We explore reinforcement learning methods for finding the optimal policy in the linear quadratic regulator (LQR) problem. In particular, we consider the convergence of policy gradient methods in the setting of known and unknown parameters. We are able to produce a global linear convergence guarantee for this approach in the setting of finite time horizon and stochastic state dynamics under weak assumptions. The convergence of a projected policy gradient method is also established in order to handle problems with constraints. We illustrate the performance of the algorithm with two examples. The first example is the optimal liquidation of a holding in an asset. We show results for the case where we assume a model for the underlying dynamics and where we apply the method to the data directly. The empirical evidence suggests that the policy gradient method can learn the global optimal solution for a larger class of stochastic systems containing the LQR framework and that it is more robust with respect to model mis-specification when compared to a model-based approach. The second example is an LQR system in a higher dimensional setting with synthetic data.
This paper is concerned with the problem of stochastic control of gene regulatory networks (GRNs) observed indirectly through noisy measurements and with uncertainty in the intervention inputs. The partial observability of the gene states and uncertainty in the intervention process are accounted for by modeling GRNs using the partially-observed Boolean dynamical system (POBDS) signal model with noisy gene expression measurements. Obtaining the optimal infinite-horizon control strategy for this problem is not attainable in general, and we apply reinforcement learning and Gaussian process techni…
School of Computer Science, Tel Aviv University（特拉维夫大学计算机科学学院）；Google Research（谷歌研究院）
We consider the task of learning to control a linear dynamical system under fixed quadratic costs, known as the Linear Quadratic Regulator (LQR) problem. While model-free approaches are often favorable in practice, thus far only model-based methods, which rely on costly system identification, have been shown to achieve regret that scales with the optimal dependence on the time horizon T. We present the first model-free algorithm that achieves similar regret guarantees. Our method relies on an efficient policy gradient scheme, and a novel and tighter analysis of the cost of exploration in polic…
Inverse reinforcement learning (IRL) seeks to infer a cost function that explains the underlying goals and preferences of expert demonstrations. This paper presents receding horizon inverse reinforcement learning (RHIRL), a new IRL algorithm for high-dimensional, noisy, continuous systems with black-box dynamic models. RHIRL addresses two key challenges of IRL: scalability and robustness. To handle high-dimensional continuous systems, RHIRL matches the induced optimal trajectories with expert demonstrations locally in a receding horizon manner and 'stitches' together the local solutions to lea…
Delft University of Technology（代尔夫特理工大学）；ABB Research（ABB研究院）
Multi-label learning is an emerging extension of the multi-class classification where an image contains multiple labels. Not only acquiring a clean and fully labeled dataset in multi-label learning is extremely expensive, but also many of the actual labels are corrupted or missing due to the automated or non-expert annotation techniques. Noisy label data decrease the prediction performance drastically. In this paper, we propose a novel Gold Asymmetric Loss Correction with Single-Label Regulators (GALC-SLR) that operates robust against noisy labels. GALC-SLR estimates the noise confusion matrix…
Risk-aware control, though with promise to tackle unexpected events, requires a known exact dynamical model. In this work, we propose a model-free framework to learn a risk-aware controller with a focus on the linear system. We formulate it as a discrete-time infinite-horizon LQR problem with a state predictive variance constraint. To solve it, we parameterize the policy with a feedback gain pair and leverage primal-dual methods to optimize it by solely using data. We first study the optimization landscape of the Lagrangian function and establish the strong duality in spite of its non-convex n…
Learning Decentralized Linear Quadratic Regulators with $\sqrt{T}$ Regret
School of Artificial Intelligence and Automation at the Huazhong University of Science and Technology（华中科技大学人工智能与自动化学院）；College of Petroleum Engineering, Yangtze University（长江大学石油工程学院）；Elmore Family School of Electrical and Computer Engineering at Purdue University（普渡大学埃尔莫尔家族电气与计算机工程学院）
University of Southern California（南加州大学）；University of Texas at Dallas（德克萨斯大学达拉斯分校）
Model-free reinforcement learning attempts to find an optimal control action for an unknown dynamical system by directly searching over the parameter space of controllers. The convergence behavior and statistical properties of these approaches are often poorly understood because of the nonconvex nature of the underlying optimization problems and the lack of exact gradient computation. In this paper, we take a step towards demystifying the performance and efficiency of such methods by focusing on the standard infinite-horizon linear quadratic regulator problem for continuous-time systems with u…
Inherent risk scoring is an important function in anti-money laundering, used for determining the riskiness of an individual during onboarding $\textit{before}$ fraudulent transactions occur. It is, however, often fraught with two challenges: (1) inconsistent notions of what constitutes as high or low risk by experts and (2) the lack of labeled data. This paper explores a new paradigm of data labeling and data collection to tackle these issues. The data labeling is choice-based; the expert does not provide an absolute risk score but merely chooses the most/least risky example out of a small ch…
VRPO: Rethinking Value Modeling for Robust RL under Noisy Supervision in LLM Post-Training
College of Computer Science and Artificial Intelligence, Fudan University（复旦大学计算机科学与人工智能学院）；Honor Device Co., Ltd（荣耀设备有限公司）；Institute of Trustworthy Embodied AI, Fudan University（复旦大学可信具身人工智能研究院）；Shanghai Key Laboratory of Multimodal Embodied AI（上海多模态具身人工智能重点实验室）
