Paper derives an error bound for stochastic LTI systems.
problem Stochastic LTI systems with inputs in control engineering and econometrics.
method PAC-Bayesian-Like error bound derivation.
result Derived an error bound for stochastic LTI systems.
Paper develops PAC-Bayes bounds for unknown linear systems.
problem Learning controllers for unknown stochastic linear discrete-time systems.
method PAC-Bayes framework for data-dependent high probability bounds.
result Proposes efficient learning algorithms with theoretical guarantees.
The study analyzes stochastic Lie systems and their applications in various models.
problem Analyzing stochastic differential equations on manifolds.
method Coalgebra method for Hamiltonian stochastic Lie systems.
result New examples of stochastic Lie systems and Hamiltonian stochastic Lie systems are analyzed.
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several e…
Efficient algorithm for unknown linear systems with convex costs.
problem Controlling an unknown linear system with stochastic convex costs.
method Optimism in the Face of Uncertainty paradigm.
result Achieves optimal T \sqrt{T} T regret-rate. Study shows certainty equivalent policy minimizes regret in continuous-time systems.
problem Minimizing regret in continuous-time stochastic linear-quadratic systems.
method Theoretical analysis of randomized certainty equivalent policy.
result Establishes square-root of time regret bounds and linear scaling with parameters.
Study optimizes resource allocation in noisy systems for better control.
problem Limited attention in stochastic systems with multiplicative noise.
method Analytical and numerical methods for optimal attention allocation.
result Effective resource allocation enhances noise estimation and control decisions.
The paper develops robust tests for detecting independence in synchronous stochastic systems with finite sample guarantees.
problem Detecting independence in synchronous stochastic systems with finite sample guarantees.
method Combines confidence region estimates with permutation tests and dependence measures to detect nonlinear dependence.
result Consistent hypothesis tests for detecting independence under mild assumptions.
Develops a new approach to optimal control of stochastic systems.
problem Optimal control of stochastic nonlinear dynamical systems is challenging.
method Formulates optimal control as input estimation, using probabilistic inference and Expectation Maximization.
result Extracts time-varying linear Gaussian feedback controllers from the joint state-action distribution.
New controller reduces regret in non-stochastic control with adversarial perturbations.
problem Non-stochastic control with adversarial perturbations and partially observed states.
method Denoised observations and online gradient descent.
result Sublinear regret bounds, optimal for known and unknown systems.
This work studies the contraction coefficients of Schrödinger bridge problems in linear systems.
problem Optimally controlling the evolution of a system's state density over time.
method Analyzes and improves the convergence rates of dynamic Schrödinger systems via geometric and control-theoretic interpretations.
result New insights into improving computation of worst-case contraction coefficients by preconditioning.
The paper develops methods to infer modes of linear systems from noisy data.
problem Detecting oscillations in power flow in AC electrical networks.
method Develops methods to infer modes (real or complex) from observations of linear systems forced by Gaussian noise.
result Inference of damping rates, frequencies, and mode shapes for real and complex modes.
Develops inverse unscented Kalman filter for non-linear systems.
problem Estimating defender's state in adversarial settings.
method Formulated inverse unscented Kalman filter (I-UKF) and reproducing kernel Hilbert space-based UKF (RKHS-UKF).
result Proposed filters are conservative estimators with upper-bounded error covariance.
Deep neural nets solve complex stochastic control problems.
problem Solving stochastic optimal control problems with control multiplicative noise.
method Deep recurrent neural networks and LSTM.
result Deep learning algorithm solves complex stochastic control problems efficiently.
New method infers dynamical systems from population data.
problem Inferring dynamical systems from population data.
method Deducing and estimating Fokker-Planck equation, projecting to test functions, sparse inference.
result Induces driving forces of dynamical systems.
Stochastic gradient descent approximates Gaussian process posteriors efficiently.
problem Efficiently sampling from Gaussian process posteriors with limited computational resources.
method Developed stochastic gradient optimization objectives for sampling from Gaussian process posteriors.
result Stochastic gradient descent produces accurate predictive distributions, even in non-convergent cases.
Method predicts future rewards from past actions in a linear Gaussian system.
problem Maximizing cumulative reward in a stochastic multi-armed bandit with linear Gaussian dynamics.
method Proposes a method using a modified Kalman filter to predict future rewards based on past rewards.
result Reward from any action can be used to predict another action's future reward.
