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Studies on massive open online courses (MOOCs) users discuss the existence of typical profiles and their impact on the learning process of the students. However defining the typical behaviors as well as classifying the users accordingly is a difficult task. In this paper we suggest two methods to model MOOC users behaviour given their log data. We mold their behavior into a Markov Decision Process framework. We associate the users intentions with the MDP reward and argue that this allows us to classify them.
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Several applications of Reinforcement Learning suffer from instability due to high variance. This is especially prevalent in high dimensional domains. Regularization is a commonly used technique in machine learning to reduce variance, at the cost of introducing some bias. Most existing regularization techniques focus on spatial (perceptual) regularization. Yet in reinforcement learning, due to the nature of the Bellman equation, there is an opportunity to also exploit temporal regularization based on smoothness in value estimates over trajectories. This paper explores a class of methods for temporal regularization. We formally characterize the bias induced by this technique using Markov chain concepts. We illustrate the various characteristics of temporal regularization via a sequence of simple discrete and continuous MDPs, and show that the technique provides improvement even in high-dimensional Atari games.
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Current reinforcement learning methods fail if the reward function is imperfect, i.e. if the agent observes reward different from what it actually receives. We study this problem within the formalism of Corrupt Reward Markov Decision Processes (CRMDPs). We show that if the reward corruption in a CRMDP is sufficiently spiky, the environment is solvable. We fully characterize the regret bound of a Spiky CRMDP, and introduce an algorithm that is able to detect its corrupt states. We show that this algorithm can be used to learn the optimal policy with any common reinforcement learning algorithm. Finally, we investigate our algorithm in a pair of simple gridworld environments, finding that our algorithm can detect the corrupt states and learn the optimal policy despite the corruption.
We consider online learning for minimizing regret in unknown, episodic Markov decision processes (MDPs) with continuous states and actions. We develop variants of the UCRL and posterior sampling algorithms that employ nonparametric Gaussian process priors to generalize across the state and action spaces. When the transition and reward functions of the true MDP are members of the associated Reproducing Kernel Hilbert Spaces of functions induced by symmetric psd kernels (frequentist setting), we show that the algorithms enjoy sublinear regret bounds. The bounds are in terms of explicit structural parameters of the kernels, namely a novel generalization of the information gain metric from kernelized bandit, and highlight the influence of transition and reward function structure on the learning performance. Our results are applicable to multidimensional state and action spaces with composite kernel structures, and generalize results from the literature on kernelized bandits, and the adaptive control of parametric linear dynamical systems with quadratic costs.
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