Shane Barratt

Shane Barratt, Guillermo Angeris, Stephen Boyd

We consider the problem of assigning weights to a set of samples or data records, with the goal of achieving a representative weighting, which happens when certain sample averages of the data are close to prescribed values. We frame the problem of finding representative sample weights as an optimization problem, which in many cases is convex and can be efficiently solved. Our formulation includes as a special case the selection of a fixed number of the samples, with equal weights, i.e., the problem of selecting a smaller representative subset of the samples. While this problem is combinatorial and not convex, heuristic methods based on convex optimization seem to perform very well. We describe rsw, an open-source implementation of the ideas described in this paper, and apply it to a skewed sample of the CDC BRFSS dataset.

Shane Barratt, Guillermo Angeris, Stephen Boyd

We consider the problem of minimizing a sum of clipped convex functions; applications include clipped empirical risk minimization and clipped control. While the problem of minimizing the sum of clipped convex functions is NP-hard, we present some heuristics for approximately solving instances of these problems. These heuristics can be used to find good, if not global, solutions and appear to work well in practice. We also describe an alternative formulation, based on the perspective transformation, which makes the problem amenable to mixed-integer convex programming and yields computationally tractable lower bounds. We illustrate one of our heuristic methods by applying it to various examples and use the perspective transformation to certify that the solutions are relatively close to the global optimum. This paper is accompanied by an open-source implementation.

Shane Barratt, Stephen Boyd

We consider the problem of predicting the covariance of a zero mean Gaussian vector, based on another feature vector. We describe a covariance predictor that has the form of a generalized linear model, i.e., an affine function of the features followed by an inverse link function that maps vectors to symmetric positive definite matrices. The log-likelihood is a concave function of the predictor parameters, so fitting the predictor involves convex optimization. Such predictors can be combined with others, or recursively applied to improve performance.

Shane Barratt, Yining Dong, Stephen Boyd

We consider the problem of forecasting multiple values of the future of a vector time series, using some past values. This problem, and related ones such as one-step-ahead prediction, have a very long history, and there are a number of well-known methods for it, including vector auto-regressive models, state-space methods, multi-task regression, and others. Our focus is on low rank forecasters, which break forecasting up into two steps: estimating a vector that can be interpreted as a latent state, given the past, and then estimating the future values of the time series, given the latent state estimate. We introduce the concept of forecast consistency, which means that the estimates of the same value made at different times are consistent. We formulate the forecasting problem in general form, and focus on linear forecasters, for which we propose a formulation that can be solved via convex optimization. We describe a number of extensions and variations, including nonlinear forecasters, data weighting, the inclusion of auxiliary data, and additional objective terms. We illustrate our methods with several examples.

Akshay Agrawal, Shane Barratt, Stephen Boyd

A convex optimization model predicts an output from an input by solving a convex optimization problem. The class of convex optimization models is large, and includes as special cases many well-known models like linear and logistic regression. We propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs, using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters. We describe three general classes of convex optimization models, maximum a posteriori (MAP) models, utility maximization models, and agent models, and present a numerical experiment for each.

Akshay Agrawal, Shane Barratt, Stephen Boyd et al.

Many control policies used in various applications determine the input or action by solving a convex optimization problem that depends on the current state and some parameters. Common examples of such convex optimization control policies (COCPs) include the linear quadratic regulator (LQR), convex model predictive control (MPC), and convex control-Lyapunov or approximate dynamic programming (ADP) policies. These types of control policies are tuned by varying the parameters in the optimization problem, such as the LQR weights, to obtain good performance, judged by application-specific metrics. Tuning is often done by hand, or by simple methods such as a crude grid search. In this paper we propose a method to automate this process, by adjusting the parameters using an approximate gradient of the performance metric with respect to the parameters. Our method relies on recently developed methods that can efficiently evaluate the derivative of the solution of a convex optimization problem with respect to its parameters. We illustrate our method on several examples.

Akshay Agrawal, Brandon Amos, Shane Barratt et al.

Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain problems, but existing software for differentiable optimization layers is rigid and difficult to apply to new settings. In this paper, we propose an approach to differentiating through disciplined convex programs, a subclass of convex optimization problems used by domain-specific languages (DSLs) for convex optimization. We introduce disciplined parametrized programming, a subset of disciplined convex programming, and we show that every disciplined parametrized program can be represented as the composition of an affine map from parameters to problem data, a solver, and an affine map from the solver's solution to a solution of the original problem (a new form we refer to as affine-solver-affine form). We then demonstrate how to efficiently differentiate through each of these components, allowing for end-to-end analytical differentiation through the entire convex program. We implement our methodology in version 1.1 of CVXPY, a popular Python-embedded DSL for convex optimization, and additionally implement differentiable layers for disciplined convex programs in PyTorch and TensorFlow 2.0. Our implementation significantly lowers the barrier to using convex optimization problems in differentiable programs. We present applications in linear machine learning models and in stochastic control, and we show that our layer is competitive (in execution time) compared to specialized differentiable solvers from past work.

