Related papers: Expected Variational Inequalities
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…
We propose to learn model invariances as a means of interpreting a model. This is motivated by a reverse engineering principle. If we understand a problem, we may introduce inductive biases in our model in the form of invariances.…
Variational AutoEncoders (VAEs) are powerful generative models that merge elements from statistics and information theory with the flexibility offered by deep neural networks to efficiently solve the generation problem for high dimensional…
Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a…
Mean payoff stochastic games can be studied by means of a nonlinear spectral problem involving the Shapley operator: the ergodic equation. A solution consists in a scalar, called the ergodic constant, and a vector, called bias. The…
We consider linear systems of equations and inequalities with coefficients varying inside given intervals. We define their solutions (so called AE solutions) and solvability (so called AE solvability) by using forall-exists quantification…
For some estimations and predictions, we solve minimization problems with asymmetric loss functions. Usually, we estimate the coefficient of regression for these problems. In this paper, we do not make such the estimation, but rather give a…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
We tackle a fundamental problem in empirical game-theoretic analysis (EGTA), that of learning equilibria of simulation-based games. Such games cannot be described in analytical form; instead, a black-box simulator can be queried to obtain…
We study a fair resource scheduling problem, where a set of interval jobs are to be allocated to heterogeneous machines controlled by agents. Each job is associated with release time, deadline, and processing time such that it can be…
In this paper, we introduce a novel, data-driven approach for solving high-dimensional Bayesian inverse problems based on partial differential equations (PDEs), called Weak Neural Variational Inference (WNVI). The method complements real…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
VAEs, or variational autoencoders, are autoencoders that explicitly learn the distribution of the input image space rather than assuming no prior information about the distribution. This allows it to classify similar samples close to each…
We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…
Variational inference (VI) is a central tool in modern machine learning, used to approximate an intractable target density by optimising over a tractable family of distributions. As the variational family cannot typically represent the…
We study the problem of computing optimal correlated equilibria (CEs) in infinite-horizon multi-player stochastic games, where correlation signals are provided over time. In this setting, optimal CEs require history-dependent policies; this…
In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…
Bayesian inference for inverse problems involves computing expectations under posterior distributions -- e.g., posterior means, variances, or predictive quantities -- typically via Monte Carlo (MC) estimation. When the quantity of interest…