相关论文: Approximating the value functions for stochastic d…

We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and…

We propose the first loss function for approximate Nash equilibria of normal-form games that is amenable to unbiased Monte Carlo estimation. This construction allows us to deploy standard non-convex stochastic optimization techniques for…

We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for…

We prove a rate of convergence for finite element approximations of stationary, second-order mean field games with nondifferentiable Hamiltonians posed in general bounded polytopal Lipschitz domains with strongly monotone running costs. In…

This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…

We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neural networks the associated neural stochastic differential…

The success of adversarial formulations in machine learning has brought renewed motivation for smooth games. In this work, we focus on the class of stochastic Hamiltonian methods and provide the first convergence guarantees for certain…

The paper is concerned with a two-player nonzero-sum differential game in the case when players are informed about the current position. We consider the game in control with guide strategies first proposed by Krasovskii and Subbotin. The…

We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of the underlying control problems/games along with dual approximations of the…

This paper shows the existence of $\mathcal{O}(\frac{1}{n^\gamma})$-Nash equilibria in $n$-player noncooperative sum-aggregative games in which the players' cost functions, depending only on their own action and the average of all players'…

Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…

By analogy with the program of McKinnon-Roth, we define and study approximation constants for points of a projective variety X defined over K the function field of an irreducible and non-singular in codimension 1 projective variety defined…

We present a method for approximating solutions of Stochastic Differential Equations (SDEs) with arbitrary rates. This approximation is derived for bounded and measurable test functions. Specifically, we demonstrate that, leveraging the…

In this paper we study a discrete-time semidiscretization and a fully discretization (discrete-time, discrete-state) of an infinite time horizon noncooperative $N$-player differential game. We prove that as either the discretization time…

In this paper we study time semi-discrete approximations of a class of polynomially stable infinite dimensional systems modeling the damped vibrations. We prove that adding a suitable numerical viscosity term in the numerical scheme, one…

First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…

The theory of first-order mean field type differential games examines the systems of infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study the…

We address the numerical approximation of Mean Field Games with local couplings. For power-like Hamiltonians, we consider both unconstrained and constrained stationary systems with density constraints in order to model hard congestion…

In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…

This paper considers a stochastic approximation algorithm, with decreasing step size and martingale difference noise. Under very mild assumptions, we prove the non convergence of this process toward a certain class of repulsive sets for the…