Study on stochastic approximation with Polyak-Ruppert averaging for linear systems.
problem Understanding the asymptotic and non-asymptotic properties of stochastic approximation procedures.
method Detailed analysis of linear stochastic approximation with Polyak-Ruppert averaging, focusing on asymptotic and non-asymptotic properties.
result Proves CLT and non-asymptotic concentration inequality for averaged iterates, providing refined understanding of linear stochastic approximation.
New method estimates SDE parameters efficiently using WCE and SGD.
problem Parameter estimation for stochastic differential equations.
method Wiener Chaos Expansion and Stochastic Gradient Descent.
result Accurate parameter recovery from noisy observations.
Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.
problem Predicting and capturing long-term behaviors of stochastic dynamical systems.
method Data-driven framework combining Reservoir Computing and Normalizing Flow, integrating error modeling and both approaches virtues.
result Successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors.
Novel approach to Nash equilibrium in mean-field stochastic games with operator resolvents.
problem Finding Nash equilibrium in mean-field stochastic games with mean-field interaction.
method Proposed a novel approach to derive Nash equilibrium semi-explicitly using operator resolvents and stochastic Fredholm equations.
result Equilibrium of the N N N -player game converges to mean-field equilibrium, and ε \varepsilon ε -Nash equilibrium derived as a by-product. Bayesian algorithm stabilizes unknown continuous-time systems from unstable data.
problem Learning and stabilizing unknown continuous-time systems with uncertain dynamics.
method Bayesian learning algorithm that learns from unstable data to stabilize the system in finite time.
result The algorithm stabilizes unknown continuous-time stochastic linear systems effectively after a short time period.
New algorithm controls linear systems with bandit feedback, achieving optimal regret.
problem Controlling linear systems with bandit feedback under adversarial costs.
method Developed a new algorithm for linear control with memory optimization technique.
result Achieved optimal regret growth proportional to square root of time horizon.
The paper solves a complex control problem with stochastic elements and switching conditions.
problem Non-homogeneous stochastic LQ control with regime switching and random coefficients.
method Explicit optimal control and value obtained through two systems of backward stochastic differential equations (BSDEs). Existence and uniqueness of solutions proved using BMO martingales and contraction mapping method.
result Explicit optimal state feedback control and optimal value derived for the problem.
In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the Stochastic Gradient Langevin Dynamics algorithm to draw samples from the posterior …
The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the expression of the stochastic process is found. An application of the model propo…
New algorithm estimates partially-observed linear systems with better rates than previous methods.
problem Estimating parameters of partially-observed linear systems with long-term dependencies and semi-parametric noise.
method Prefiltered least squares estimator with semi-parametric noise model.
result First algorithm provably estimates parameters of partially-observed linear systems with rates not dependent on dependency decay rate.
We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system. Even though the objective function is non-convex, we provide polynomial running …
Weak correlations explain linear dynamics in deep learning models.
problem Understanding the linear structure in gradient-based learning algorithms.
method Characterization of weak correlations between derivatives and parameters.
result Weak correlations are the underlying principle for linearization in deep learning models.
We propose a model of inter-bank lending and borrowing which takes into account clearing debt obligations. The evolution of log-monetary reserves of N N N banks is described by coupled diffusions driven by controls with delay in their drifts. Banks are minimizing their finite-horizon objective functions which take into a…
Investigates financial and economic systems using statistical mechanics and information theory.
problem Complexity, asymmetry, stochasticity, and non-linearity in financial and economic systems.
method Model-based and empirical analyses using statistical mechanics and information theory.
result Derives probability distribution functions for better understanding of financial and economic dynamics.
Unified framework for solving fixed-point equations in deterministic and stochastic settings.
problem Solving fixed-point equations for seminorm-contractive operators in both deterministic and stochastic contexts.
method Fixed-point theorem and stochastic approximation analysis.
result Unified finite-sample bounds for various reinforcement learning algorithms.
Develops a new theory for neural systems stability and width effects.
problem Stability and finite-width effects in deep neural systems.
method Gauge-covariant stochastic effective field theory using classical commuting fields.
result Predicts the edge of chaos and low-frequency spectral deformation.
New method disentangles perceptual uncertainty and behavioral costs in partially observable systems.
problem Tackles inverse optimal control for non-linear partially observable systems.
method Probabilistic approach using maximum causal entropy formulations and local linearization.
result Disentangles perceptual factors and behavioral costs in sequential decision-making.
