Question: Question 5. The basic idea behind many reinforcement learning algorithms is to estimate the action-value function Q(s,a) by using the Bellman equation as an iterative

 Question 5. The basic idea behind many reinforcement learning algorithms is

Question 5. The basic idea behind many reinforcement learning algorithms is to estimate the action-value function Q(s,a) by using the Bellman equation as an iterative update, Qi+1(s,a)=Es[r+maxaQi(s,a)s,a] where {a} are the actions, {s} are the states, r is the reward and is a discounting factor. In practice, such iterative methods converge to the optimal value function as i. [If you're not familiar with Reinforcement Learning, read this short introduction to understand the terminologies used: Reinforcement Learning, although it is not required to solve the question.] It is seen that, this is infeasible and a neural network Q(s,a,) is used as an approximator to estimate this optimal action-value function as Q(s,a;)Q(s,a). During training, we minimize the mean-squared error in the Bellman equation, and the loss function of such a network is given as Li(i)=E(s,a,r,s)U(D)[(r+maxaQ(s,a;i)Q(s,a;i))2] where e=(s,a,r+s) are the experiences forming the dataset D. It is known that iis fixed. Find the gradient of the above loss function w.r.t

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