= Value function
{title2=$V_t(s)$}
{wiki}
A <value function> assigns each <dynamic programming state> and time the best <objective function> value attainable over the remaining decisions. It is a score, whereas a <control policy> specifies the actions producing that score. In the <0-1 knapsack problem> above, $V_3(5)=7$ is the score, and choosing the items of weights $2$ and $3$ attains it. In sequential <mathematical optimization>, the <Bellman equation> computes a <value function> by comparing immediate reward plus continuation value. Use a <supremum> or <infimum> when the best score need not be attained by any admissible <control policy>.
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