lecture 3 Flashcards
formal percpective of adverserial search
The state space we consider is a game tree. each level (called a ply) consists of the states a player can be in when at play in that round. we use the term move to denote a full round of play.
since the agent no longer controls all actions from initial to goal state, we are forced to look for winning strategy where the actions are contingent on those taken by the opponent,
this corresponds to a subtree with only positive states as leaves.
Minimax algorithm
because it traverses the game tree depth-first, minimax has space complexity only O(b*w).
furthermore, unlike depthfirst search it is always optimal( though still incomplete for infinite depth).
however, this is at the cost of visiting the entire game tree, giving it a time complexity of O(b^w). as in last lecture, this can be an overestimation, but for real-world games this is still far too large!
Alpha - Beta pruning
while propagating the minimax values, we maintain the current optimal values for maximisier (alpha)and minimizer (beta).
as soon as we find that some branch will not improve on this value, we remove this branch
Alpha - Beta pruning (analysis)
we can only guarantee an improvment in performance over minimax (O(n^w/2)) if we assume that we consider better plays first.
this ordered search is reasonably doable in real - world cases, which means alphs beta pruning effectively reduces b to square d
tjis value remains exponential, and in practice it is still impossible to explore the entire game tree even with aplh- beta pruning.
Closing remarks of lecture 3
we have covered some of the basic techniques for adverserial search which neverthrlrss play an important role in applications.
more recent developments like masterig a game through self-play are not fully understood yet from a theoretical perspective.
Hence there is still interesting research to be done beyond simply learning to implement exisiting algorithms/
