-augmented algorithm, the average cost performance can be highly u…
