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The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…
Chance constrained optimal power flow (OPF) has been recognized as a promising framework to manage the risk from variable renewable energy (VRE). In presence of VRE uncertainties, this paper discusses a distributionally robust chance…
The heating, ventilation and air condition (HVAC) system consumes the most energy in commercial buildings, consisting over 60% of total energy usage in the U.S. Flexible HVAC system setpoint scheduling could potentially save building energy…
Using only retrospective data, we study the problem of predicting treatment effects for the same treatment/policy implemented in a different location or time period. We propose a distributionally robust estimator that minimizes the…
Classical stochastic control assumes perfect knowledge of the uncertainty affecting the plant. In practice, however, such information is often incomplete. To address this limitation, we consider a distributionally robust control (DRC)…
Off-policy evaluation and learning are concerned with assessing a given policy and learning an optimal policy from offline data without direct interaction with the environment. Often, the environment in which the data are collected differs…
We consider distributionally robust optimal control of stochastic linear systems under signal temporal logic (STL) chance constraints when the disturbance distribution is unknown. By assuming that the underlying predicate functions are…
The design and testing of supervised machine learning models combine two fundamental distributions: (1) the training data distribution (2) the testing data distribution. Although these two distributions are identical and identifiable when…
The effects of treatments are often heterogeneous, depending on the observable characteristics, and it is necessary to exploit such heterogeneity to devise individualized treatment rules (ITRs). Existing estimation methods of such ITRs…
Specifying a proper input distribution is often a challenging task in simulation modeling. In practice, there may be multiple plausible distributions that can fit the input data reasonably well, especially when the data volume is not large.…
This paper studies Markov Decision Processes under parameter uncertainty. We adapt the distributionally robust optimization framework, and assume that the uncertain parameters are random variables following an unknown distribution, and…
We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case…
We consider multiperiod stochastic control problems with non-parametric uncertainty on the underlying probabilistic model. We derive a new metric on the space of probability measures, called the adapted $(p, \infty)$--Wasserstein distance…
We propose Distributionally Balanced Designs (DBD), a new class of probability sampling designs that target representativeness at the level of the full auxiliary distribution rather than selected moments. In disciplines such as ecology,…
This paper introduces a framework for Chance-Constrained Optimization with Complex Variables, addressing complex linear programming for both individual and joint probabilistic constraints in the complex domain. We first analyze the 3CP…
Data-driven decision-making under uncertainty typically presumes the collection of historical data from an unknown target probability distribution. However, one may have no access to any data from the target distribution prior to…
The Wasserstein barycenter is a geometric construct which captures the notion of centrality among probability distributions, and which has found many applications in machine learning. However, most algorithms for finding even an approximate…
The Stackelberg game model, where a leader commits to a strategy and the follower best responds, has found widespread application, particularly to security problems. In the security setting, the goal is for the leader to compute an optimal…
Utility preference robust optimization (PRO) has recently been proposed to deal with optimal decision making problems where the decision maker's (DM) preference over gains and losses is ambiguous. In this paper, we take a step further to…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…