Problem 1. An MDP state transition graph is given below. The agent wants to go from S1 or S2 to the goal state S3. Suppose that the agent follows a fixed policy where it takes action a2 in state S1 and takes action a3 in state S2. For this fixed policy, calculate the expected cost to go from S1 to the goal, denoted as V" (S1); and calculate the expected cost to go from S2 to the goal, denoted as V" (S2). In the graph below, 0.5/2 means the state transition probability T (S1, a2, S1) = 0.5 and the associated immediate cost c(S1, a2, S1) = 2. Show your work. 0.5/2 S1 a2 al 0.75/2 0.5/1 0.4/2 S2 a3 0.6/1 0.25/1 S3 Goal state
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- Consider a maximization problem that is being solved by Simulated Annealing. Let the objective function value of the current state, s, be 1000. Let this state have 5 successors/neighbors: s1(950), s2(975), s3(1000), s4(1000), and s5(1050). The numbers in parentheses represent the corresponding objective function values. The current temperature is 100. The probability that the next state is: 1. s1 = [Select] 2. s2 = [Select] 3. s3 [Select] = 4. s4= [Select] [Select] 5. s5 0.778 0.121 0.156 0.2 0.606where square a is the initial position and O is the goal position. The goal of our agent is to find a way from the initial position to the final position. The possible actions are move up, down, left and right to an adjacent square. The shaded squares are obstacles, and the cost of each action is 1, except for (d, h) which has cost 4, (i, k) which has cost 2 and (h, O) which has cost 3. Assume that the actions are ordered according to their resulting state alphabetically. For example, the action (a, b) comes before (a, c). Draw the search graph corresponding to this Give the: final search tree, final explored list (the order is important), final frontier list (the order is important: the leftmost node is the next one to be explored, indicate the priority when applicable), solution found, cost of the solution, for each of each of the following algorithms: a-Depth first search (DFS): graph search version. (b)Uniform cost search (UCS): graph search version.Consider the case of a simple Markov Decision Process (MDP) with a discount factor gamma = 1. The MDP has three states (x, y, and z), with rewards -1, -2, 0, respectively. State z is considered a terminal state. In states and y there are two possible actions: a₁ and a2. The transition model is as follows: In state x, action a1 moves the agent to state y with probability 0.9 and makes the agent stay put with probability 0.1. In state y, action a1 moves the agent to state with probability 0.9 and makes the agent stay put with probability 0.1. In either state or state y, action a2 moves the agent to state z with probability 0.1 and makes the agent stay put with probability 0.9. Please answer the following questions: Draw a picture of the MDP What can be determined qualitatively about the optimal policy in states x and y? Apply the policy iteration algorithm discuss in class, showing each step in full, to determine the optimal policy and the…
- A materials engineer wants to study the effects of two different processes for sintering copper (aprocess by which copper powder coalesces into a solid but porous copper) on two different typesof copper powders. From each type of copper powder, she randomly selects two samples andthen randomly assigns one of the two sintering processes to each sample by the flip of a coin.The response of interest measured is the porosity of the resulting copper. Explain what type ofstudy this is and why.Write a python code of this problem Problem Statement Assume that there are two teams and they are team attacker and team defender. Therefore, at a state of the game one agent in each team is left alive respectively. Here, the defender is given a lifeline called HP which will be assigned randomly. Furthermore, the attacker agent will try to give maximum negative HP to the defender agent to decrease his(d) chances of survival in the game. On the other hand, the defender agent will try to protect himself by receiving the lowest negative HP possible from the attacker agent. Furthermore, the attacker can have a choice from a number of bullets from his gun and the optimal moves will cost a certain maximum negative HP (chosen from randomly assigned values within the range of minimum and maximum negative HP). Here, are the following things you need to do using Alpha-Beta Pruning algorithm: Sample Input 1: Enter your student id: 17301106 Minimum and Maximum value for the…Consider an undiscounted MDP having three states, (1, 2, 3), with rewards -1, -2, 0, respectively. State 3 is a terminal state. In states 1 and 2 there are two possible actions: a and b. The transition model is as follows: - In state 1, action a moves the agent to state 2 with probability 0.6 and makes the agent stay put with probability 0.4. In state 2, action a moves the agent to state 1 with probability 0.6 and makes the agent stay put with probability 0.4 - In either state 1 or state 2, action b moves the agent to state 3 with probability 0.2 and makes the agent stay put with probability 0.8. Answer the following questions: 1. What can be determined qualitatively about the optimal policy in states 1 and 2? 2. Apply policy iteration, showing each step in full, to determine the optimal policy and the values of states 1 and 2. Assume that the initial policy has action b in both states. 3. What happens to policy iteration if the initial policy has action a in both states? Does…
- Question 1 For the problem represented by the graph below, A start state. G: Goal state. Let us define the following Heuristics H1: NA- 4, h(B)-1, hG)- 0 6. H2 HA)- 5, h(B)- 2, h(G)- 0 which heuristics is admissible O Hi and H2 O Hi only O H3 only O NoneConsider the decision model/game theoretic model from Chapter 19 for the spread of a new behavior through a social network. Suppose we have the social network depicted in Figure 2; suppose that each node starts with the behavior B, and each node has a threshold of q = 2/5 for switching to behavior A. Now, let c and d form a two-node set S of initial adopters of behavior A. If other nodes follow the threshold rule for choosing behaviors, which nodes will eventually switch to A? Give a brief (1-2 sentence) explanation for your answer. Find a cluster of density greater than 1 − q = 3/5 in the part of the graph outside S that blocks behavior A from spreading to all nodes, starting from S, at threshold q. Give a brief (1-2 sentence) explanation for your answer. Suppose you were allowed to add a single edge to the given network, connecting one of nodes c or d to any one node that it is not currently connected to. Could you do this in such a way that now behavior A, starting from S and…10 Multi-Agent Interaction Exercise Consider the following payoff matrix (A) for a game: y defects y cooperates 1 x defects 1 4 3 x cooperates 3 State True or False for the following statements regarding the nash equilibria in this game: a Mutual cooperation True False b Mutual defection True False c y cooperates, x defects True False d x cooperates, y defects True False
- You are required to create a Julia program that does the following in this problem:Analyze every policy you are given, then tweak it until a solution is discovered. Real-time recording and saving of the Markov decision process (MDP).10 a b C d e Actions: East, West, and Exit (only available in exit states a, f) Transitions: deterministic For discount factor, y = 1, what is the optimal policy? Use E for East, W for West and X for Exit b. For discount factor, y- 0.5, what is the optimal policy? Use E for East, W for West and X for Exit e 2.You are required to create a Julia program that does the following in this problem: Analyze every policy you are given, then tweak it until a solution is discovered. Real-time recording and saving of the Markov decision process (MDP).