[GradAI] Problem & Search

Since AI agent is crated for specific task, specialized environment, let’s see what problem we are trying to solve because “the first step in solving any problem is recognizing there is one”

A problem comprises of

  • initial state : where it starts out with
  • operators
  • goal test
  • cost

=> Solution : operator sequence to achieve goal state from initial state.

*Problem types

  • Single state ( deterministic, accessible) : agent knows everything abt the environment => easy to come up with optimal solution. E.g: chess
  •  Multiple state( deterministic, inaccessible) : partially know states => assume state during execution. E.g:
  •  Contingency( nondeterministic, inaccessible ) : search + execute
  • Exploration : unexplored state space => learn abt the environment while exploring

And our friend vacuum cleaner

Each problem type spans a solution space and most of the times , we just have to search this space for the solution we need…That brings us back to:

*Search Algorithm

Most of the times, search algorithm is related to tree or graph and searching is just expanding this tree branch/leaf by way of queuing function. Different way of expansion nodes results in different traversal/search algorithm. Two most common one are : Depth First Search(DFS)[ FIFO order ] and Breadth First Search(BFS)[ LIFO ].

Suppose our algorithm for traverse tree is line so

def search(s, g, q, qf):
   """s : start node, 
        g: goal node, 
        q: queue,
        qf: queuing-fn a.k.a expand_nodes( q, n)
        e.g : search('A', 'E', ['A'], lambda: expand_nodes( q, n ) )
   if s == g:
      return True
   if not q:
      return False
   return search( n, g, qf( q, n ), qf )

def expand_nodes_dfs( q, n ):
   return n.children + q

def expand_nodes_bfs( q, n ):
   return q + n.children

Evaluating a search algorithm relies on 4 criteria:

  • completeness : guaranteed a solution?
  • time complexity : how long does it run. for tree its by the order of node
  • space complexity : memory usage
  • optimality : least cost ?

For search algorithm complexity( time & space ), we look at b ( max branching ), d ( depth of solution ),  m ( max depth of solution )


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