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Register a new userOptimizing the Long-Term Average Reward for Continuing MDPs: A Technical Report
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Added by
Yiping Xie
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Recently, we have struck the balance between the information freshness, in terms of age of information (AoI), experienced by users and energy consumed by sensors, by appropriately activating sensors to update their current status in caching enabled Internet of Things (IoT) networks [1]. To solve this problem, we cast the corresponding status update procedure as a continuing Markov Decision Process (MDP) (i.e., without termination states), where the number of state-action pairs increases exponentially with respect to the number of considered sensors and users. Moreover, to circumvent the curse of dimensionality, we have established a methodology for designing deep reinforcement learning (DRL) algorithms to maximize (resp. minimize) the average reward (resp. cost), by integrating R-learning, a tabular reinforcement learning (RL) algorithm tailored for maximizing the long-term average reward, and traditional DRL algorithms, initially developed to optimize the discounted long-term cumulative reward rather than the average one. In this technical report, we would present detailed discussions on the technical contributions of this methodology.
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We develop several new algorithms for learning Markov Decision Processes in an infinite-horizon average-reward setting with linear function approximation. Using the optimism principle and assuming that the MDP has a linear structure, we first propose a computationally inefficient algorithm with optimal $widetilde{O}(sqrt{T})$ regret and another computationally efficient variant with $widetilde{O}(T^{3/4})$ regret, where $T$ is the number of interactions. Next, taking inspiration from adversarial linear bandits, we develop yet another efficient algorithm with $widetilde{O}(sqrt{T})$ regret under a different set of assumptions, improving the best existing result by Hao et al. (2020) with $widetilde{O}(T^{2/3})$ regret. Moreover, we draw a connection between this algorithm and the Natural Policy Gradient algorithm proposed by Kakade (2002), and show that our analysis improves the sample complexity bound recently given by Agarwal et al. (2020).
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