New algorithm learns LQR with regret using Langevin dynamics and excitation.
problem Learning LQR with a regret bound.
method Thompson sampling with Langevin dynamics and excitation mechanism.
result Achieved regret bound for LQR learning.
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48 results for “Linear Quadratic Regulator”
Linear quadratic control of nonlinear systems with Koopman operator learning and the Nyström methodmath.OC
Paper uses Koopman operator and Nyström method for efficient nonlinear control.
problem Control of nonlinear dynamical systems.
method Combines Koopman operator framework with Nyström approximation for kernel methods.
result Theoretical guarantees on the convergence rates of the approximated Riccati operator and regulator objective.
We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high…
New model-free algorithm achieves similar LQR regret guarantees.
problem Model-free control of linear dynamical systems under quadratic costs.
method Online policy gradient scheme with policy space cost analysis.
result Achieves regret scaling with √T, matching model-based methods.
We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through persistent excitation, while maintaining safety by guaranteeing the satisfaction of st…
We present the first computationally-efficient algorithm with regret for learning in Linear Quadratic Control systems with unknown dynamics. By that, we resolve an open question of Abbasi-Yadkori and Szepesvári (2011) and Dean, Mania, Matni, Recht, and Tu (2018).
We study the global convergence of generative adversarial imitation learning for linear quadratic regulators, which is posed as minimax optimization. To address the challenges arising from non-convex-concave geometry, we analyze the alternating gradient algorithm and establish its Q-linear rate of convergence to a uniq…
Policy Gradient Converges to the Globally Optimal Policy for Nearly Linear-Quadratic Regulatorscs.LG
Policy gradient converges to globally optimal policy in nearly linear-quadratic systems.
problem Finding optimal policies in nonlinear control systems with partial information.
method Policy gradient algorithm designed for nearly linear-quadratic regulators with small Lipschitz nonlinear components.
result Policy gradient algorithm converges to globally optimal policy with linear rate.
Efficiently solves exploration-exploitation in LQR using Lagrangian relaxation.
problem Exploration-exploitation dilemma in linear quadratic regulator (LQR) setting.
method Relax optimistic optimization into a constrained extended LQR problem, then solve using Riccati equations.
result Computes -optimistic controller efficiently with Riccati equations.
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.
We study the variance of the REINFORCE policy gradient estimator in environments with continuous state and action spaces, linear dynamics, quadratic cost, and Gaussian noise. These simple environments allow us to derive bounds on the estimator variance in terms of the environment and noise parameters. We compare the pr…
Policy gradient methods converge for LQR problems with noisy state dynamics.
problem Finding optimal policies in noisy LQR problems over finite time horizons.
method Policy gradient methods with convergence guarantees for finite time and stochastic state dynamics.
result Global linear convergence for policy gradient methods in LQR problems with weak assumptions.
Multi-agent reinforcement learning has been successfully applied to a number of challenging problems. Despite these empirical successes, theoretical understanding of different algorithms is lacking, primarily due to the curse of dimensionality caused by the exponential growth of the state-action space with the number o…
This work establishes safe reinforcement learning for LQR with nonlinear baselines.
problem Safe reinforcement learning in LQR with unknown dynamics and safety constraints.
method General framework for nonlinear baselines, focusing on 1D spaces.
result Achieves optimal regret bounds for constrained reinforcement learning.
The main challenge for adaptive regulation of linear-quadratic systems is the trade-off between identification and control. An adaptive policy needs to address both the estimation of unknown dynamics parameters (exploration), as well as the regulation of the underlying system (exploitation). To this end, optimism-based…
On the Global Convergence of Actor-Critic: A Case for Linear Quadratic Regulator with Ergodic Costcs.LG
Despite the empirical success of the actor-critic algorithm, its theoretical understanding lags behind. In a broader context, actor-critic can be viewed as an online alternating update algorithm for bilevel optimization, whose convergence is known to be fragile. To understand the instability of actor-critic, we focus o…
New bounds for adaptive control in high dimensions without fixed state space.
problem Adaptive control of linear systems in high or infinite dimensions.
method Novel perturbation bound for certainty equivalence, scaling with prediction error.
result First regret bounds for LQR in infinite dimensional systems, independent of ambient dimension.
