A Fully Adaptive DRO Multistage Framework Based on MDR for Generation Scheduling under Uncertainty

The growing proliferation of wind power into the power grid achieves a low-cost sustainable electricity supply while introducing technical challenges with associated intermittency. This paper proposes a fully adaptive distributionally robust multistage framework based on mixed decision rules (MDR) for generation scheduling under uncertainty to adapt wind power respecting non-anticipativity in quick-start unit status decision … Read more

Data-Driven Stochastic Dual Dynamic Programming: Performance Guarantees and Regularization Schemes

We propose a data-driven scheme for multistage stochastic linear programming with Markovian random parameters by extending the stochastic dual dynamic programming (SDDP) algorithm. In our data-driven setting, only a finite number of historical trajectories are available. The proposed SDDP scheme evaluates the cost-to-go functions only at the observed sample points, where the conditional expectations are … Read more

Distributionally Robust Optimal Allocation with Costly Verification

We consider the mechanism design problem of a principal allocating a single good to one of several agents without monetary transfers. Each agent desires the good and uses it to create value for the principal. We designate this value as the agent’s private type. Even though the principal does not know the agents’ types, she … Read more

Submodularity and pairwise independence

In this paper, we provide a characterization of the expected value of submodular set functions with pairwise independent random input. The set of pairwise independent (uncorrelated) probability distributions contains the mutually independent distribution and is contained within the set of arbitrarily dependent (correlated) distributions. We study the ratio of the maximum expected value of a … Read more

Decision Rule Approaches for Pessimistic Bilevel Linear Programs under Moment Ambiguity with Facility Location Applications

We study a pessimistic stochastic bilevel program in the context of sequential two-player games, where the leader makes a binary here-and-now decision, and the follower responds a continuous wait-and-see decision after observing the leader’s action and revelation of uncertainty. Only the information of the mean, covariance, and support is known. We formulate the problem as … Read more

On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affecting the safety condition(s) is only known to belong to some ambiguity set. We study two popular approximation schemes for distributionally robust … Read more

Adjusted Distributionally Robust Bounds on Expected Loss Functions

Optimization problems in operations and finance often include a cost that is proportional to the expected amount by which a random variable exceeds some fixed quantity, known as the expected loss function. Representation of this function often leads to computational challenges, depending on the distribution of the random variable of interest. Moreover, in practice, a … Read more

Wasserstein Logistic Regression with Mixed Features

Recent work has leveraged the popular distributionally robust optimization paradigm to combat overfitting in classical logistic regression. While the resulting classification scheme displays a promising performance in numerical experiments, it is inherently limited to numerical features. In this paper, we show that distributionally robust logistic regression with mixed (i.e., numerical and categorical) features, despite amounting … Read more

Distributionally Robust Inventory Management with Advance Purchase Contracts

We propose a distributionally robust inventory model for finding an optimal ordering policy that attains the minimum worst-case expected total cost. In a classical stochastic setting, this problem is typically addressed by dynamic programming and is solved by the famous base-stock policy. This approach however crucially relies on two controversial assumptions: the demands are serially … Read more

Distributionally Robust Disaster Relief Planning under the Wasserstein Set

We study a two-stage natural disaster management problem modeled as a stochastic program, where the first stage consists of a facility location problem, deciding where to open facilities and pre-allocate resources such as medical and food kits, and the second stage is a fixed-charge transportation problem, routing resources to affected areas after observing a disaster. … Read more