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Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
We consider perturbation-based extremum seeking, which recovers an approximate gradient of an analytically unknown objective function through measurements. Using classical needle variation analysis, we are able to explicitly quantify the…
Classification tasks are usually evaluated in terms of accuracy. However, accuracy is discontinuous and cannot be directly optimized using gradient ascent. Popular methods minimize cross-entropy, hinge loss, or other surrogate losses, which…
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…
In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…
While data-driven decision-making is transforming modern operations, most large-scale data is of an observational nature, such as transactional records. These data pose unique challenges in a variety of operational problems posed as…
Inspired by multi-fidelity methods in computer simulations, this article introduces procedures to design surrogates for the input/output relationship of a high-fidelity code. These surrogates should be learned from runs of both the…
Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem is non-convex when considering standard Barrier and Density methods for invariant sets, and has been treated heuristically by…
Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is…
We study planning with submodular objective functions, where instead of maximizing the cumulative reward, the goal is to maximize the objective value induced by a submodular function. Our framework subsumes standard planning and submodular…
This paper studies the problem of learning an unknown function $f$ from given data about $f$. The learning problem is to give an approximation $\hat f$ to $f$ that predicts the values of $f$ away from the data. There are numerous settings…
We revisit the optimization from samples (OPS) model, which studies the problem of optimizing objective functions directly from the sample data. Previous results showed that we cannot obtain a constant approximation ratio for the maximum…
The need for fast, effective and accurate surveys have become increasingly necessary. A major part of the research is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
Reinforcement learning (RL) problems are fundamental in online decision-making and have been instrumental in finding an optimal policy for Markov decision processes (MDPs). Function approximations are usually deployed to handle large or…
Deep neural networks, when optimized with sufficient data, provide accurate representations of high-dimensional functions; in contrast, function approximation techniques that have predominated in scientific computing do not scale well with…