Optimal dynamic allocation of carbon allowances reduces emissions efficiently.
problem Reducing carbon emissions from firms over time with dynamic allocation and trading.
method Variational approach to solve the Stackelberg game between regulator and firms.
result Optimal policies lead to constant abatement effort and allowance price, outperforming static allocations.
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 cost incurred by playing the certainty equivalent controller on the true system …
Implicit Bias of Policy Gradient in Linear Quadratic Control: Extrapolation to Unseen Initial Statescs.LG
This paper studies how gradient descent in control systems can perform well on unseen data.
problem The extent of a learned controller's ability to extrapolate to unseen initial states.
method Theoretical study of policy gradient in Linear Quadratic Regulator (LQR) problems, focusing on the role of exploration.
result The performance of a learned controller on unseen initial states depends on the degree of exploration induced by the system.
Reinforcement learning (RL) has been successfully used to solve many continuous control tasks. Despite its impressive results however, fundamental questions regarding the sample complexity of RL on continuous problems remain open. We study the performance of RL in this setting by considering the behavior of the Least-S…
Direct policy gradient methods for reinforcement learning and continuous control problems are a popular approach for a variety of reasons: 1) they are easy to implement without explicit knowledge of the underlying model 2) they are an "end-to-end" approach, directly optimizing the performance metric of interest 3) they…
Safe Reinforcement Learning-Based Vibration Control: Overcoming Training Risks with LQR Guidancecs.LG
Safe RL-based vibration control using LQR guidance.
problem Training risks in RL-based vibration control.
method Hybrid control framework combining LQR and RL.
result LQR controller outperforms uncontrolled scenario.
Study task-guided exploration in linear dynamical systems, improving sample complexity.
problem Efficiently learning about an environment to complete a specific task.
method Proposed a computationally efficient experiment-design based exploration algorithm.
result Optimally explores the environment, collecting precise information needed to complete the task.
Modeling pollution from competing firms using mean-field games.
problem Pollution regulation of competitive firms producing similar goods.
method Developed a mean-field game model with cap-and-trade regulation.
result Explicit solutions found through Riccati differential equations.
This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown. We propose a multi-stage procedure, called Coarse-ID control, that estimates a model from a few experimental trials, estimates the error in that model with respect to the truth, and then d…
We consider the problem of learning in Linear Quadratic Control systems whose transition parameters are initially unknown. Recent results in this setting have demonstrated efficient learning algorithms with regret growing with the square root of the number of decision steps. We present new efficient algorithms that ach…
TSAC achieves optimal frequentist regret in adaptive control of LQRs.
problem Adaptive control of stabilizable linear-quadratic regulators with unknown dynamics.
method Thompson Sampling (TS) for adaptive control of LQRs, with a novel early exploration strategy.
result Achieves regret, optimal for multidimensional systems.
Optimal trading strategy using LQR framework with price mean-reversion.
problem Developing a dynamic trading strategy in a market with linear and quadratic costs.
method Model Predictive Control (MPC) approach to optimize trading curve with positivity constraints.
result Optimal trading curve reacts opportunistically to price changes while satisfying constraints.
We study the sample complexity of approximate policy iteration (PI) for the Linear Quadratic Regulator (LQR), building on a recent line of work using LQR as a testbed to understand the limits of reinforcement learning (RL) algorithms on continuous control tasks. Our analysis quantifies the tension between policy improv…
The effectiveness of model-based versus model-free methods is a long-standing question in reinforcement learning (RL). Motivated by recent empirical success of RL on continuous control tasks, we study the sample complexity of popular model-based and model-free algorithms on the Linear Quadratic Regulator (LQR). We show…
Finding optimal feedback controllers for nonlinear dynamic systems from data is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful framework for direct controller tuning from experimental trials. For selecting the next query point and finding the global optimum, BO relies on a probabilistic desc…
We study optimal regret bounds for control in linear dynamical systems under adversarially changing strongly convex cost functions, given the knowledge of transition dynamics. This includes several well studied and fundamental frameworks such as the Kalman filter and the linear quadratic regulator. State of the art met…
Paper proposes a COP model for Algo trading using LQR.
problem Complexities in child order placement in Algo trading.
method Stochastic LQR model for passive limit orders and aggressive takeout orders.
result Closed-form solutions for optimal child order placement.
