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In many learning based control methodologies, learning the unknown dynamic model precedes the control phase, while the aim is to control the system such that it remains in some safe region of the state space. In this work, our aim is to…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
Learning or identifying dynamics from a sequence of high-dimensional observations is a difficult challenge in many domains, including reinforcement learning and control. The problem has recently been studied from a generative perspective…
Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…
In this paper, we examine the convergence landscape of multi-agent learning under uncertainty. Specifically, we analyze two stochastic models of regularized learning in continuous games -- one in continuous and one in discrete time with the…
Stochastic approximation is a powerful class of algorithms with celebrated success. However, a large body of previous analysis focuses on stochastic approximations driven by contractive operators, which is not applicable in some important…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
Recent work of Klivans, Stavropoulos, and Vasilyan initiated the study of testable learning with distribution shift (TDS learning), where a learner is given labeled samples from training distribution $\mathcal{D}$, unlabeled samples from…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
Random label noises (or observational noises) widely exist in practical machine learning settings. While previous studies primarily focus on the affects of label noises to the performance of learning, our work intends to investigate the…
We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and…
We investigate the dynamical stability of the holographic system with two order parameters, which exhibits competition and coexistence of condensations. In the linear regime, we have developed the gauge dependent formalism to calculate the…
Given a stochastic nonlinear system controlled over a possibly noisy communication channel, the paper studies the largest class of channels for which there exist coding and control policies so that the closed-loop system is stochastically…
We study generalization in an overparameterized continual linear regression setting, where a model is trained with L2 (isotropic) regularization across a sequence of tasks. We derive a closed-form expression for the expected generalization…
Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…
We study the problem of identification of linear dynamical system from a single trajectory, via excitations of isotropic Gaussian. In stark contrast with previously reported results, Ordinary Least Squares (OLS) estimator for even…
The problem of remotely stabilizing a noisy linear time invariant plant over a Gaussian relay network is addressed. The network is comprised of a sensor node, a group of relay nodes and a remote controller. The sensor and the relay nodes…
Reinforcement learning (RL) algorithms allow artificial agents to improve their selection of actions to increase rewarding experiences in their environments. Temporal Difference (TD) Learning -- a model-free RL method -- is a leading…
The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…