Consider a run of value iteration on MDP M = (S, A, T, R, y). The...

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Consider a run of value iteration on MDP M = (S, A, T, R, y). The initial value function guess is Vº: SR, and for t≥ 0, we set Vt+1 = B*(V), where B* is the Bellman optimality operator. Prove or disprove each of the following statements. Proof of truth must hold for every MDP M, whereas a single (counterexample) MDP can establish the falsity of a statement. Vo. [2 marks] 4a. If V* Vº, then V5 4b. If VV, then V* V5. [2 marks] Consider a run of value iteration on MDP M = (S, A, T, R, y). The initial value function guess is Vº: SR, and for t≥ 0, we set Vt+1 = B*(V), where B* is the Bellman optimality operator. Prove or disprove each of the following statements. Proof of truth must hold for every MDP M, whereas a single (counterexample) MDP can establish the falsity of a statement. Vo. [2 marks] 4a. If V* Vº, then V5 4b. If VV, then V* V5. [2 marks]

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