New algorithm minimizes regret in unknown LQ control systems.
problem Online learning in Linear Quadratic Control systems with unknown matrices.
method Developed an online learning algorithm with guarantees on expected regret.
result Upper bounds on regret are minimal and match existing lower bounds.
New algorithm learns linear dynamical systems from measurements.
problem Learning system dynamics from linear measurements efficiently and accurately.
method Method of moments estimator to directly estimate Markov parameters.
result First polynomial time algorithm for learning linear dynamical systems.
Efficiently extracts linear dynamics from complex observations.
problem Learning policies directly from rich, high-dimensional observations.
method Modeling linear dynamics in a hidden subspace and developing an efficient algorithm.
result Successfully extracts linear dynamics from rich observations.
We present the perceptor gradients algorithm -- a novel approach to learning symbolic representations based on the idea of decomposing an agent's policy into i) a perceptor network extracting symbols from raw observation data and ii) a task encoding program which maps the input symbols to output actions. We show that t…
We describe an optimal adversarial attack formulation against autoregressive time series forecast using Linear Quadratic Regulator (LQR). In this threat model, the environment evolves according to a dynamical system; an autoregressive model observes the current environment state and predicts its future values; an attac…
RichID learns optimal control policies from nonlinear observations.
problem Continuous control with unknown nonlinearity in system model.
method RichID algorithm using a least-squares regression oracle.
result First provable sample complexity guarantee for continuous control.
Survey on statistical learning theory for control, focusing on linear systems.
problem Applying machine learning techniques to control systems, especially linear ones.
method Adapting tools from modern high-dimensional statistics and learning theory.
result Recent advances in statistical learning theory for control, particularly for linear systems.
Survey of theoretical foundations for policy optimization in control.
problem Understanding the theoretical properties of gradient-based methods in control and reinforcement learning.
method Interdisciplinary review of optimization landscape, convergence, and sample complexity for various control problems.
result Recent theoretical results on stability and robustness in learning-based control.
We present a reinforcement learning approach to goal based wealth management problems such as optimization of retirement plans or target dated funds. In such problems, an investor seeks to achieve a financial goal by making periodic investments in the portfolio while being employed, and periodically draws from the acco…
Distribution grids are currently challenged by frequent voltage excursions induced by intermittent solar generation. Smart inverters have been advocated as a fast-responding means to regulate voltage and minimize ohmic losses. Since optimal inverter coordination may be computationally challenging and preset local contr…
It is shown that the sum of class numbers of orders in totally complex quartic fields with no real quadratic subfield obeys an asymptotic law similar to the prime numbers, as the bound on the regulators tends to infinity. Here only orders which are maximal at a given set of primes containing an even number of elements …
The paper sets bounds on how much regret is unavoidable in adaptive LQR with unknown B-matrix.
problem Understanding the limits of adaptive LQR with unknown B-matrix.
method Local asymptotic minimax regret lower bounds using van Trees' inequality and Bellman error representation.
result Logarithmic regret is impossible if the parametrization induces an uninformative optimal policy.
Survey explores geometric aspects of policy optimization in control systems.
problem Understanding the geometric relationships between control design and optimization.
method Geometric perspective on policy optimization, focusing on parameterization and topology.
result Implications of policy geometry on stability and performance of local search algorithms.
Learning to control linear systems is statistically hard, especially for underactuated systems.
problem Statistical difficulty of learning to control linear systems, especially underactuated ones.
method Utilized minimax lower bounds and structural assumptions to prove learning complexity can be exponential.
result Learning complexity can be at most exponential with the controllability index of the system.