Reinforcement Learning for a Discrete-Time Linear-Quadratic Control Problem with an Application

• URL: http://arxiv.org/abs/2412.05906v2
• Date: Tue, 04 Feb 2025 10:22:04 GMT
• Title: Reinforcement Learning for a Discrete-Time Linear-Quadratic Control Problem with an Application
• Authors: Lucky Li,
• Abstract summary: 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 apply the results of the discrete-time LQ model to solve the discrete-time mean-variance asset-liability management problem and prove our RL algorithm's policy improvement and convergence.
• Score: 0.0
• License:
• Abstract: 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 apply the results of the discrete-time LQ model to solve the discrete-time mean-variance asset-liability management problem and prove our RL algorithm's policy improvement and convergence. Finally, a numerical example sheds light on the theoretical results established using simulations.

Related papers

• Attribute Controlled Fine-tuning for Large Language Models: A Case Study on Detoxification [76.14641982122696]
  We propose a constraint learning schema for fine-tuning Large Language Models (LLMs) with attribute control. We show that our approach leads to an LLM that produces fewer inappropriate responses while achieving competitive performance on benchmarks and a toxicity detection task.
  arXiv  Detail & Related papers  (2024-10-07T23:38:58Z)
• Full error analysis of policy gradient learning algorithms for exploratory linear quadratic mean-field control problem in continuous time with common noise [0.0]
  We study policy gradient (PG) learning and first demonstrate convergence in a model-based setting. We prove the global linear convergence and sample complexity of the PG algorithm with two-point gradient estimates in a model-free setting. In this setting, the parameterized optimal policies are learned from samples of the states and population distribution.
  arXiv  Detail & Related papers  (2024-08-05T14:11:51Z)
• Sublinear Regret for a Class of Continuous-Time Linear--Quadratic Reinforcement Learning Problems [10.404992912881601]
  We study reinforcement learning for a class of continuous-time linear-quadratic (LQ) control problems for diffusions. We apply a model-free approach that relies neither on knowledge of model parameters nor on their estimations, and devise an actor-critic algorithm to learn the optimal policy parameter directly.
  arXiv  Detail & Related papers  (2024-07-24T12:26:21Z)
• Continuous-Time Model-Based Reinforcement Learning [4.427447378048202]
  We propose a continuous-time MBRL framework based on a novel actor-critic method. We implement and test our method on a new ODE-RL suite that explicitly solves continuous-time control systems.
  arXiv  Detail & Related papers  (2021-02-09T11:30:19Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)
• Logistic Q-Learning [87.00813469969167]
  We propose a new reinforcement learning algorithm derived from a regularized linear-programming formulation of optimal control in MDPs. The main feature of our algorithm is a convex loss function for policy evaluation that serves as a theoretically sound alternative to the widely used squared Bellman error.
  arXiv  Detail & Related papers  (2020-10-21T17:14:31Z)
• Robust Reinforcement Learning: A Case Study in Linear Quadratic Regulation [23.76925146112261]
  This paper studies the robustness of reinforcement learning algorithms to errors in the learning process. It is shown that policy iteration for LQR is inherently robust to small errors in the learning process.
  arXiv  Detail & Related papers  (2020-08-25T11:11:28Z)
• A spectral algorithm for robust regression with subgaussian rates [0.0]
  We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples. The goal is to design a procedure which attains the optimal sub-gaussian error bound even though the data have only finite moments.
  arXiv  Detail & Related papers  (2020-07-12T19:33:50Z)
• Control as Hybrid Inference [62.997667081978825]
  We present an implementation of CHI which naturally mediates the balance between iterative and amortised inference. We verify the scalability of our algorithm on a continuous control benchmark, demonstrating that it outperforms strong model-free and model-based baselines.
  arXiv  Detail & Related papers  (2020-07-11T19:44:09Z)
• Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting [91.43582419264763]
  We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model.
  arXiv  Detail & Related papers  (2020-03-12T19:56:38Z)
• Certified Reinforcement Learning with Logic Guidance [78.2286146954051]
  We propose a model-free RL algorithm that enables the use of Linear Temporal Logic (LTL) to formulate a goal for unknown continuous-state/action Markov Decision Processes (MDPs) The algorithm is guaranteed to synthesise a control policy whose traces satisfy the specification with maximal probability.
  arXiv  Detail & Related papers  (2019-02-02T20:09:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.