State Space Search: Uninformed Methods in AI, Study notes of Artificial Intelligence

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State Space Search

Overview

• Problem-solving as search
• How to formulate an AI problem as search.
• Uninformed search methods

Environmental factors needed

• Static — The world does not change on its own, and our actions don't change it.
• Discrete — A finite number of individual states exist rather than a continuous space of options.
• Observable — States can be determined by observations.
• Deterministic — Action have certain outcomes.

• The environment is all the information about the world that remains constant while we are solving the problem.
• A state is a set of properties that define the current conditions of the world our agent is in. - Think of this as a snapshot of the world at a given point in time. - The entire set of possible states is called the state space.
• The initial state is the state the agent begins in.
• A goal state is a state where the agent may end the search.
• An agent may take different actions that will lead the agent to new states.

Formulating problems as search

• Define:
  • What do my states look like?
  • What is my initial state? What are my goal state(s)? What does the state space "look like?" Is is a graph or a tree?
  • What is my cost function?
    • How do I know how "good" a state or action is?
    • Usually desirous to minimize, rather than maximize.
    • Usually phrased as a function of the path from the initial state to a goal state.

Formulating problems as search

• Solution:
  • A path between the initial state and a goal state.
  • Quality is measured by path cost.
  • Optimal solutions have the lowest cost of any possible path.

• There are two simultaneous graph-ish structures used in search: - (1) Tree or graph of underlying state space. - (2) Tree maintaining the record of the current search in progress (the search tree ).
• (1) does not depend on the current search being run.
• (1) is sometimes not even stored in memory (too big!)
• (2) always depends on the current search, and is always stored in memory.

Recap

• What things do we need to define in order to formulate a problem as a search problem?

Trees vs graphs

• If your search space is a tree, that implies there is only one path from the start state to any goal state. - Equivalently: only one sequence of actions for each possible goal state.

Search tree

• Frontier: a data structure storing the collection of nodes that are available to be examined next in the algorithm. - Often represented as a stack, queue, or priority queue.
• Explored set: stores the collection of states we have already examined (and therefore don’t need to look at again). - Often stored using a data structure that enables quick look-up for membership tests.

How do you evaluate a search

strategy?

• Completeness — Does it always find a solution if one exists?
• Optimality — Does it find the best solution?
• Time complexity
• Space complexity

Frontier = stack, queue, or priority queue. Explored set = hash table.

Search strategies

• Breadth-first search
  • Variant — Uniform-cost search
• Depth-first search
• Depth-limited search
• Iterative deepening depth-first search