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Monte Carlo Tree Search: Insights and Applications BCS Real AI Event. Simon Lucas Game Intelligence Group University of Essex. Outline. General machine intelligence: the ingredients Monte Carlo Tree Search A quick overview and tutorial Example application: Mapello

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Monte carlo tree search insights and applications bcs real ai event

Monte Carlo Tree Search:Insights and ApplicationsBCS Real AI Event

Simon Lucas

Game Intelligence Group

University of Essex


  • General machine intelligence: the ingredients

  • Monte Carlo Tree Search

    • A quick overview and tutorial

  • Example application: Mapello

    • Note: Game AI is Real AI !!!

  • Example test problem: Physical TSP

  • Results of open competitions

  • Challenges and future directions

General machine intelligence the ingredients
General Machine Intelligence: the ingredients

  • Evolution

  • Reinforcement Learning

  • Function approximation

    • Neural nets, N-Tuples etc

  • Selective search / Sample based planning / Monte Carlo Tree Search

Conventional game tree search
Conventional Game Tree Search

  • Minimax with alpha-beta pruning, transposition tables

  • Works well when:

    • A good heuristic value function is known

    • The branching factor is modest

  • E.g. Chess: Deep Blue, Rybka

    • Super-human on a smartphone!

  • Tree grows exponentially with search depth


  • Much tougher for computers

  • High branching factor

  • No good heuristic value function

  • MCTS to the rescue!

“Although progress has been steady, it will take many decades of research and development before world-championship–calibre go programs exist”. Jonathan Schaeffer, 2001

Attractive features
Attractive Features Trees (UCT)

  • Anytime

  • Scalable

    • Tackle complex games and planning problems better than before

    • May be logarithmically better with increased CPU

  • No need for heuristic function

    • Though usually better with one

  • Next we’ll look at:

    • General MCTS

    • UCT in particular

Mcts the main idea
MCTS: the main idea Trees (UCT)

  • Tree policy: choose which node to expand (not necessarily leaf of tree)

  • Default (simulation) policy: random playout until end of game

Mcts algorithm
MCTS Algorithm Trees (UCT)

  • Decompose into 6 parts:

  • MCTS main algorithm

    • Tree policy

      • Expand

      • Best Child (UCT Formula)

    • Default Policy

    • Back-propagate

  • We’ll run through these then show demos

Mcts main algorithm
MCTS Main Algorithm Trees (UCT)

  • BestChild simply picks best child node of root according to some criteria: e.g. best mean value

  • In our pseudo-code BestChild is called from TreePolicy and from MctsSearch, but different versions can be used

    • E.g. final selection can be the max value child or the most frequently visited one

TreePolicy Trees (UCT)

  • Note that node selected for expansion does not need to be a leaf of the tree

  • But it must have at least one untried action

Expand Trees (UCT)

Best child uct
Best Child (UCT) Trees (UCT)

  • This is the standard UCT equation

    • Used in the tree

  • Higher values of c lead to more exploration

  • Other terms can be added, and usually are

    • More on this later

DefaultPolicy Trees (UCT)

  • Each time a new node is added to the tree, the default policy randomly rolls out from the current state until a terminal state of the game is reached

  • The standard is to do this uniformly randomly

    • But better performance may be obtained by biasing with knowledge

Backup Trees (UCT)

  • Note that v is the new node added to the tree by the tree policy

  • Back up the values from the added node up the tree to the root

All moves as first amaf rapid value action estimates rave
All Moves As First (AMAF), Trees (UCT)Rapid Value Action Estimates (RAVE)

  • Additional term in UCT equation:

    • Treat actions / moves the same independently of where they occur in the move sequence

Using for a new problem implement the state interface
Using for a new problem: Trees (UCT)Implement the State interface

Example application mapello
Example Application: Trees (UCT)Mapello

Othello Trees (UCT)

  • Each move you must Pincer one or more opponent counters between the one you place and an existing one of your colour

  • Pincered counters are flipped to your own colour

  • Winner is player with most pieces at the end

Basics of good game design
Basics of Good Game Design Trees (UCT)

  • Simple rules

  • Balance

  • Sense of drama

  • Outcome should not be obvious

Othello example white leads 58 from http radagast se othello help strategy html
Othello Example – white leads: -58 Trees (UCT)(from )

Trees (UCT)

Trees (UCT)

Trees (UCT)

Mapello Trees (UCT)

  • Take the counter-flipping drama of Othello

  • Apply it to novel situations

    • Obstacles

    • Power-ups (e.g. triple square score)

    • Large maps with power-plays e.g. line fill

  • Novel games

    • Allow users to design maps that they are expert in

    • The map design is part of the game

  • Research bonus: large set of games to experiment with

Or how about this
Or how about this? Trees (UCT)

Need rapidly smart ai
Need Rapidly Smart AI Trees (UCT)

  • Give players a challenging game

    • Even when the game map can be new each time

  • Obvious easy to apply approaches

    • TD Learning

    • Monte Carlo Tree Search (MCTS

    • Combinations of these …

      • E.g. Silver et al, ICML 2008

      • Robles et al, CIG 2011

Mcts see browne et al tciaig 2012
MCTS (see Browne et al, TCIAIG 2012) Trees (UCT)

  • Simple algorithm

  • Anytime

  • No need for a heuristic value function

  • E-E balance

  • Works well across a range of problems

Demo Trees (UCT)

  • TDL learns reasonable weights rapidly

  • How well will this play at 1 ply versus limited toll-out MCTS?

For strong play
For Strong Play … Trees (UCT)

  • Combine MCTS, TDL, N-Tuples

Where to play buy
Where to play / buy Trees (UCT)

  • Coming to Android (November 2012)

  • Nestorgames (

Mcts in real time games ptsp
MCTS in Real-Time Games: PTSP Trees (UCT)

  • Hard to get long-term planning without good heuristics

Mcts challenges and future directions
MCTS: Challenges and Trees (UCT)Future Directions

  • Better handling of problems with continuous action spaces

    • Some work already done on this

  • Better understanding of handling real-time problems

    • Use of approximations and macro-actions

  • Stochastic and partially observable problems / games of incomplete and imperfect information

  • Hybridisation:

    • with evolution

    • with other tree search algorithms

Conclusions Trees (UCT)

  • MCTS: a major new approach to AI

  • Works well across a range of problems

    • Good performance even with vanilla UCT

    • Best performance requires tuning and heuristics

    • Sometimes the UCT formula is modified or discarded

  • Can be used in conjunction with RL

    • Self tuning

  • And with evolution

    • E.g. evolving macro-actions

Further reading and links
Further reading and links Trees (UCT)