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g(n) - actual cost from start to current node. h(n) estimated cost of path from current
node n to goal - heuristic. f(n) -estimated cost of cheapest solution through node node
n.
Choose an answer
(^1) Average Cost of All Paths - Random Search 2 Estimated Cost of Optimal Path - Informed Search
3 Actual Cost of Completed Path - Uninformed Search
4 Maximum Possible Cost From Start - Blind Search
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Definition of AI The creation and study of computation agents that act intelligently; an agent is an entity that acts in an environment
Goals of AI To understand the principles that make intelligent behavior possible
Turing Test In 1950, Alan Turing invented a game to test whether an unseen agent was intelligent; claimed external intelligence should be considered intelligence
Chinese Room John Searle;Inside room there is a person who does not speak chinese. In the room there is a rule book that people can look things up in. Lots of blank paper. Someone could come up to the room, pass the person a character and then the person in the room writes down a response from the rule book and passes it back to the person. Searle argues that there is no actual Chinese learning happening here; Although the whole entity does know Chinese
Agents An agent perceives its environment through sensors and acts upon its environment through actuators
Fully Observable Environment If the agent's sensors give it complete access to the state of the task environment, then it is fully observable; easier to deal with because the agent need not maintain state between decisions; Crossword puzzle
Partially Observable Environment The agent's sensors do not have complete access to the state of the task environment; poker
Single Agent The agent need only consider its own actions to complete the task, then it is a single agent environment; crossword
Multi agent Agent needs to consider other players actions; poker
Deterministic If the next state of the environment is completely determined by the current state and the action taken by the agent, then the environment is deterministic; crossword
Stochastic The next state is not necessarily determined by the current state and the action taken by the agent; poker
Dynamic If the environment can change while the agent is deciding what action to take; safety features in a car
Lowest Cost Search Uses a PQ to store the frontier; Expands the node with the lowest cost path
Lowest Cost Performance Complete; Optimal yes because it expands nodes based on path cost; Space efficient No but better than BFS; Time efficient? No, but better than BFS.
Depth First Search Uses a LIFO queue as frontier; Always expands deepest node in the frontier; can get caught in loops if repeated states are not checked
Depth First Performance Complete? Nope - can go down forever. Optimal? No - May find a suboptimal path when shorter paths exist. Space Efficient? Yes- only stores one path from root to leaf. Time efficient? Sometimes works well but if tree is unfavorable can take a lot of time.
Depth Limited Search Can handle infinite spaces; Provide predetermined depth limit, when limit is reached, backtrack
Depth Limited Performance Complete? - No, only complete if shallowest goal is within chosen limit. Optimal? No. May find suboptimal path. Space Efficient? Yes. Time Efficient? Depends - Sometimes works well but if tree is unfavorable can take a lot of time.
Iterative Deepening DFS Perform repeated Depth Limited searches, where the limit starts at 0 and is incremented each time; Uses DFS
Iterative Deepening Performance Complete? Yes. Optimal? Will find shallowest goal node, optimal when step costs are equal. Space Efficient? Yes, similar to DFS - only stores what it needs. Time Efficient? Surprisingly no worse than BFS; Combines the completeness and optimality of BFS with space efficiency of DFS; Preferred method for large state space and unknown depth
Estimated Cost of Optimal Path - Informed Search g(n) - actual cost from start to current node. h(n) estimated cost of path from current node n to goal - heuristic. f(n) -estimated cost of cheapest solution through node node n.
Greedy Best First Only looks ahead at estimated distance to goal. Uses a PQ sorted on h(n). Only uses the heuristic.
A* Search Looks at both path cost and estimated distance to goal; Uses PQ sorted on g(n) + h(n).
A* Search Performance A* is complete and optimal. When heuristic is admissible: never overestimates the cost to reach the goal. When heuristic is consistent: Let n be a node, n' be a successor of n, a be the action that leads from n to n' h(n) <= cost(n, a, n') + h(n'); creates nondecreasing f(n) values
A* Completeness and Optimality Given a consistent heuristic, A is optimal because by exploring all nodes with f(n) < C (the optimal path) it can't miss a better path; Given a positive step cost and a finite branching factor, A* is also complete because all path costs on the frontier will exceed the solution cost
Local Search State description contains all of the information for a solution; operate using a single current node; only move to neighbors of that node.
