Policy Gradient with Advantage Function Formula

A2C Loss Function Formulation

In a reinforcement learning scenario, an agent is in a particular state. The estimated value of being in this state, averaged over all possible actions the agent could take, is +10. If the agent chooses a specific action, the estimated value of taking that particular action in that state is +8. Based on this information, what can be concluded about this specific action?

If an action has a positive advantage value, it means that taking this action is guaranteed to result in a higher immediate reward than any other action available in that state.

Interpreting Action Advantage

A2C Loss Function Formulation

An agent is being trained using a policy gradient method. The objective is to maximize the function $U = \sum_{t} \log \pi_{\theta}(a_t|s_t)A(s_t, a_t)$, where $\pi_{\theta}$ is the policy and $A$ is the advantage function which indicates how much better an action is than the average.

At a specific state $s$, the agent can choose from three actions: $a_1, a_2, a_3$. The calculated advantage values for these actions are:

• $A(s, a_1) = +2.5$
• $A(s, a_2) = -1.0$
• $A(s, a_3) = -1.5$

Assuming the agent performs one optimization step to maximize the objective, how will the policy probabilities $\pi_{\theta}(a|s)$ for these actions most likely change?

Impact of a Zero Advantage Value

Policy Gradient with Advantage Function Formula

Rationale for Using the Advantage Function in Policy Gradients

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