StarNet trains deep models without gradients using linear equations.
problem Training deep generative models with gradients.
method Solving determined systems of linear equations.
result Least-square bounds for latent codes and model parameters.
Paper proposes adaptive control for unknown systems using reinforcement learning.
problem Adaptive control for unknown, linearizable systems.
method On-policy reinforcement learning for discrete-time, stochastic systems.
result Stability and tracking errors concentrate near zero with high probability.
New estimator learns symmetric dynamics from few observations.
problem Learning parameters of stochastic linear dynamics from limited data.
method Method of moments estimator using T = O ( log N ) T=\mathcal{O}(\log N) T = O ( log N ) observations. result Achieves small maximum element-wise error on symmetric matrices.
DeepONet accelerates reliability analysis of stochastic nonlinear systems.
problem Time-dependent reliability analysis of systems with stochastic forcing.
method DeepONet, a novel operator network, learns function-to-function mappings.
result DeepONet efficiently and accurately predicts system responses.
Improved SGD for robust linear and ReLU regression with adversarial corruptions.
problem Robust regression with adversarial corruptions in streaming data.
method Stochastic gradient descent (SGD-exp) with exponentially decaying step size.
result Nearly linear convergence to true parameter with up to 50% Massart corruption rate.
First robust bandit algorithm for contextual bandits with sub-linear regret.
problem Vulnerability of linear contextual bandit algorithms to adversarial attacks.
method Proposes a robust bandit algorithm for stochastic linear contextual bandits under fully adaptive and omniscient attacks.
result Sub-linear regret under various attacks without requiring attack information.
AI systems can be corrected without rebuilding them, using simple linear methods.
problem Errors in AI systems can lead to serious consequences.
method Developed fast non-destructive methods using linear Fisher discriminant.
result Simple linear methods can separate error-prone situations from correct ones.
Paper solves time-inconsistent control problems with BSDEs.
problem Time-inconsistent stochastic control in continuous time.
method Probabilistic representation via BSDEs.
result Equilibrium value function resolved for inconsistent cases.
The paper offers precise bounds for averaged LSA iterates in linear systems.
problem Computing approximate solutions of linear systems with noisy observations.
method Finite-time analysis of LSA algorithms with Polyak-Ruppert averaging.
result Sharp high-probability bounds for averaged LSA iterates.
A new method for estimating adversarial strategies in nonlinear systems.
problem Inferring an intelligent adversarial agent's strategy in highly nonlinear systems.
method Formulated inverse cognition as a nonlinear Gaussian state-space model and developed an inverse UKF (IUKF) system.
result The estimation error of IUKF converges and closely follows the recursive Cramér-Rao lower bound.
A new framework for bilevel optimization tackles stochastic and global variance reduction.
problem Bilevel optimization challenges in large-scale empirical risk minimization.
method Introducing a novel framework where inner and main variables evolve simultaneously, leading to unbiased estimates and global variance reduction algorithms.
result SABA algorithm achieves $O( rac{1}{T})$ convergence rate and linear convergence under Polyak-Lojasciewicz assumption.
Overview of high-dimensional dynamical systems and their applications to machine learning.
problem Characterizing behavior of high-dimensional dynamical systems driven by random matrices.
method Cavity method arguments, path integrals, dynamical mean field theory (DMFT), and random matrix resolvents.
result Connections between random matrix resolvents and DMFT response, and non-monotonic loss curves in training.
Paper tackles online control of linear systems with unbounded noise.
problem Online control of linear systems under unbounded noise with unknown convex cost functions.
method Developed an algorithm achieving i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) high-probability regret under unbounded noise, and established O ( m p o l y ( log T ) ) O({
m poly} (\log T)) O ( m p o l y ( log T )) regret bound for strongly convex costs and sub-Gaussian noise. result Achieved i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) high-probability regret under unbounded noise, and O ( m p o l y ( log T ) ) O({
m poly} (\log T)) O ( m p o l y ( log T )) regret bound for specific noise and cost conditions. Stochastic gradient descent improves Gaussian process regression.
problem Efficiently solving large linear systems in Gaussian process regression.
method Developed a stochastic dual descent algorithm using insights from optimisation and kernel communities.
result Stochastic gradient descent is highly effective when done right.