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Standard methods for synthesis of control policies in Markov decision processes with unknown transition probabilities largely rely on a combination of exploration and exploitation. While these methods often offer theoretical guarantees on system performance, the number of time steps and samples needed to initially explore the environment before synthesizing a well-performing control policy is impractically large. This paper partially alleviates such a burden by incorporating a priori existing knowledge into learning, when such knowledge is available. Based on prior information about bounds on the differences between the transition probabilities at different states, we propose a learning approach where the transition probabilities at a given state are not only learned from outcomes of repeatedly performing a certain action at that state, but also from outcomes of performing actions at states that are known to have similar transition probabilities. Since the directly obtained information is more reliable at determining transition probabilities than second-hand information, i.e., information obtained from similar but potentially slightly different states, samples obtained indirectly are weighted with respect to the known bounds on the differences of transition probabilities. While the proposed strategy can naturally lead to errors in learned transition probabilities, we show that, by proper choice of the weights, such errors can be reduced, and the number of steps needed to form a near-optimal control policy in the Bayesian sense can be significantly decreased. 

Abstract Electrooculography (EOG) is a method to record the electrical potential between the cornea and the retina of human eyes. Despite many applications of EOG in both research and medical diagnosis for many decades, state-of-the-art EOG sensors are still bulky, stiff, and uncomfortable to wear. Since EOG has to be measured around the eye, a prominent area for appearance with delicate skin, mechanically and optically imperceptible EOG sensors are highly desirable. Here, we report an imperceptible EOG sensor system based on noninvasive graphene electronic tattoos (GET), which are ultrathin, ultrasoft, transparent, and breathable. The GET EOG sensors can be easily laminated around the eyes without using any adhesives and they impose no constraint on blinking or facial expressions. High-precision EOG with an angular resolution of 4° of eye movement can be recorded by the GET EOG and eye movement can be accurately interpreted. Imperceptible GET EOG sensors have been successfully applied for human–robot interface (HRI). To demonstrate the functionality of GET EOG sensors for HRI, we connected GET EOG sensors to a wireless transmitter attached to the collar such that we can use eyeball movements to wirelessly control a quadcopter in real time.