Related papers: Optimal e-variables under constraints
E-variables are nonnegative random variables with expected value at most one under any distribution from a given null hypothesis. Every nonasymptotically valid test can be obtained by thresholding some e-variable. As such, e-variables arise…
We provide a general condition under which e-variables in the form of a simple-vs.-simple likelihood ratio exist when the null hypothesis is a composite, multivariate exponential family. Such `simple' e-variables are easy to compute and…
Hypothesis testing via e-variables can be framed as a sequential betting game, where a player each round picks an e-variable. A good player's strategy results in an effective statistical test that rejects the null hypothesis as soon as…
In this paper we deal with stochastic optimization problems where the data distributions change in response to the decision variables. Traditionally, the study of optimization problems with decision-dependent distributions has assumed…
Safe reinforcement learning (RL) aims to learn policies that satisfy certain constraints before deploying them to safety-critical applications. Previous primal-dual style approaches suffer from instability issues and lack optimality…
We consider growth-optimal e-variables with maximal e-power, both in an absolute and relative sense, for simple null hypotheses for a $d$-dimensional random vector, and multivariate composite alternatives represented as a set of…
We derive the unique e-values with optimal (relative) growth rate in the worst case for testing the mean of a bounded random variable, hereby contributing with the first application beyond the assumption of mutually absolutely continuous…
We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, It\^{o}-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk}…
Different types of evolutionary algorithms have been developed for constrained continuous optimization. We carry out a feature-based analysis of evolved constrained continuous optimization instances to understand the characteristics of…
The key element of the approach to the theory of necessary conditions in optimal control discussed in the paper is reduction of the original constrained problem to unconstrained minimization with subsequent application of a suitable…
Optimization problems with an auxiliary latent variable structure in addition to the main model parameters occur frequently in computer vision and machine learning. The additional latent variables make the underlying optimization task…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
We study the problem of differentially private optimization with linear constraints when the right-hand-side of the constraints depends on private data. This type of problem appears in many applications, especially resource allocation.…
We show that for any concave utility, the expected utility of an e-variable can only increase after conditioning on a sufficient statistic. The simplest form of the result has an extremely straightforward proof, which follows from a single…
In this paper, we derive a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. Our framework is actually much more general, and we treat optimal control problems for…
In this paper we consider multiple constrained resource allocation problems, where the constraints can be specified by formulating activity dependency restrictions or by using game-theoretic models. All the problems are focused on generic…
E-values have recently emerged as a robust and flexible alternative to p-values for hypothesis testing, especially under optional continuation, i.e., when additional data from further experiments are collected. In this work, we define…
We study worst-case-growth-rate-optimal (GROW) e-statistics for hypothesis testing between two group models. It is known that under a mild condition on the action of the underlying group G on the data, there exists a maximally invariant…
Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have been applied to this scenario and shown to…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…