Related papers: Optimal Regularization Under Uncertainty: Distribu…
We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local…
Data used to train machine learning models can be adversarial--maliciously constructed by adversaries to fool the model. Challenge also arises by privacy, confidentiality, or due to legal constraints when data are geographically gathered…
Building on a recent framework for distributionally robust optimization, we consider estimation of the inverse covariance matrix for multivariate data. We provide a novel notion of a Wasserstein ambiguity set specifically tailored to this…
Distributionally Robust Optimization (DRO) is a worst-case approach to decision making when there is model uncertainty. It is also well known that for certain uncertainty sets, DRO is approximated by a regularized nominal problem. We show…
We study optimal transport-based distributionally robust optimization problems where a fictitious adversary, often envisioned as nature, can choose the distribution of the uncertain problem parameters by reshaping a prescribed reference…
This paper explores the role of regularization in data-driven predictive control (DDPC) through the lens of convex relaxation. Using a bi-level optimization framework, we model system identification as an inner problem and predictive…
This article introduces a decentralized robust optimization framework for safe multi-agent control under uncertainty. Although stochastic noise has been the primary form of modeling uncertainty in such systems, these formulations might fall…
Calibration and uncertainty estimation are crucial topics in high-risk environments. We introduce a new diversity regularizer for classification tasks that uses out-of-distribution samples and increases the overall accuracy, calibration and…
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…
In this paper we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
This paper builds on classical distributionally robust optimization techniques to construct a comprehensive framework that can be used for solving inverse problems. Given an estimated distribution of inputs in $X$ and outputs in $Y$, an…
Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…
In this paper, we develop a two-stage data-driven approach to address the adjustable robust optimization problem, where the uncertainty set is adjustable to manage infeasibility caused by significant or poorly quantified uncertainties. In…
Feedback optimization optimizes the steady state of a dynamical system by implementing optimization iterations in closed loop with the plant. It relies on online measurements and limited model information, namely, the input-output…
This paper proposes a unified framework for designing robustness in optimization under uncertainty using gauge sets, convex sets that generalize distance and capture how distributions may deviate from a nominal reference. Representing…
This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability…