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What is the difference between Q-learning and G-learning in Reinforcement Learning? Please explain with formulas.

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Instead of relying on a utility of consumption, we present G-Learner: a reinforcement learning algorithm that operates with explicitly defined one-step rewards, does not assume a data generation process, and is suitable for noisy data. Our approach is based on G-learning - a probabilistic extension of the Q-learning method of reinforcement learning. In this paper, we demonstrate how G-learning, when applied to a quadratic reward and Gaussian reference policy, gives an entropy-regulated Linear Quadratic Regulator (LQR).

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Shortly said, they differ in the value function they optimize:

  • Q-learning estimates the optimal action-value function (Q-function) and directly learns the values associated with state-action pairs.
  • G-learning estimates the optimal value function (V-function) and focuses on learning the values associated with states.

These reinforcement learning algorithms are comparable in that they try to find an optimal policy by optimising their value functions. Q-Learning is used when you have a discrete action space. This is why it includes the actions in its value function. G-Learning is more suitable for continuous action spaces.

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