Related papers: Optimization Under Unknown Constraints
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
Estimation of individual treatment effects is commonly used as the basis for contextual decision making in fields such as healthcare, education, and economics. However, it is often sufficient for the decision maker to have estimates of…
Agent behavior is arguably the greatest source of uncertainty in trajectory planning for autonomous vehicles. This problem has motivated significant amounts of work in the behavior prediction community on learning rich distributions of the…
Black-box problems are common in real life like structural design, drug experiments, and machine learning. When optimizing black-box systems, decision-makers always consider multiple performances and give the final decision by comprehensive…
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
Optimization in machine learning typically deals with the minimization of empirical objectives defined by training data. However, the ultimate goal of learning is to minimize the error on future data (test error), for which the training…
We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to…
Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…
A solution that is only reliable under favourable conditions is hardly a safe solution. Min Max Optimization is an approach that returns optima that are robust against worst case conditions. We propose algorithms that perform Min Max…
We investigate the connections between compression learning and scenario based optimization. We first show how to strengthen, or relax the consistency assumption at the basis of compression learning and study the learning and generalization…
Bayesian optimization is a class of data efficient model based algorithms typically focused on global optimization. We consider the more general case where a user is faced with multiple problems that each need to be optimized conditional on…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…
Test functions are important to validate new optimization algorithms and to compare the performance of various algorithms. There are many test functions in the literature, but there is no standard list or set of test functions one has to…
Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used…
We develop our previous works concerning the identification of the collection of significant factors determining some, in general, non-binary random response variable. Such identification is important, e.g., in biological and medical…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
Empirical analysis serves as an important complement to theoretical analysis for studying practical Bayesian optimization. Often empirical insights expose strengths and weaknesses inaccessible to theoretical analysis. We define two metrics…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
Bayesian optimization is normally performed within fixed variable bounds. In cases like hyperparameter tuning for machine learning algorithms, setting the variable bounds is not trivial. It is hard to guarantee that any fixed bounds will…