= Dynamic programming state
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A <dynamic programming state> is an element of a <state space> that summarizes all information needed for a remaining <mathematical optimization> problem. Histories can share a <value function> entry only when their allowed continuations and future rewards agree, or have the same conditional laws in a <stochastic control> problem. Time or the remaining item index may be part of the summary. If past decisions still affect feasibility or rewards, enlarge the <dynamic programming state>; forgetting those effects invalidates the <Bellman equation>.
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