Shahriar Talebi

Larsen Bier, Shahriar Talebi

Kalman filtering is a cornerstone of estimation theory, yet learning the optimal filter under unknown and potentially singular noise covariances remains a fundamental challenge. In this paper, we revisit this problem through the lens of control--estimation duality and data-driven policy optimization, formulating the learning of the steady-state Kalman gain as a stochastic policy optimization problem directly from measurement data. Our key contribution is a Riemannian regularization that reshapes the optimization landscape, restoring structural properties such as coercivity and gradient dominance. This geometric perspective enables the effective use of first-order methods under significantly relaxed conditions, including unknown and rank-deficient noise covariances. Building on this framework, we develop a computationally efficient algorithm with a data-driven gradient oracle, enabling scalable stochastic implementations. We further establish non-asymptotic convergence and error guarantees enabled by the Riemannian regularization, quantifying the impact of bias and variance in gradient estimates and demonstrating favorable scaling with problem dimension. Numerical results corroborate the effectiveness of the proposed approach and robustness to the choice of stepsize in challenging singular estimation regimes.

Mohammadreza Rostami, Shahriar Talebi, Solmaz S. Kia

We propose ScalarFedLQR, a communication-efficient federated algorithm for model-free learning of a common policy in linear quadratic regulator (LQR) control of heterogeneous agents. The method builds on a decomposed projected gradient mechanism, in which each agent communicates only a scalar projection of a local zeroth-order gradient estimate. The server aggregates these scalar messages to reconstruct a global descent direction, reducing per-agent uplink communication from O(d) to O(1), independent of the policy dimension. Crucially, the projection-induced approximation error diminishes as the number of participating agents increases, yielding a favorable scaling law: larger fleets enable more accurate gradient recovery, admit larger stepsizes, and achieve faster linear convergence despite high dimensionality. Under standard regularity conditions, all iterates remain stabilizing and the average LQR cost decreases linearly fast. Numerical results demonstrate performance comparable to full-gradient federated LQR with substantially reduced communication.

Yuyang Zhang, Shahriar Talebi, Na Li

In this paper, we focus on learning a linear time-invariant (LTI) model with low-dimensional latent variables but high-dimensional observations. We provide an algorithm that recovers the high-dimensional features, i.e. column space of the observer, embeds the data into low dimensions and learns the low-dimensional model parameters. Our algorithm enjoys a sample complexity guarantee of order $\tilde{\mathcal{O}}(n/ε^2)$, where $n$ is the observation dimension. We further establish a fundamental lower bound indicating this complexity bound is optimal up to logarithmic factors and dimension-independent constants. We show that this inevitable linear factor of $n$ is due to the learning error of the observer's column space in the presence of high-dimensional noises. Extending our results, we consider a meta-learning problem inspired by various real-world applications, where the observer column space can be collectively learned from datasets of multiple LTI systems. An end-to-end algorithm is then proposed, facilitating learning LTI systems from a meta-dataset which breaks the sample complexity lower bound in certain scenarios.

Siavash Alemzadeh, Hesam Talebiyan, Shahriar Talebi et al.

From an optimization point of view, resource allocation is one of the cornerstones of research for addressing limiting factors commonly arising in applications such as power outages and traffic jams. In this paper, we take a data-driven approach to estimate an optimal nodal restoration sequence for immediate recovery of the infrastructure networks after natural disasters such as earthquakes. We generate data from td-INDP, a high-fidelity simulator of optimal restoration strategies for interdependent networks, and employ deep neural networks to approximate those strategies. Despite the fact that the underlying problem is NP-complete, the restoration sequences obtained by our method are observed to be nearly optimal. In addition, by training multiple models---the so-called estimators---for a variety of resource availability levels, our proposed method balances a trade-off between resource utilization and restoration time. Decision-makers can use our trained models to allocate resources more efficiently after contingencies, and in turn, improve the community resilience. Besides their predictive power, such trained estimators unravel the effect of interdependencies among different nodal functionalities in the restoration strategies. We showcase our methodology by the real-world interdependent infrastructure of Shelby County, TN.

Shahriar Talebi, Siavash Alemzadeh, Niyousha Rahimi et al.

Learning, say through direct policy updates, often requires assumptions such as knowing a priori that the initial policy (gain) is stabilizing, or persistently exciting (PE) input-output data, is available. In this paper, we examine online regulation of (possibly unstable) partially unknown linear systems with no prior access to an initial stabilizing controller nor PE input-output data; we instead leverage the knowledge of the input matrix for online regulation. First, we introduce and characterize the notion of "regularizability" for linear systems that gauges the extent by which a system can be regulated in finite-time in contrast to its asymptotic behavior (commonly characterized by stabilizability/controllability). Next, having access only to the input matrix, we propose the Data-Guided Regulation (DGR) synthesis procedure that -- as its name suggests -- regulates the underlying state while also generating informative data that can subsequently be used for data-driven stabilization or system identification. We further improve the computational performance of DGR via a rank-one update and demonstrate its utility in online regulation of the X-29 aircraft.