Jonathan Tuck, Shane Barratt, Stephen Boyd

Stratified models are models that depend in an arbitrary way on a set of selected categorical features, and depend linearly on the other features. In a basic and traditional formulation a separate model is fit for each value of the categorical feature, using only the data that has the specific categorical value. To this formulation we add Laplacian regularization, which encourages the model parameters for neighboring categorical values to be similar. Laplacian regularization allows us to specify one or more weighted graphs on the stratification feature values. For example, stratifying over the days of the week, we can specify that the Sunday model parameter should be close to the Saturday and Monday model parameters. The regularization improves the performance of the model over the traditional stratified model, since the model for each value of the categorical `borrows strength' from its neighbors. In particular, it produces a model even for categorical values that did not appear in the training data set. We propose an efficient distributed method for fitting stratified models, based on the alternating direction method of multipliers (ADMM). When the fitting loss functions are convex, the stratified model fitting problem is convex, and our method computes the global minimizer of the loss plus regularization; in other cases it computes a local minimizer. The method is very efficient, and naturally scales to large data sets or numbers of stratified feature values. We illustrate our method with a variety of examples.

Shane Barratt, Stephen Boyd

Least squares is by far the simplest and most commonly applied computational method in many fields. In almost all applications, the least squares objective is rarely the true objective. We account for this discrepancy by parametrizing the least squares problem and automatically adjusting these parameters using an optimization algorithm. We apply our method, which we call least squares auto-tuning, to data fitting.

Shane Barratt, Mykel Kochenderfer, Stephen Boyd

Models for predicting aircraft motion are an important component of modern aeronautical systems. These models help aircraft plan collision avoidance maneuvers and help conduct offline performance and safety analyses. In this article, we develop a method for learning a probabilistic generative model of aircraft motion in terminal airspace, the controlled airspace surrounding a given airport. The method fits the model based on a historical dataset of radar-based position measurements of aircraft landings and takeoffs at that airport. We find that the model generates realistic trajectories, provides accurate predictions, and captures the statistical properties of aircraft trajectories. Furthermore, the model trains quickly, is compact, and allows for efficient real-time inference.

Rishi Sharma, Shane Barratt, Stefano Ermon et al.

In this paper we introduce Curriculum GANs, a curriculum learning strategy for training Generative Adversarial Networks that increases the strength of the discriminator over the course of training, thereby making the learning task progressively more difficult for the generator. We demonstrate that this strategy is key to obtaining state-of-the-art results in image generation. We also show evidence that this strategy may be broadly applicable to improving GAN training in other data modalities.

Shane Barratt, Rishi Sharma

Cross-validation is the workhorse of modern applied statistics and machine learning, as it provides a principled framework for selecting the model that maximizes generalization performance. In this paper, we show that the cross-validation risk is differentiable with respect to the hyperparameters and training data for many common machine learning algorithms, including logistic regression, elastic-net regression, and support vector machines. Leveraging this property of differentiability, we propose a cross-validation gradient method (CVGM) for hyperparameter optimization. Our method enables efficient optimization in high-dimensional hyperparameter spaces of the cross-validation risk, the best surrogate of the true generalization ability of our learning algorithm.

Colin de Vrieze, Shane Barratt, Daniel Tsai et al.

Traditional radio systems are strictly co-designed on the lower levels of the OSI stack for compatibility and efficiency. Although this has enabled the success of radio communications, it has also introduced lengthy standardization processes and imposed static allocation of the radio spectrum. Various initiatives have been undertaken by the research community to tackle the problem of artificial spectrum scarcity by both making frequency allocation more dynamic and building flexible radios to replace the static ones. There is reason to believe that just as computer vision and control have been overhauled by the introduction of machine learning, wireless communication can also be improved by utilizing similar techniques to increase the flexibility of wireless networks. In this work, we pose the problem of discovering low-level wireless communication schemes ex-nihilo between two agents in a fully decentralized fashion as a reinforcement learning problem. Our proposed approach uses policy gradients to learn an optimal bi-directional communication scheme and shows surprisingly sophisticated and intelligent learning behavior. We present the results of extensive experiments and an analysis of the fidelity of our approach.

Shane Barratt, Rishi Sharma

Deep generative models are powerful tools that have produced impressive results in recent years. These advances have been for the most part empirically driven, making it essential that we use high quality evaluation metrics. In this paper, we provide new insights into the Inception Score, a recently proposed and widely used evaluation metric for generative models, and demonstrate that it fails to provide useful guidance when comparing models. We discuss both suboptimalities of the metric itself and issues with its application. Finally, we call for researchers to be more systematic and careful when evaluating and comparing generative models, as the advancement of the field depends upon it.

Shane Barratt

We propose an approach to learning agents for active robotic mapping, where the goal is to map the environment as quickly as possible. The agent learns to map efficiently in simulated environments by receiving rewards corresponding to how fast it constructs an accurate map. In contrast to prior work, this approach learns an exploration policy based on a user-specified prior over environment configurations and sensor model, allowing it to specialize to the specifications. We evaluate the approach through a simulated Disaster Mapping scenario and find that it achieves performance slightly better than a near-optimal myopic exploration scheme, suggesting that it could be useful in more complicated problem scenarios.

Shane Barratt

Humans are able to explain their reasoning. On the contrary, deep neural networks are not. This paper attempts to bridge this gap by introducing a new way to design interpretable neural networks for classification, inspired by physiological evidence of the human visual system's inner-workings. This paper proposes a neural network design paradigm, termed InterpNET, which can be combined with any existing classification architecture to generate natural language explanations of the classifications. The success of the module relies on the assumption that the network's computation and reasoning is represented in its internal layer activations. While in principle InterpNET could be applied to any existing classification architecture, it is evaluated via an image classification and explanation task. Experiments on a CUB bird classification and explanation dataset show qualitatively and quantitatively that the model is able to generate high-quality explanations. While the current state-of-the-art METEOR score on this dataset is 29.2, InterpNET achieves a much higher METEOR score of 37.9.