Advantages of Local Search Uses very little memory; Often finds reasonably good solution in large or infinite state space
Disadvantages of Local Search Does not explore a state space systematically; not guaranteed to be complete or optimal
Requirements of local search 1. State Representation
- An objective function that we are trying to maximize
- A successor function for choosing successors
Local Search Visualization Has plateaus, local maxima, goal is to find global maximum
Problems with Basic Local Search Once local maxima is reached, the algorithm will halt because every step would leads down. Once plateau is reached the algorithm will halt since every possible step is no better than the current location
Handling Plateaus with Hill Climbing Let algorithm take sideways steps to attempt to move away from plateau; can lead to stagnation
Hill Climbing with Random Restart Algorithm now ends when we have to take a step down (i.e. reached a local maxima). Then randomly restart search from a new state
Hill Climbing Space Issues A very spiky search space which is flat between the spikes will be quite difficult to solve. The final version that limits side steps and does a repeated random restarts is incomplete, but is likely to work on smooth search spaces.
Simulated Annealing Uses a temperature parameter to control the probability of downward steps, high temperature equates with a high chance of trying locally bad moves; temperature begins high and gradually decreases over time based on a schedule
Minimax Have a max and min player; Backup the terminal values through the parent nodes to the root. If it is MAX's turn, backup the maximum value from the successors. If it is MIN's turn, backup the minimum value from the successors. Choose the move at the root with the maximum value
Minimax Algorithm Practicality Performs depth first traversal of tree; optimal assuming that the leaf node evaluations are correct; the tree is likely too large.
Evaluation Function In Minimax, a way to look at a game state without knowing any context and trying to assign a value to it. How Minimax performs is largely dependent on the evaluation function.
Features of a good evaluation function When a terminal state is reached, score it correctly, should be efficient because it will be calculated a bunch. Should be correlated with success in the game
Limitations of Minimax When we bound the search we may cut off before something interesting happens; can be too time/space consuming.
Bounded Minimax A technique for searching two-player game trees where each level of the tree alternates player perspectives: One player is maximizing scores while the other player is minimizing scores. Finds the best action to take from the current game configuration by conducting a depth-limited, depth-first search
Alpha Beta Pruning A method for eliminating branches during the search that will not affect the outcome; Minimax with Alpha-Beta pruning always returns the same scores as Minimax would when using the same depth limit; Potentially much faster than minimax
Alpha Current best score for max; initialized to -infinity
Beta Current best score for min; initialized to infinity
How is pruning improved Order of expanded children matters. For MIN nodes, seeing lower valued children first improves pruning. For MAX nodes, seeing higher valued children first improves pruning. Therefore, if you have some idea about which children might be better, you should order them to improve speed of search.
Normal Form Games Agents move simultaneously; Represented as a matrix; Each agent controls a dimension; Actions select a row/column; Matrix cells are outcomes; Each player has access to all outcomes
Nash Equilibrium An equilibrium is an outcome where no player can gain by unilaterally deviating, this game has two equilibria
Mixed Strategy Apply probabilities to each move in a game yielding an optimal outcome
Monte Carlo Tree Search 1. Selection: Starting at the root, recursively select optimal child nodes until a leaf L is reached
- Expansion: If L is not a terminal node, then choose one of its children, call it C
- Simulation: Run a simulated playout from C until the end of game is reached
- Backpropagation: Update the tree with the simulation results
Selecting Nodes in MCTS Each node stores wins and visits. Exploiting moves with a high average winning rate, and exploring moves with few visits.
Upper Confidence Bound Formula vi + C*sqrt(ln N/ni); vi is the estimated value of the node based on playouts; ni is the number of times the node has been visited; N is the number of times the parent has been visited; C is a tunable bias parameter
Advantages of MCTS over other search methods 1. Does not require any domain knowledge; Simply needs to know the legal moves and ending conditions
- Focuses search on most relevant branches: grows tree asymmetrically, visits more interesting nodes more often, makes it more suitable for game with large branching factors
- Anytime algorithm: can be halted at any time and will return current best estimate
- Easy to implement
Disadvantages of MCTS 1. Strength of play - can fail to find good moves for many games in a reasonable amount of time
- Search Speed - Nodes must be visited many times before they begin to yield reliable estimates
Domain dependent MCTS Filters out implausible moves, favors playouts that are similar to human opponent play
Minimax vs. MCTS Minimax: Optimal once entire tree has been explored. A heuristic is required unless game tree is small. Can be sort of anytime-like if iterative deepening used. Works best on games with complete information MCTS: Optimal with infinite rollouts. A heuristic is not required, though can be used. Anytime algorithm. Handles incomplete information gracefully
