Introduction to AI

Module 4: Adversarial search


  • Topics:
    • Search with adversaries (e.g. games)
    • Minimax search
    • Alpha-beta pruning
    • Handling large and more challenging games 
  • Length: This module will take two weeks to complete
  • Assigned chapters: Chapter 5
  • Project: Project 3 (will stay open one week beyond this module)

Adversarial search

Many games can be fully solved through search techniques but the problem formulation and the search approaches that we have studied so far cannot handle searching in a strategic situation with multiple agents.  In this module, we will discuss adversarial search techniques, starting from simple games that can be fully searched and moving to more advanced games where we must use approximations to the full search.

Hybrid machine learning and search approaches have been in the news lately especially with the AlphaZero series of games (see link and photo to the right).  Although we will discuss the foundational search approaches for these methods, we will not cover the machine learning methods until a later module.

Real World search

Chess with alpha zero

Photo from this DeepMind blog post about AlphaZero

reading and videos for module 4

Topic 1: Optimal search for games

Before we can dive into search methods for games, we need to look at how we formulate search for an adversarial situation as it is different than what we have been doing so far.  We will then look at MiniMax search, which can give us an approach to playing games optimally, in many situations.  

  • (30 min) Reading
    • Read Sections 5.1-5.2.2 of Chapter 5 (Game Theory through Optimal Decisions in Games but don’t read about alpha-beta pruning)


Topic 2: alpha-beta pruning

MiniMax will give the optimal strategy but it cannot handle large search spaces.  We will discuss multiple ways to handle larger (and more difficult/interesting) games.  In this topic, we start with alpha-beta pruning which is a strategy to prune a MiniMax tree while still guaranteeing optimality.  

Remember, if you get stuck, please chat in slack and ask your fellow students plus the TA and Dr McGovern for help!  Go to #general for help in general!

  • (30 min) Reading
    • Read Section 5.2.3-5.3 of Chapter 5 (alpha-beta pruning through Heuristic alpha-beta tree search)
  • (60 min) Pruning
    • Watch the video on Alpha-Beta pruning
    • Copy of the slides
    • Watch the video on other approaches to searching in larger spaces.  This includes a discussion of evaluation functions, which can replace utility functions if the search is terminated before the game ends.


Topic 3: monte-carlo tree search

Although Alpha-Beta pruning is efficient and guaranteed to still give an optimal answer, it is not sufficient to enable search in very large games such as Go.  Here, we examine the approach used by Alpha Go called Monte Carlo Tree Search.  Although I draw on material from the book in this section, I also reference a paper (linked below) which gives an excellent overview of MCTS. 

  • (30 min) Reading
    • Read Section 5.4 of Chapter 5 (Monte Carlo Tree Search)
    • Optional:  If you are eagerly wanting to learn more about MCTS, I highly recommend this overview paper.  It is a free PDF download.
  • (60 min) MCTS
  •  What is the game solution that has been in the news lately that has excited you the most?  Post on #random and share!


Topic 4: stochastic games and partial observability

In our final topic for this module, we discuss a method called rollouts that is related to MCTS (it is based on Monte Carlo sampling).  It is not discussed much in the book but it is simple to implement and is very useful for large-scale games.  We end with a discussion of a theoretical method that works well in tiny games with chance but is of limited practical use.

  • (30 min) Reading
    • Read Section 5.5 through end of of Chapter 5 (stochastic games through end of chapter)
  • (60 min) Stochastic and partially observable games
      • Watch the video on rollouts
      • Watch the video on Expectiminimax

projects for module 4

Project 2

  • Remember Project 2 is due one week into this module – due Sep 26  

Project 3

  • On week 2 of this module, you will start Project 3, which focuses on adversarial search.  This will be due one week into the next module, on Oct 10. 

suggested schedule for module 4

week 1 (Sep 19 – Sep 26)

  • Complete Topic 1 by Tuesday
  • Work on Project 2 throughout the week
  • Complete Topic 2 by Friday
  • Finish Project 2 by Sunday

Week 2 (Sep 26 – Oct 3)

  • Complete Topic 3 by Wednesday 
  • Begin Project 3 
  • Complete Topic 4 by Friday

Week 3 (Oct 3 – Oct 10)