Policy Gradient Reformulation using Advantage Function

Advantage Function Estimation using Reward-to-Go

An autonomous agent in a reinforcement learning environment is in a particular state. From this state, the expected cumulative future reward, when averaged across all possible actions, is calculated to be 50 points. The agent is evaluating three specific actions:

• Action X: The expected cumulative reward for taking this action is 65 points.
• Action Y: The expected cumulative reward for taking this action is 40 points.
• Action Z: The expected cumulative reward for taking this action is 50 points.

Based on this information, which statement provides the most accurate analysis for guiding the agent's next policy update?

In a reinforcement learning scenario, an agent in a specific state calculates that the 'advantage' of performing a particular action is exactly zero. What is the most accurate interpretation of this finding?

Temporal Difference (TD) Error as an Advantage Function Estimator

Analysis of an Agent's Suboptimal Policy

An agent is in a state 'S' and must choose between two policies, Policy A and Policy B. The sequence of rewards the agent will receive after starting in state 'S' and following each policy is deterministic and known:

• Policy A Reward Sequence: [+10, +1, +1, +1, ...]
• Policy B Reward Sequence: [+3, +3, +3, +3, ...]

Given the formula for the value of a state, $V(s) = \mathbb{E}[\sum_{t=0}^{\infty} \gamma^t r_t | s_0 = s, \pi]$, which of the following statements correctly analyzes the relationship between the discount factor γ and the value of state 'S' for each policy?

Calculating State Value in a Deterministic Environment

Advantage Function Formula

Temporal Difference (TD) Error as an Advantage Function Estimator

An agent is in a state 'S' and follows a fixed policy. From this state, the environment is stochastic: there is a 50% chance the agent will enter a trajectory with a reward sequence of [+10, 0, 0, ...] and a 50% chance it will enter a different trajectory with a reward sequence of [0, +10, 0, ...]. Given the state-value formula $V(s) = \mathbb{E}[\sum_{t=0}^{\infty} \gamma^t r_t | s_0 = s, \pi]$ and a discount factor (γ) of 0.9, what is the value of state 'S'?