We design and analyze reinforcement learning algorithms for Graphon Mean-Field Games (GMFGs). In contrast to previous works that require the precise values of the graphons, we aim to learn the Nash Equilibrium (NE) of...
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We design and analyze reinforcement learning algorithms for Graphon Mean-Field Games (GMFGs). In contrast to previous works that require the precise values of the graphons, we aim to learn the Nash Equilibrium (NE) of the regularized GMFGs when the graphons are unknown. Our contributions are threefold. First, we propose the Proximal Policy Optimization for GMFG (GMFG-PPO) algorithm and show that it converges at a rate of Õ(T1-3) after T iterations with an estimation oracle, improving on a previous work by Xie et al. (ICML, 2021). Second, using kernel embedding of distributions, we design efficient algorithms to estimate the transition kernels, reward functions, and graphons from sampled agents. Convergence rates are then derived when the positions of the agents are either known or unknown. Results for the combination of the optimization algorithm GMFG-PPO and the estimation algorithm are then provided. These algorithms are the first specifically designed for learning graphons from sampled agents. Finally, the efficacy of the proposed algorithms are corroborated through simulations. These simulations demonstrate that learning the unknown graphons reduces the exploitability effectively.
The resilience of transport systems, facing natural or man-made disruptions, has been widely discussed in literature in terms of recovery capabilities concerning infrastructures, suggesting solutions to provide users ...
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The macroeconomic indicator of energy efficiency represents the energy performance in spatial terms (nation, region and macro-region) or the amount of energy used to produce a given unit of Gross Domestic Product. How...
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Conventional notions of generalization often fail to describe the ability of learned models to capture meaningful information from dynamical data. A neural network that learns complex dynamics with a small test error ...
ISBN:
(纸本)9798331314385
Conventional notions of generalization often fail to describe the ability of learned models to capture meaningful information from dynamical data. A neural network that learns complex dynamics with a small test error may still fail to reproduce its physical behavior, including associated statistical moments and Lyapunov exponents. To address this gap, we propose an ergodic theoretic approach to generalization of complex dynamical models learned from time series data. Our main contribution is to define and analyze generalization of a broad suite of neural representations of classes of ergodic systems, including chaotic systems, in a way that captures emulating underlying invariant, physical measures. Our results provide theoretical justification for why regression methods for generators of dynamical systems (Neural ODEs) fail to generalize, and why their statistical accuracy improves upon adding Jacobian information during training. We verify our results on a number of ergodic chaotic systems and neural network parameterizations, including MLPs, ResNets, Fourier Neural layers, and RNNs.
This paper studies the problem of computing a linear approximation of quadratic Wasserstein distance W2. In particular, we compute an approximation of the negative homogeneous weighted Sobolev norm whose connection to...
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This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain hardening and strain softening. The existence, stab...
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This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain hardening and strain softening. The existence, stability, and bifurcation structure of such solutions, as well as the system dynamics in the presence of damping and driving, are studied systematically. It is found that the linear resonant peaks in the system bend toward the frequency gap in the presence of nonlinearity. The time-periodic solutions that lie within the frequency gap compare well to Hamiltonian breathers if the damping and driving are small. In the Hamiltonian limit of the problem, we use a multiple scale analysis to derive a nonlinear Schrödinger equation to construct both acoustic and optical breathers. The latter compare very well with the numerically obtained breathers in the Hamiltonian limit.
In this paper, we explore the capabilities of a number of deep neural network models in generating whole-brain 3T-like MR images from clinical 1.5T MRIs. The models include a fully convolutional network (FCN) method a...
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For linearly parametrized nonlinear systems in normal form, we first develop a new prescribed-time (PT) least-squares identification scheme (abbreviated PT-LS) characterized by a blow-up function, and then design a ne...
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This paper deals with a nonlinear hybrid differential equation written using a fractional derivative with a Mittag–Leffler kernel. Firstly, we establish the existence of solutions to the studied problem by using the ...
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Classical queuing theory may be described as a branch of applied probability theory dealing with a model denoted by GI|G|S and with special cases and variants of this model. In the model GI|G|S we assume that customer...
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