Artificial Intelligence Homework Assignment 2025 PDF

Artificial Intelligence Homework Assignment January 16, 2025 Instructions Due Date: 24 January 2025 Submissions must be individual, even if collaboration occurred during preparation. Ensure all work is shown and fully justified. Adhere to the...

Artificial Intelligence Homework Assignment January 16, 2025 Instructions Due Date: 24 January 2025 Submissions must be individual, even if collaboration occurred during preparation. Ensure all work is shown and fully justified. Adhere to the provided template for submission format. Question 1: Pathfinding in Dynamic Mazes 1.1 Define an expanded state space representation for a dynamic maze where some walls can appear or disappear randomly. 1.2 Calculate the upper bound of the state space size if walls can toggle states and the maze is represented as an M × N grid. 1.3 Derive the maximum branching factor for a robot navigating the maze with the addi- tional rule that it can jump over one wall per move if necessary. 1.4 Suggest and evaluate two heuristics for this problem. Discuss whether they are admis- sible and consistent. 1.5 Propose conditions under which the combination of two admissible heuristics, h1 and h2 , remains admissible. Question 2: Rational Decision-Making 2.1 A lottery L = [0.25, A; 0.35, B; 0.4, C] has utilities U (A) = 5, U (B) = 3, U (C) = 7. Calculate U (L). 2.2 Consider two lotteries: L1 = [0.6, A; 0.4, L2 ] and L2 = [0.5, X; 0.5, Y ], with U (A) = 8, U (X) = 6, U (Y ) = 9. Compute U (L1 ). 1 2.3 Assume A ≻ B ≻ L, where L = [0.4, C; 0.6, D], and C ≻ A. Which of the following must hold under rational preferences? A≻C B≻D A≻L Question 3: Preferences and Utility Functions 3.1 A robot prefers smaller energy-consuming moves over larger ones. Which of the follow- ing functions for energy E represent this preference? Justify your choices: U (E) = E 2 , U (E) = −E, U (E) = ln(E), U (E) = 1/E. 3.2 A Pacman prefers larger food pellets but hesitates if the food radius exceeds 5. Design a utility function U (r) that reflects this behavior. 3.3 Consider P1 ≻ P2 ≻ P3 and P2 ≻ (50-50 lottery between P1 and P3 ). Identify a utility function consistent with this preference. 3.4 Propose a utility function for a risk-averse robot navigating obstacles, ensuring that it avoids paths with high variance in difficulty. 2