Related papers: Learning Convex Optimization Models
Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this…
Non-probabilistic convex model utilizes a convex set to quantify the uncertainty domain of uncertain-but-bounded parameters, which is very effective for structural uncertainty analysis with limited or poor-quality experimental data. To…
The performance of many machine learning models depends on their hyper-parameter settings. Bayesian Optimization has become a successful tool for hyper-parameter optimization of machine learning algorithms, which aims to identify optimal…
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…
Many real-life optimization problems frequently contain one or more constraints or objectives for which there are no explicit formulas. If data is however available, these data can be used to learn the constraints. The benefits of this…
Formulating real-world optimization problems often begins with making predictions from historical data (e.g., an optimizer that aims to recommend fast routes relies upon travel-time predictions). Typically, learning the prediction model…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
The increasing reliance on numerical methods for controlling dynamical systems and training machine learning models underscores the need to devise algorithms that dependably and efficiently navigate complex optimization landscapes.…
Controlling the dispersion of a subset of decision variables in an optimization problem is crucial for enforcing fairness or load-balancing across a wide range of applications. Building on the well-known equivalence of finite-dimensional…
In this paper we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable…
This paper considers risk-sensitive model predictive control for stochastic systems with a decision-dependent distribution. This class of systems is commonly found in human-robot interaction scenarios. We derive computationally tractable…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
Uncertainty in optimization is often represented as stochastic parameters in the optimization model. In Predict-Then-Optimize approaches, predictions of a machine learning model are used as values for such parameters, effectively…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
Modeling how a robot interacts with the environment around it is an important prerequisite for designing control and planning algorithms. In fact, the performance of controllers and planners is highly dependent on the quality of the model.…
This paper firstly proposes a convex bilevel optimization paradigm to formulate and optimize popular learning and vision problems in real-world scenarios. Different from conventional approaches, which directly design their iteration schemes…