Tightening CVaR Approximations via Scenario-Wise Scaling for Chance-Constrained Programming
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Stochastic Programming
Globalized Adversarial Regret Optimization: Robust Decisions with Uncalibrated Predictions
Optimization problems routinely depend on uncertain parameters that must be predicted before a decision is made. Classical robust and regret formulations are designed to handle erroneous predictions and can provide statistical error bounds in simple settings. However, when predictions lack rigorous error bounds (as is typical of modern machine learning methods) classical robust models often … Read more
Zeroth-Order Methods for Nonconvex-Strongly Concave Stochastic Minimax Problems with Decision-Dependent Distributions
Stochastic minimax problems with decision-dependent distributions (SMDD) have emerged as a crucial framework for modeling complex systems where data distributions drift in response to decision variables. Most existing methods for SMDD rely on an explicit functional relationship between the decision variables and the probability distribution. In this paper, we propose two sample-based zeroth-order algorithms, namely … Read more
Data-driven Policies For Two-stage Stochastic Linear Programs
A stochastic program typically involves several parameters, including deterministic first-stage parameters and stochastic second-stage elements that serve as input data. These programs are re-solved whenever any input parameter changes. However, in practical applications, quick decision-making is necessary, and solving a stochastic program from scratch for every change in input data can be computationally costly. This … Read more
Solving Chance Constrained Programs via a Penalty based Difference of Convex Approach
We develop two penalty based difference of convex (DC) algorithms for solving chance constrained programs. First, leveraging a rank-based DC decomposition of the chance constraint, we propose a proximal penalty based DC algorithm in the primal space that does not require a feasible initialization. Second, to improve numerical stability in the general nonlinear settings, we … Read more
Chance-Constrained Linear Complementarity Problems
We study linear complementarity problems (LCPs) under uncertainty, which we model using chance constraints. Since the complementarity condition of the LCP is an equality constraint, it is required to consider relaxations, which naturally leads to optimization problems in which the relaxation parameters are minimized for given probability levels. We focus on these optimization problems and … Read more
Heuristics for two-stage stochastic K-adaptability
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Normalization of ReLU Dual for Cut Generation in Stochastic Mixed-Integer Programs
We study the Rectified Linear Unit (ReLU) dual, an existing dual formulation for stochastic programs that reformulates non-anticipativity constraints using ReLU functions to generate tight, non-convex, and mixed-integer representable cuts. While this dual reformulation guarantees convergence with mixed-integer state variables, it admits multiple optimal solutions that can yield weak cuts. To address this issue, we … Read more
Projected Stochastic Momentum Methods for Nonlinear Equality-Constrained Optimization for Machine Learning
Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of a stochastic Newton-SQP-type algorithm for solving equality-constrained problems. One is an extension of the heavy-ball method and the other is an extension … Read more
Contextual Distributionally Robust Optimization with Causal and Continuous Structure: An Interpretable and Tractable Approach
In this paper, we introduce a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution by developing interpretable and tractable decision rules that prescribe decisions using covariates. We first introduce the causal Sinkhorn discrepancy (CSD), an entropy-regularized causal Wasserstein distance that encourages continuous transport plans while … Read more