8 - Monte Carlo Tree Search

ucla | CS 161 | 2024-02-12 14:25

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Table of Contents

• Algo
  • Steps
  • Upper Confidence Bound (UCB)
  • Generalization
  • Probabilistic Nodes

Algo

• random simulation
• start with root node of value $N$
• each child node has two characteristics $n_i$ and a value $v_i$

  Steps

  

Upper Confidence Bound (UCB)

• select node with highest UCB $UCB=v_i+c\sqrt{\frac{\ln N}{n_i}}\text{s.t.}{v}_i=\frac{w_i}{n_i}$

  Generalization

• taking to the limit of max children nodes tells us MCTS will approach the full minimax tree

  Probabilistic Nodes

• introduction of chance nodes between max and min players
• each nodes $n_i$ is a probability between its sister nodes
• total probability law applies between a subtree such that probs of all sister nodes under the same parent add up to 1
• the value we assign is the expectation (weighted sum)
• probs can be assigned using some model, independence assumption is not required, probs can be conditional