ADMISSIBLE HEURISTICS

• Recall the general form of our evaluation function:
  
  
  f(H) = g(H) + h(H)
  
  Where g() represents the evaluation function for the partial path up to time t, and h() represents the estimate of the remaining path.
  
  
• An admissible heuristic function is one that always underestimates the true cost of the remaining path (e.g., a zero function).
  
  
• The evaluation function can simply be the forward probability.
  
  
• The expected cost of the remaining part of the path can be estimated by gathering statistics from the training data:
  
  
  h(H) = (T-t)P_min
  
  
• It can be shown that this same heuristic can be applied to the problem of extending the path into the next word.