Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamilton-Jacobi-Bellman Equations for Q-Learning in Continuous Time   In this paper, we introduce Hamilton-Jacobi-Bellman (HJB) equations for
Q-functions in continuous time optimal control problems with Lipschitz
continuous controls. The standard Q-function used in reinforcement learning is
shown to be the unique viscosity solution of the HJB equation. A necessary and
sufficient condition for optimality is provided using the viscosity solution
framework. By using the HJB equation, we develop a Q-learning method for
continuous-time dynamical systems. A DQN-like algorithm is also proposed for
high-dimensional state and control spaces. The performance of the proposed
Q-learning algorithm is demonstrated using 1-, 10- and 20-dimensional dynamical
systems.

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The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an