Which measure assesses the expected cumulative future rewards from a given state, ignoring the specific actions taken?

Which measure assesses the expected cumulative future rewards from a given state, ignoring the specific actions taken?

• A. Action-Value Function
• B. Value Function
• C. Reward
• D. Policy

Answer: (B)

The value function measures how good it is to be in a given state when you follow a specific policy, by looking at the expected total reward from that point onward. It captures the future, discounted rewards but does not pin down a particular action for that state. In other words, V(s) averages over all actions the policy might take in state s and the resulting future states, weighting by how the policy behaves, to give a single number for the state's desirability under that policy. Formally, you’re looking at the expected sum of discounted rewards starting from state s and following the policy: V(s) = E_π [ ∑_{t=0}^∞ γ^t R_{t+1} | S0 = s ]. This focus on the state value under the policy distinguishes it from the action-value function Q(s,a), which would require choosing a specific action a in that state and then continuing. The immediate reward is just the snippet of reward at one step, whereas the value function concerns the entire future return from the state under the policy.

The value function measures how good it is to be in a given state when you follow a specific policy, by looking at the expected total reward from that point onward. It captures the future, discounted rewards but does not pin down a particular action for that state. In other words, V(s) averages over all actions the policy might take in state s and the resulting future states, weighting by how the policy behaves, to give a single number for the state's desirability under that policy.

Formally, you’re looking at the expected sum of discounted rewards starting from state s and following the policy: V(s) = E_π [ ∑{t=0}^∞ γ^t R{t+1} | S0 = s ]. This focus on the state value under the policy distinguishes it from the action-value function Q(s,a), which would require choosing a specific action a in that state and then continuing. The immediate reward is just the snippet of reward at one step, whereas the value function concerns the entire future return from the state under the policy.