Browsing by Author "Luedtke, James R."

Now showing 1 - 4 of 4
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    Data-Driven Sample Average Approximation with Covariate Information
    Kannan, Rohit; Bayraksan, Guezin; Luedtke, James R. (INFORMS, 2025-01-06)
    We study optimization for data-driven decision-making when we have observations of the uncertain parameters within an optimization model together with concurrent observations of covariates. The goal is to choose a decision that minimizes the expected cost conditioned on a new covariate observation. We investigate two data-driven frameworks that integrate a machine learning prediction model within a stochastic programming sample average approximation (SAA) for approximating the solution to this problem. One SAA framework is new and uses leave-one-out residuals for scenario generation. The frameworks we investigate are flexible and accommodate parametric, nonparametric, and semiparametric regression techniques. We derive conditions on the data generation process, the prediction model, and the stochastic program under which solutions of these data-driven SAAs are consistent and asymptotically optimal, and also derive finite sample guarantees. Computational experiments validate our theoretical results, demonstrate examples where our datadriven formulations have advantages over existing approaches (even if the prediction model is misspecified), and illustrate the benefits of our data-driven formulations in the limited data regime.
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    Residuals-based distributionally robust optimization with covariate information
    Kannan, Rohit; Bayraksan, Guezin; Luedtke, James R. (Springer, 2023-09-26)
    We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified.
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    A stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs
    Kannan, Rohit; Luedtke, James R. (Springer, 2021-01-23)
    We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraints violation. To this end, we construct a reformulated problem whose objective is to minimize the probability of constraints violation subject to deterministic convex constraints (which includes a bound on the objective function value). We adapt existing smoothing-based approaches for chance-constrained problems to derive a convergent sequence of smooth approximations of our reformulated problem, and apply a projected stochastic subgradient algorithm to solve it. In contrast with exterior sampling-based approaches (such as sample average approximation) that approximate the original chance-constrained program with one having finite support, our proposal converges to stationary solutions of a smooth approximation of the original problem, thereby avoiding poor local solutions that may be an artefact of a fixed sample. Our proposal also includes a tailored implementation of the smoothing-based approach that chooses key algorithmic parameters based on problem data. Computational results on four test problems from the literature indicate that our proposed approach can efficiently determine good approximations of the efficient frontier.
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    Stochastic DC optimal power flow with reserve saturation
    Kannan, Rohit; Luedtke, James R.; Roald, Line A. (Elsevier, 2020-12)
    We propose an optimization framework for stochastic optimal power flow with uncertain loads and renewable generator capacity. Our model follows previous work in assuming that generator outputs respond to load imbalances according to an affine control policy, but introduces a model of saturation of generator reserves by assuming that when a generator's target level hits its limit, it abandons the affine policy and produces at that limit. This is a particularly interesting feature in models where wind power plants, which have uncertain upper generation limits, are scheduled to provide reserves to balance load fluctuations. The resulting model is a nonsmooth nonconvex two-stage stochastic program, and we use a stochastic approximation method to find stationary solutions to a smooth approximation. Computational results on 6-bus and 118-bus test instances demonstrate that by considering the effects of saturation, our model can yield solutions with lower expected generation costs (at the same target line violation probability level) than those obtained from a model that enforces the affine policy to stay within generator limits with high probability.