On Using Hamiltonian Monte Carlo Sampling for Reinforcement Learning Problems in High-dimension

• URL: http://arxiv.org/abs/2011.05927v3
• Date: Mon, 28 Mar 2022 17:00:25 GMT
• Title: On Using Hamiltonian Monte Carlo Sampling for Reinforcement Learning Problems in High-dimension
• Authors: Udari Madhushani, Biswadip Dey, Naomi Ehrich Leonard, Amit Chakraborty
• Abstract summary: Hamiltonian Monte Carlo (HMC) sampling offers a tractable way to generate data for training RL algorithms. We introduce a framework, called textitHamiltonian $Q$-Learning, that demonstrates, both theoretically and empirically, that $Q$ values can be learned from a dataset generated by HMC samples of actions, rewards, and state transitions.
• Score: 7.200655637873445
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Value function based reinforcement learning (RL) algorithms, for example, $Q$-learning, learn optimal policies from datasets of actions, rewards, and state transitions. However, when the underlying state transition dynamics are stochastic and evolve on a high-dimensional space, generating independent and identically distributed (IID) data samples for creating these datasets poses a significant challenge due to the intractability of the associated normalizing integral. In these scenarios, Hamiltonian Monte Carlo (HMC) sampling offers a computationally tractable way to generate data for training RL algorithms. In this paper, we introduce a framework, called \textit{Hamiltonian $Q$-Learning}, that demonstrates, both theoretically and empirically, that $Q$ values can be learned from a dataset generated by HMC samples of actions, rewards, and state transitions. Furthermore, to exploit the underlying low-rank structure of the $Q$ function, Hamiltonian $Q$-Learning uses a matrix completion algorithm for reconstructing the updated $Q$ function from $Q$ value updates over a much smaller subset of state-action pairs. Thus, by providing an efficient way to apply $Q$-learning in stochastic, high-dimensional settings, the proposed approach broadens the scope of RL algorithms for real-world applications.

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