Related papers: Sparse Linear-Quadratic Feedback Design Using Affi…
Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) control are foundational and extensively researched problems in optimal control. We investigate LQR and LQG problems with semi-adversarial perturbations and time-varying…
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the…
We study a signature-driven numerical scheme to solve multi-dimensional linear-quadratic (LQ) stochastic control problems. Using that linear signature functionals are dense in the natural class of admissible controls, we show that our…
It was recently established that for convex optimization problems with sparse optimal solutions (be it entry-wise sparsity or matrix rank-wise sparsity) it is possible to design first-order methods with linear convergence rates that depend…
There has been growing interest in high-order tensor methods for nonconvex optimization, with adaptive regularization, as they possess better/optimal worst-case evaluation complexity globally and faster convergence asymptotically. These…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
Optimization problems with $L^1$-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discretized…
The Linear Quadratic Regulator (LQR) framework considers the problem of regulating a linear dynamical system perturbed by environmental noise. We compute the policy regret between three distinct control policies: i) the optimal online…
We address the problem of designing optimal linear time-invariant (LTI) sparse controllers for LTI systems, which corresponds to minimizing a norm of the closed-loop system subject to sparsity constraints on the controller structure. This…
In this work, we propose a feedback control based temporal discretization for linear quadratic optimal control problems (LQ problems) governed by controlled mean-field stochastic differential equations. We firstly decompose the original…
We focus on finding sparse and least-$\ell_1$-norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, nevertheless recent versions of Newton method for under-determined…
We study the performance of the certainty equivalent controller on Linear Quadratic (LQ) control problems with unknown transition dynamics. We show that for both the fully and partially observed settings, the sub-optimality gap between the…
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…
We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…
This paper presents a state and state-input constrained variant of the discrete-time iterative Linear Quadratic Regulator (iLQR) algorithm, with linear time-complexity in the number of time steps. The approach is based on a projection of…
The convergence of policy gradient algorithms in reinforcement learning hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of…
We consider the linear quadratic (LQ) optimal control problem for a class of evolution equations in infinite dimensions, in the presence of distributed and nonlocal inputs. Following the perspective taken in our previous research work on…
Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions.…
We study the discrete-time linear-quadratic (LQ) control model using reinforcement learning (RL). Using entropy to measure the cost of exploration, we prove that the optimal feedback policy for the problem must be Gaussian type. Then, we…