Related papers: Conformal Predictive Programming for Chance Constr…
This paper addresses biquadratic polynomial programming (BPP), an NP-hard optimization problem closely related to biquadratic tensors. We first establish several necessary and sufficient conditions for the positive semi-definiteness and…
Conformal prediction (CP) is an emerging uncertainty quantification framework that allows us to construct a prediction set to cover the true label with a pre-specified marginal or conditional probability. Although the valid coverage…
Constrained combinatorial optimization problems (CCOPs) are challenging to solve due to the exponential growth of the solution space. When tackled with Ising machines, constraints are typically enforced by the penalty function method, whose…
This paper considers optimization problems where the objective is the sum of a function given by an expectation and a closed convex composite function, and proposes stochastic composite proximal bundle (SCPB) methods for solving it.…
Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…
The Rank Pricing Problem (RPP) is a challenging bilevel optimization problem with binary variables whose objective is to determine the optimal pricing strategy for a set of products to maximize the total benefit, given that customer…
Robust optimization safeguards decisions against uncertainty by optimizing against worst-case scenarios, yet their effectiveness hinges on a prespecified robustness level that is often chosen ad hoc, leading to either insufficient…
A general-purpose C++ software program called $\mathbb{CGPOPS}$ is described for solving multiple-phase optimal control problems using adaptive Gaussian quadrature collocation. The software employs a Legendre-Gauss-Radau direct orthogonal…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
We propose a data-driven method to establish probabilistic performance guarantees for parametric optimization problems solved via iterative algorithms. Our approach addresses two key challenges: providing convergence guarantees to…
Conformal prediction is a powerful tool to generate uncertainty sets with guaranteed coverage using any predictive model, under the assumption that the training and test data are i.i.d.. Recently, it has been shown that adversarial examples…
Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems.…
Uncertainty estimates must be calibrated (i.e., accurate) and sharp (i.e., informative) in order to be useful. This has motivated a variety of methods for recalibration, which use held-out data to turn an uncalibrated model into a…
Conformal risk control (CRC) is a recently proposed technique that applies post-hoc to a conventional point predictor to provide calibration guarantees. Generalizing conformal prediction (CP), with CRC, calibration is ensured for a set…
Designing robust algorithms for the optimal power flow (OPF) problem is critical for the control of large-scale power systems under uncertainty. The chance-constrained OPF (CCOPF) problem provides a natural formulation of the trade-off…
Conformal prediction has emerged as a widely used framework for constructing valid prediction sets in classification and regression tasks. In this work, we extend the split conformal prediction framework to hierarchical classification,…
Conformal prediction (CP) constructs uncertainty sets for model outputs with finite-sample coverage guarantees. A candidate output is included in the prediction set if its non-conformity score is not considered extreme relative to the…
This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…