1 Bellman Optimality Operator Is a Contraction [25pt] Recall the definition of the Bellman optimality operator T* : RSI + RSI, where |S| is the number of states in state space S: (T*V)(s) : := max R(s, a) +~P(s'|s, a)V(s) for each s S. Suppose y (T*V)(s), try to show that the following holds: |(T*V')(s) (T*V)(*)] =(T*V')(s) (T*V)(s) (Since we assumed (T*V')(s) > (T*V)(s)) =R(s, a'm') + P(s'|s, a'")V'(s) (R(s,a;) + P(s||8, a.;)V(s')) ||V' V || 20 What if (T*V')(s) (T*V)(s), try to show that the following holds: |(T*V')(s) (T*V)(*)] =(T*V')(s) (T*V)(s) (Since we assumed (T*V')(s) > (T*V)(s)) =R(s, a'm') + P(s'|s, a'")V'(s) (R(s,a;) + P(s||8, a.;)V(s')) ||V' V || 20 What if (T*V')(s)