Related papers: Robust SVM Optimization in Banach spaces
Nash equilibria and Pareto optimality are two distinct concepts when dealing with multiple criteria. It is well known that the two concepts do not coincide. However, in this work we show that it is possible to characterize the set of all…
This work introduces a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may fail. For the sake of simplicity, we focus on a simple…
We address the challenge of designing optimal adversarial noise algorithms for settings where a learner has access to multiple classifiers. We demonstrate how this problem can be framed as finding strategies at equilibrium in a two-player,…
We study a general version of the adversarial online learning problem. We are given a decision set $\mathcal{X}$ in a reflexive Banach space $X$ and a sequence of reward vectors in the dual space of $X$. At each iteration, we choose an…
We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of…
In this paper, we unify the theory of SSD spaces, part of the theory of strongly representable multifunctions, and the theory of the equivalence of various classes of maximally monotone multifunctions.
The aim of this paper is to establish a strong convergence theorem for a strongly nonexpansive sequence in a Banach space. We also deal with some applications of the convergence theorem.
We study an optimal targeting problem for super-modular games with binary actions and finitely many players. The considered problem consists in the selection of a subset of players of minimum size such that, when the actions of these…
This paper deals with the application of Approximation Theory type techniques to study a classical problem in Probability: estimating the parameter of a biased coin. For this purpose, a Minimax Estimation problem is considered and the…
This paper considers the problem of inverse reinforcement learning in zero-sum stochastic games when expert demonstrations are known to be not optimal. Compared to previous works that decouple agents in the game by assuming optimality in…
In this letter, we study distributed optimization and Nash equilibrium-seeking dynamics from a contraction theoretic perspective. Our first result is a novel bound on the logarithmic norm of saddle matrices. Second, for distributed gradient…
The idea of best approximation in linear n-normed space is presented and some examples showing various possibilities of best approximations in linear n-normed space is given. Also, we study strictly convex n-norm and enquire about the…
We present a computational formulation for the approximate version of several variational inequality problems, investigating their computational complexity and establishing PPAD-completeness. Examining applications in computational game…
The goal of this work is to serve as a foundation for deep studies of the topology of state, action, and policy spaces in reinforcement learning. By studying these spaces from a mathematical perspective, we expect to gain more insight into…
In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution…
This paper introduces a novel theoretical framework for the analysis of vector-valued neural networks through the development of vector-valued variation spaces, a new class of reproducing kernel Banach spaces. These spaces emerge from…
Maximal monotone operators on a Banach space into its dual can be represented by convex functions bounded below by the duality product. It is natural to ask under which conditions a convex function represents a maximal monotone operator. A…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
This article develops optimality conditions for a large class of non-smooth variational models. The main results are based on standard tools of functional analysis and calculus of variations. Firstly we address a model with equality…
We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces.…