arXiv research

New algorithm reduces learning regret in multi-agent systems with unknown dynamics.

This work achieves finite-time stabilization of uncertain LQ systems using random feedbacks.

We study the problem of adaptive control of a high dimensional linear quadratic (LQ) system. Previous work established the asymptotic convergence to an optimal controller for various adaptive control schemes. More recently, for the average cost LQ problem, a regret bound of ${O}(\sqrt{T})$ was shown, apart form logarit…

New theory extends LQ control to non-exponential discount scenarios.

Developed LQ MFG theory with common noise, proving existence and uniqueness.

Study of LQ MFGs in infinite-dimensional Hilbert spaces.

The paper solves a complex control problem with stochastic elements and switching conditions.

We solve a complex trade execution problem by simplifying it into a known LQ control problem.

Certainty equivalent controllers perform nearly optimally in LQ control problems with unknown dynamics.

Model-free approaches for reinforcement learning (RL) and continuous control find policies based only on past states and rewards, without fitting a model of the system dynamics. They are appealing as they are general purpose and easy to implement; however, they also come with fewer theoretical guarantees than model-bas…

RL solves discrete LQ control with Gaussian optimal policy.

Policy optimization converges to Nash equilibria in zero-sum LQ games.

Paper solves MV portfolio selection in jump-diffusion models with no-shorting constraint.

Article presents QR and LQ decomposition algorithms for various matrix sizes and ranks.

We consider the exploration-exploitation tradeoff in linear quadratic (LQ) control problems, where the state dynamics is linear and the cost function is quadratic in states and controls. We analyze the regret of Thompson sampling (TS) (a.k.a. posterior-sampling for reinforcement learning) in the frequentist setting, i.…

We study in this paper a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk management. The linear constraint on both the control and state variables considered…

Neural operators learn to solve LQ MFGs efficiently in infinite dimensions.

Introduces cofrontal mappings and studies their properties.

A new method solves complex control problems with random coefficients.

Choquet regularization improves exploration in RL.

Motivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate time…

This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop the explicit solution for this class of problem. The revealed optimal control poli…

This work optimizes RL algorithms using entropy regularisation for continuous-time LQ problems.

Study on PG learning for LQ MFC problems with common noise, proving convergence and sample complexity.

We discuss two generalizations of the collar lemma. The first is the stable neighborhood theorem which says that a (not necessarily simple) closed geodesic in a hyperbolic surface has a \lq\lq stable neighborhood\rq\rq whose width only depends on the length of the geodesic. As an application, we show that there is a lo…

New method handles robust and adaptive control of linear systems with non-convex costs.

Development systems for deep learning (DL), such as Theano, Torch, TensorFlow, or MXNet, are easy-to-use tools for creating complex neural network models. Since gradient computations are automatically baked in, and execution is mapped to high performance hardware, these models can be trained end-to-end on large amounts…

New algorithms improve blind source separation for linear-quadratic mixtures.

The paper connects non-abelian zeta functions, Fokker-Planck equations, and projective flat connections.

This paper develops q-learning methods for mean-field control problems.

Post-training optimizes model performance beyond base model limits.

Unitons, i.e.\ harmonic spheres in a unitary group, correspond to \lq uniton bundles\rq, i.e.\ holomorphic bundles over the compactified tangent space to the complex line with certain triviality and other properties. In this paper, we use a monad representation similar to Donaldson's representation of instanton bundles…

This paper formulates and studies a stochastic maximum principle for forward-backward stochastic Volterra integral equations (FBSVIEs in short), while the control area is assumed to be convex. Then a linear quadratic (LQ in short) problem for backward stochastic Volterra integral equations (BSVIEs in short) is present …

New formula for 3-manifold invariants using combinatorial methods.

This paper is devoted to study the effects arising from imposing a value-at-risk (VaR) constraint in mean-variance portfolio selection problem for an investor who receives a stochastic cash flow which he/she must then invest in a continuous-time financial market. For simplicity, we assume that there is only one investm…

This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This includes novel theoretical guarantees based on the Rademacher complexity of the corres…

In this paper, we continue our study on a general time-inconsistent stochastic linear--quadratic (LQ) control problem originally formulated in [6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional…

Study evaluates various regularization methods for electricity price forecasting.

The paper solves TIC LQ control problems using stochastic differential games.

Study of geometric analysis on asymmetric metric spaces, including heat flow and Sobolev spaces.

New algorithm minimizes regret in unknown LQ control systems.

In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution withi…

Optimal reinsurance and investment strategies are derived under mean-variance criteria with partial information.

Invariants count inflections and vertices in singular plane curves.

Paper proposes a RL approach for ALM with superior performance.

We develop robust Markov Decision Processes with risk measures for uncertain environments.

In this work we introduce the concept of Modular Framization or simply Framization. We construct a framization $F_{d,n}$ of the Birman--Wenzl--Murakami algebra, also known as BMW algebra, and start a systematic study of this framization. We show that $F_{d,n}$ is finite dimensional and the \lq braid generators\rq\ of t…

We focus in this paper on high-dimensional regression problems where each regressor can be associated to a location in a physical space, or more generally a generic geometric space. Such problems often employ sparse priors, which promote models using a small subset of regressors. To increase statistical power, the so-c…