We determine how prediction methods combine with optimization methods in two-stage knowledge-based planning (KBP) pipelines to produce radiation therapy treatment plans. We trained two dose prediction methods, a generative adversarial network (GAN) and a random forest (RF) with the same 130 treatment plans. The models were applied to 87 out-of-sample patients to create two sets of predicted dose distributions that were used as input to two optimization models. The first optimization model, inverse planning (IP), estimates weights for dose-objectives from a predicted dose distribution and generates new plans using conventional inverse planning. The second optimization model, dose mimicking (DM), minimizes the sum of one-sided quadratic penalties between the predictions and the generated plans using several dose-objectives. Altogether, four KBP pipelines (GAN-IP, GAN-DM, RF-IP, and RF-DM) were constructed and benchmarked against the corresponding clinical plans using clinical criteria; the error of both prediction methods was also evaluated. The best performing plans were GAN-IP plans, which satisfied the same criteria as their corresponding clinical plans (78%) more often than any other KBP pipeline. However, GAN did not necessarily provide the best prediction for the second-stage optimization models. Specifically, both the RF-IP and RF-DM plans satisfied all clinical criteria 25% and 15% more often than GAN-DM plans (the worst performing planning), respectively. GAN predictions also had a higher mean absolute error (3.9 Gy) than those from RF (3.6 Gy). We find that state-of-the-art prediction methods when paired with different optimization algorithms, produce treatment plans with considerable variation in quality.

Constructing gene regulatory networks is a critical step in revealing disease mechanisms from transcriptomic data. In this work, we present NO-BEARS, a novel algorithm for estimating gene regulatory networks. The NO-BEARS algorithm is built on the basis of the NOTEARS algorithm with two improvements. First, we propose a new constraint and its fast approximation to reduce the computational cost of the NO-TEARS algorithm. Next, we introduce a polynomial regression loss to handle non-linearity in gene expressions. Our implementation utilizes modern GPU computation that can decrease the time of hours-long CPU computation to seconds. Using synthetic data, we demonstrate improved performance, both in processing time and accuracy, on inferring gene regulatory networks from gene expression data.

For joint inference over multiple variables, a variety of structured prediction techniques have been developed to model correlations among variables and thereby improve predictions. However, many classical approaches suffer from one of two primary drawbacks: they either lack the ability to model high-order correlations among variables while maintaining computationally tractable inference, or they do not allow to explicitly model known correlations. To address this shortcoming, we introduce `Graph Structured Prediction Energy Networks,' for which we develop inference techniques that allow to both model explicit local and implicit higher-order correlations while maintaining tractability of inference. We apply the proposed method to tasks from the natural language processing and computer vision domain and demonstrate its general utility.

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks on both the graph structure and the node attributes. We propose the first method for verifying certifiable (non-)robustness to graph perturbations for a general class of models that includes graph neural networks and label/feature propagation. By exploiting connections to PageRank and Markov decision processes our certificates can be efficiently (and under many threat models exactly) computed. Furthermore, we investigate robust training procedures that increase the number of certifiably robust nodes while maintaining or improving the clean predictive accuracy.

Alongside derivative-based methods, which scale better to higher-dimensional problems, derivative-free methods play an essential role in the optimization of many practical engineering systems, especially those in which function evaluations are determined by statistical averaging, and those for which the function of interest is nonconvex in the adjustable parameters. This work focuses on the development of a new family of surrogate-based derivative-free optimization schemes, namely $\Delta$-DOGS schemes. The idea unifying this efficient and (under the appropriate assumptions) provably-globally-convergent family of schemes is the minimization of a search function which linearly combines a computationally inexpensive ''surrogate (that is, an interpolation, or in some cases a regression, of recent function evaluations - we generally favor some variant of polyharmonic splines for this purpose), to summarize the trends evident in the data available thus far, with a synthetic piecewise-quadratic ''uncertainty function (built on the framework of a Delaunay triangulation of existing datapoints), to characterize the reliability of the surrogate by quantifying the distance of any given point in parameter space to the nearest function evaluations. The grid is successively refined as convergence is approached. Moreover, it handles the linear constraint domain. This work also introduces a method to scale the parameter domain under consideration based on adaptive variation of the seen data in the optimization process, thereby obtaining a significantly smoother surrogate.

Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression problems. We adopt "Iterative Hessian Sketching" (IHS) and show that the fast CountSketch and sparse Johnson-Lindenstrauss Transforms yield state-of-the-art accuracy guarantees under IHS, while drastically improving the time cost. As a result, we obtain significantly faster algorithms for constrained regression, for both sparse and dense inputs. Our empirical results show that we can summarize data roughly 100x faster for sparse data, and, surprisingly, 10x faster on dense data! Consequently, solutions accurate to within machine precision of the optimal solution can be found much faster than the previous state of the art.

In this paper, we proposed a general framework for data poisoning attacks to graph-based semi-supervised learning (G-SSL). In this framework, we first unify different tasks, goals, and constraints into a single formula for data poisoning attack in G-SSL, then we propose two specialized algorithms to efficiently solve two important cases --- poisoning regression tasks under $\ell_2$-norm constraint and classification tasks under $\ell_0$-norm constraint. In the former case, we transform it into a non-convex trust region problem and show that our gradient-based algorithm with delicate initialization and update scheme finds the (globally) optimal perturbation. For the latter case, although it is an NP-hard integer programming problem, we propose a probabilistic solver that works much better than the classical greedy method. Lastly, we test our framework on real datasets and evaluate the robustness of G-SSL algorithms. For instance, on the MNIST binary classification problem (50000 training data with 50 labeled), flipping two labeled data is enough to make the model perform like random guess (around 50\% error).

In Interactive Machine Learning (IML), we iteratively make decisions and obtain noisy observations of an unknown function. While IML methods, e.g., Bayesian optimization and active learning, have been successful in applications, on real-world systems they must provably avoid unsafe decisions. To this end, safe IML algorithms must carefully learn about a priori unknown constraints without making unsafe decisions. Existing algorithms for this problem learn about the safety of all decisions to ensure convergence. This is sample-inefficient, as it explores decisions that are not relevant for the original IML objective. In this paper, we introduce a novel framework that renders any existing unsafe IML algorithm safe. Our method works as an add-on that takes suggested decisions as input and exploits regularity assumptions in terms of a Gaussian process prior in order to efficiently learn about their safety. As a result, we only explore the safe set when necessary for the IML problem. We apply our framework to safe Bayesian optimization and to safe exploration in deterministic Markov Decision Processes (MDP), which have been analyzed separately before. Our method outperforms other algorithms empirically.

Communication overhead is one of the key challenges that hinders the scalability of distributed optimization algorithms. In this paper, we study local distributed SGD, where data is partitioned among computation nodes, and the computation nodes perform local updates with periodically exchanging the model among the workers to perform averaging. While local SGD is empirically shown to provide promising results, a theoretical understanding of its performance remains open. We strengthen convergence analysis for local SGD, and show that local SGD can be far less expensive and applied far more generally than current theory suggests. Specifically, we show that for loss functions that satisfy the Polyak-{\L}ojasiewicz condition, $O((pT)^{1/3})$ rounds of communication suffice to achieve a linear speed up, that is, an error of $O(1/pT)$, where $T$ is the total number of model updates at each worker. This is in contrast with previous work which required higher number of communication rounds, as well as was limited to strongly convex loss functions, for a similar asymptotic performance. We also develop an adaptive synchronization scheme that provides a general condition for linear speed up. Finally, we validate the theory with experimental results, running over AWS EC2 clouds and an internal GPU cluster.

We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic function using finite differences within a common random number framework. We employ modified versions of a norm test and an inner product quasi-Newton test to control the sample sizes used in the stochastic approximations. We provide preliminary numerical experiments to illustrate potential performance benefits of the proposed method.