相关论文: Global stability in a mathematical model of de-rad…

Cooperative systems often remain in persistently suboptimal yet stable states. This paper explains such "rational stagnation" as an equilibrium sustained by a rational adversary whose utility follows the principle of potential loss, $u_{D}…

In the Bayesian reinforcement learning (RL) setting, a prior distribution over the unknown problem parameters -- the rewards and transitions -- is assumed, and a policy that optimizes the (posterior) expected return is sought. A common…

Disaffected youth are among the most susceptible in espousing and acting on extremist ideals, as confirmed by demographic studies. To study age-dependent radicalization we introduce a three-stage model where individuals progress through…

Deep neural networks obtained by standard training have been constantly plagued by adversarial examples. Although adversarial training demonstrates its capability to defend against adversarial examples, unfortunately, it leads to an…

Regularization, whether explicit in terms of a penalty in the loss or implicit in the choice of algorithm, is a cornerstone of modern machine learning. Indeed, controlling the complexity of the model class is particularly important when…

We study the global dynamics of a reaction-diffusion SEIR infection model with distributed delay and nonlinear incidence rate. The well-posedness of the proposed model is proved. By means of Lyapunov functionals, we show that the disease…

Coalition forming is investigated among countries, which are coupled with short range interactions, under the influence of external fields produced by the existence of global alliances. The model rests on the natural model of coalition…

This article presents novel methods for synthesizing distributionally robust stabilizing neural controllers and certificates for control systems under model uncertainty. A key challenge in designing controllers with stability guarantees for…

We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…

Generalization is one of the fundamental issues in machine learning. However, traditional techniques like uniform convergence may be unable to explain generalization under overparameterization. As alternative approaches, techniques based on…

As the use of machine learning in high impact domains becomes widespread, the importance of evaluating safety has increased. An important aspect of this is evaluating how robust a model is to changes in setting or population, which…

Consider $\operatorname{Sym}(n)$, endowed with the normalized Hamming metric $d_n$. A finitely-generated group $\Gamma$ is \emph{P-stable} if every almost homomorphism $\rho_{n_k}\colon \Gamma\rightarrow\operatorname{Sym}(n_k)$ (i.e., for…

We study a spatially explicit harvesting model in periodic or bounded environments. The model is governed by a parabolic equation with a spatially dependent nonlinearity of Kolmogorov--Petrovsky--Piskunov type, and a negative external…

This paper investigates model robustness in reinforcement learning (RL) to reduce the sim-to-real gap in practice. We adopt the framework of distributionally robust Markov decision processes (RMDPs), aimed at learning a policy that…

When does a crisis-induced surge in radical-party support fade away, and when does it become a durable realignment? We address this in a mathematical sociology threshold model on a conserved population. The baseline admits a global…

Reinforcement learning (RL) excels in applications such as video games, but ensuring safety as well as the ability to achieve the specified goals remains challenging when using RL for real-world problems, such as human-aligned tasks where…

In a very recent work [J. D. Hern\'andez Guill\'en, A. Mart\'in del Rey, A mathematical model for malware spread on WSNs with population dynamics, Physica A: Statistical Mechanics and its Applications 545(2020) 123609], a novel theoretical…

The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be…

Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…

We study a class of SIRS epidemic dynamical models with a general non-linear incidence rate and transfer from infectious to susceptible. The incidence rate includes a wide range of monotonic, con- cave incidence rates and some non-monotonic…