Hanchen Xu

Xiao Li, Hanchen Xu, Jinming Zhang et al.

In this paper, we formulate the adaptive learning problem---the problem of how to find an individualized learning plan (called policy) that chooses the most appropriate learning materials based on learner's latent traits---faced in adaptive learning systems as a Markov decision process (MDP). We assume latent traits to be continuous with an unknown transition model. We apply a model-free deep reinforcement learning algorithm---the deep Q-learning algorithm---that can effectively find the optimal learning policy from data on learners' learning process without knowing the actual transition model of the learners' continuous latent traits. To efficiently utilize available data, we also develop a transition model estimator that emulates the learner's learning process using neural networks. The transition model estimator can be used in the deep Q-learning algorithm so that it can more efficiently discover the optimal learning policy for a learner. Numerical simulation studies verify that the proposed algorithm is very efficient in finding a good learning policy, especially with the aid of a transition model estimator, it can find the optimal learning policy after training using a small number of learners.

Hanchen Xu, Xiao Li, Xiangyu Zhang et al.

In this letter, we address the problem of controlling energy storage systems (ESSs) for arbitrage in real-time electricity markets under price uncertainty. We first formulate this problem as a Markov decision process, and then develop a deep reinforcement learning based algorithm to learn a stochastic control policy that maps a set of available information processed by a recurrent neural network to ESSs' charging/discharging actions. Finally, we verify the effectiveness of our algorithm using real-time electricity prices from PJM.

Xiao Li, Hanchen Xu, Jinming Zhang et al.

E-learning systems are capable of providing more adaptive and efficient learning experiences for students than the traditional classroom setting. A key component of such systems is the learning strategy, the algorithm that designs the learning paths for students based on information such as the students' current progresses, their skills, learning materials, and etc. In this paper, we address the problem of finding the optimal learning strategy for an E-learning system. To this end, we first develop a model for students' hierarchical skills in the E-learning system. Based on the hierarchical skill model and the classical cognitive diagnosis model, we further develop a framework to model various proficiency levels of hierarchical skills. The optimal learning strategy on top of the hierarchical structure is found by applying a model-free reinforcement learning method, which does not require information on students' learning transition process. The effectiveness of the proposed framework is demonstrated via numerical experiments.

Hanchen Xu, Alejandro D. Domínguez-García, Peter W. Sauer

In this paper, we address the problem of setting the tap positions of load tap changers (LTCs) for voltage regulation in radial power distribution systems under uncertain load dynamics. The objective is to find a policy to determine the tap positions that only uses measurements of voltage magnitudes and topology information so as to minimize the voltage deviation across the system. We formulate this problem as a Markov decision process (MDP), and propose a batch reinforcement learning (RL) algorithm to solve it. By taking advantage of a linearized power flow model, we propose an effective algorithm to estimate the voltage magnitudes under different tap settings, which allows the RL algorithm to explore the state and action spaces freely offline without impacting the system operation. To circumvent the "curse of dimensionality" resulted from the large state and action spaces, we propose a sequential learning algorithm to learn an action-value function for each LTC, based on which the optimal tap positions can be directly determined. The effectiveness of the proposed algorithm is validated via numerical simulations on the IEEE 13-bus and 123-bus distribution test feeders.