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We introduce a new framework, Bayesian Distributionally Robust Optimization (Bayesian-DRO), for data-driven stochastic optimization where the underlying distribution is unknown. Bayesian-DRO contrasts with most of the existing DRO…
Safety assurance is uncompromisable for safety-critical environments with the presence of drastic model uncertainties (e.g., distributional shift), especially with humans in the loop. However, incorporating uncertainty in safe learning will…
Safety is a core challenge of autonomous robot motion planning, especially in the presence of dynamic and uncertain obstacles. Many recent results use learning and deep learning-based motion planners and prediction modules to predict…
In this paper, we study the distributionally robust joint chance constrained Markov decision process. {Utilizing the logarithmic transformation technique,} we derive its deterministic reformulation with bi-convex terms under the…
We study piecewise affine policies for multi-stage adjustable robust optimization (ARO) problems with non-negative right-hand side uncertainty. First, we construct new dominating uncertainty sets and show how a multi-stage ARO problem can…
In this paper, we develop an exact reformulation and a deterministic approximation for distributionally robust joint chance-constrained programmings (DRCCPs) with a general class of convex uncertain constraints under data-driven Wasserstein…
Convex optimization problems with staged structure appear in several contexts, including optimal control, verification of deep neural networks, and isotonic regression. Off-the-shelf solvers can solve these problems but may scale poorly. We…
This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
We develop an analytical synthesis that bridges data-driven Distributionally Robust Optimization (DRO) and Economic Decision Theory under Ambiguity (DTA). By reinterpreting standard regularization and DRO techniques as data-driven…
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
In many operational settings, decision-makers must commit to actions before uncertainty resolves, but existing optimization tools rarely quantify how consistently a chosen decision remains optimal across plausible scenarios. This paper…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $\phi$-divergences and Wasserstein distances, respectively. While the former focuses on ambiguity in…
This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable…
The Robust Satisficing (RS) model is an emerging approach to robust optimization, offering streamlined procedures and robust generalization across various applications. However, the statistical theory of RS remains unexplored in the…
We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…
In network congestion games, system operators often utilize latency models, estimated from real-world traffic flow and travel time data, to design monetary incentives which steer equilibrium user behaviors towards lowering system-wide…
We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed…