Related papers: Sample Complexity of the Linear Quadratic Regulato…
We study the problem of policy evaluation with linear function approximation and present efficient and practical algorithms that come with strong optimality guarantees. We begin by proving lower bounds that establish baselines on both the…
Policy optimization methods are powerful algorithms in Reinforcement Learning (RL) for their flexibility to deal with policy parameterization and ability to handle model misspecification. However, these methods usually suffer from slow…
We study reinforcement learning (RL) for a class of continuous-time linear-quadratic (LQ) control problems for diffusions, where states are scalar-valued and running control rewards are absent but volatilities of the state processes depend…
Understanding the optimization landscape of linear quadratic regulation (LQR) problems is fundamental to the design of efficient reinforcement learning solutions. Recent work has made significant progress in characterizing the landscape of…
We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret…
The Linear-Quadratic Regulation (LQR) problem with unknown system parameters has been widely studied, but it has remained unclear whether $\tilde{ \mathcal{O}}(\sqrt{T})$ regret, which is the best known dependence on time, can be achieved…
This paper focuses on adaptive control of the discrete-time linear quadratic regulator (adaptive LQR). Recent literature has made significant contributions in proving non-asymptotic convergence rates, but existing approaches have a few…
Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard…
We consider optimization of nonlinear objective functions that balance $d$ linear criteria over $n$-element independence systems presented by linear-optimization oracles. For $d=1$, we have previously shown that an $r$-best approximate…
We study the problem of maximizing a monotone submodular function subject to a matroid constraint, and present for it a deterministic non-oblivious local search algorithm that has an approximation guarantee of $1 - 1/e - \varepsilon$ (for…
Many engineering problems have multiple objectives, and the overall aim is to optimize a non-linear function of these objectives. In this paper, we formulate the problem of maximizing a non-linear concave function of multiple long-term…
This work pioneers regret analysis of risk-sensitive reinforcement learning in partially observable environments with hindsight observation, addressing a gap in theoretical exploration. We introduce a novel formulation that integrates…
We derive a family of efficient constrained dynamics algorithms by formulating an equivalent linear quadratic regulator (LQR) problem using Gauss principle of least constraint and solving it using dynamic programming. Our approach builds…
We develop the first quantum algorithm for the constrained portfolio optimization problem. The algorithm has running time $\widetilde{O} \left( n\sqrt{r} \frac{\zeta \kappa}{\delta^2} \log \left(1/\epsilon\right) \right)$, where $r$ is the…
We design differentially private algorithms for the bandit convex optimization problem in the projection-free setting. This setting is important whenever the decision set has a complex geometry, and access to it is done efficiently only…
Many reinforcement learning methods achieve great success in practice but lack theoretical foundation. In this paper, we study the convergence analysis on the problem of the Linear Quadratic Regulator (LQR). The global linear convergence…
Modern Reinforcement Learning (RL) is commonly applied to practical problems with an enormous number of states, where function approximation must be deployed to approximate either the value function or the policy. The introduction of…
Online optimization has recently opened avenues to study optimal control for time-varying cost functions that are unknown in advance. Inspired by this line of research, we study the distributed online linear quadratic regulator (LQR)…
Value function approximation has demonstrated phenomenal empirical success in reinforcement learning (RL). Nevertheless, despite a handful of recent progress on developing theory for RL with linear function approximation, the understanding…
We consider the problem of online learning in Linear Quadratic Control systems whose state transition and state-action transition matrices $A$ and $B$ may be initially unknown. We devise an online learning algorithm and provide guarantees…