Related papers: Gaussian Process-based Approach for Bilevel Optimi…
Solving a bilevel optimization problem is at the core of several machine learning problems such as hyperparameter tuning, data denoising, meta- and few-shot learning, and training-data poisoning. Different from simultaneous or…
This article studies the joint problem of uplink-downlink scheduling and power allocation for controlling a large number of actuators that upload their states to remote controllers and download control actions over wireless links. To…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
Model Predictive Control (MPC) is a common tool for the control of nonlinear, real-world systems, such as legged robots. However, solving MPC quickly enough to enable its use in real-time is often challenging. One common solution is given…
Scaling hyperparameter optimisation to very large datasets remains an open problem in the Gaussian process community. This paper focuses on iterative methods, which use linear system solvers, like conjugate gradients, alternating…
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
This paper presents an approximate Reinforcement Learning (RL) methodology for bi-level power management of networked Microgrids (MG) in electric distribution systems. In practice, the cooperative agent can have limited or no knowledge of…
Improving the reliability of power distribution systems is critically important for both utilities and customers. This calls for an efficient service restoration module within a distribution management system to support the implementation…
Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. The practical implementation of the gradient descent method to bilevel optimization encounters computational…
Bilevel optimization is characterized by a two-level optimization structure, where the upper-level problem is constrained by optimal lower-level solutions, and such structures are prevalent in real-world problems. The constraint by optimal…
Bilevel learning is a powerful optimization technique that has extensively been employed in recent years to bridge the world of model-driven variational approaches with data-driven methods. Upon suitable parametrization of the desired…
We consider a bilevel optimization problem in which the ground set is partitioned between two decision makers, a leader and a follower, whose optimization problems are interleaved. We study the Bilevel Independent Set problem, and its…
Bayesian Optimization, leveraging Gaussian process models, has proven to be a powerful tool for minimizing expensive-to-evaluate objective functions by efficiently exploring the search space. Extensions such as constrained Bayesian…
In this paper we propose a bilevel optimization approach for the placement of space and time observations in variational data assimilation problems. Within the framework of supervised learning, we consider a bilevel problem where the…
Gaussian Process Regression (GPR) is a nonparametric supervised learning method, widely valued for its ability to quantify uncertainty. Despite its advantages and broad applications, classical GPR implementations face significant…
Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…