Monster Behavior: Building A Decision Tree

Hey there, AI enthusiasts! Let's dive into the fascinating world of behavior trees and how we can use them to make our virtual monsters smarter. Imagine you're building a dungeon crawler game, and you want your monsters to make smart choices. They need to decide when to attack, cast spells, or even run away. That's where decision trees come in handy! This article will walk you through the process, using the ID3 algorithm, and explain why a different method, CAL2, wouldn't be the best fit for our task.

The Data: Monster Actions

First, let's set the stage. We've been tracking a monster's actions in a dungeon crawler. We've gathered data on the monster's characteristics and the actions it took. Think of it like a training dataset. Here's a breakdown of the monster's features and possible actions:

• Distance: Near, Medium, Far
• HP: High, Low
• Mana: Enough, Low
• Ranged Weapon: Yes, No
• Actions: Melee Attack, Ranged Attack, Spellcasting, Retreat

Here’s a table of the recorded data from previous games:

With this data in hand, we can now use this to train our behavior tree. It's all about making the monster smarter!

Training the Decision Tree with ID3

Alright, time to roll up our sleeves and build this decision tree. We'll be using the ID3 algorithm. The main goal here is to create a tree that helps the monster make the best decision based on its current state (distance, HP, etc.).

• Step 1: Calculate the Entropy of the Whole Dataset (H(S))

  First, we calculate the entropy of our entire dataset. Entropy is a measure of the disorder or uncertainty in our data. In simple terms, how mixed up are the actions? The formula is: H(S) = - Σ p(k) * log2(p(k)), where p(k) is the proportion of each action.

  • Melee Attack: 2/10 = 0.2
  • Ranged Attack: 3/10 = 0.3
  • Spellcasting: 3/10 = 0.3
  • Retreat: 2/10 = 0.2

  H(S) = - (0.2 * log2(0.2) + 0.3 * log2(0.3) + 0.3 * log2(0.3) + 0.2 * log2(0.2)) ≈ 1.971

• Step 2: Calculate the Information Gain for Each Attribute

  Next, we calculate the information gain for each attribute (Distance, HP, Mana, Ranged Weapon). Information gain tells us how much each attribute helps reduce the entropy, i.e., how much it helps us make a decision. The formula is: Gain(S, A) = H(S) - Σ (|Sv| / |S|) * H(Sv), where A is the attribute, Sv is the subset of S for which attribute A has value v, and |S| is the total number of samples. This step is about figuring out which attribute is the most informative.

  • Distance:
    • Near: 1, 2, 7} => 3/10, H {Melee, Retreat, Melee = - (2/3 * log2(2/3) + 1/3 * log2(1/3)) ≈ 0.9183
    • Medium: 5, 6, 9, 10} => 4/10, H {2x Spellcasting, 2x Ranged = - (2/4 * log2(2/4) + 2/4 * log2(2/4)) = 1.0000
    • Far: 3, 4, 8} => 3/10, H {Ranged, Spellcasting, Retreat = - (1/3 * log2(1/3) + 1/3 * log2(1/3) + 1/3 * log2(1/3)) ≈ 1.5849
    • Gain(Distance) = (3/10 * 0.9183) + (4/10 * 1.0000) + (3/10 * 1.5849) ≈ 1.1509
    • Gain: 1.971 - 1.1509 = 0.820
  • HP:
    • Low: 1, 2, 8, 9, 10} => 5/10, H {Melee, 2x Retreat, Spellcasting, Ranged = 1.9219
    • High: 3, 4, 5, 6, 7} => 5/10, H {Ranged, 2x Ranged, 2x Spellcasting = 1.5219
    • Gain(HP) = (5/10 * 1.9219) + (5/10 * 1.5219) = 1.7219
    • Gain: 1.971 - 1.7219 = 0.249
  • Mana:
    • Enough: 4, 5, 7, 9} => 4/10, H {3x Spellcasting, Melee = 0.8113
    • Low: 1, 2, 3, 6, 8, 10} => 6/10, H {Melee, 3x Ranged, 2x Retreat = 1.4591
    • Gain(Mana) = (4/10 * 0.8113) + (6/10 * 1.4591) = 1.19998
    • Gain: 1.971 - 1.19998 = 0.771
  • Ranged Weapon:
    • Yes: 3, 4, 6, 7, 9, 10} => 6/10, H {3x Ranged, 2x Spellcasting, Melee = 1.4591
    • No: 1, 2, 5, 8} => 4/10, H {2x Retreat, Melee, Spellcasting = 1.5000
    • Gain(Ranged Weapon) = (6/10 * 1.4591) + (4/10 * 1.5) = 1.47546
    • Gain: 1.971 - 1.47546 = 0.496

  The attribute with the highest gain (0.820) is 'Distance', so it becomes the root of our tree.

• Step 3: Building the Tree Recursively

  Now we create branches for each value of the 'Distance' attribute (Near, Medium, Far). We repeat the process for each branch. For example, for the 'Near' branch, we calculate the information gain for the remaining attributes (HP, Mana, Ranged Weapon) using only the data where Distance is 'Near'. The attribute with the highest gain becomes the next node, and we repeat until we reach a leaf node (a final decision).

  • Branch: Distance = Near: {1, 2, 7} = {Melee, Retreat, Melee}. Calculate the gain for HP, Mana, and Ranged Weapon.

    • HP: Low {Melee, Retreat}, High {Melee} => 0.918 - (2/3 * 1) - (1/3 * 0) = 0.251

    • Mana: Low {Melee, Retreat}, Enough {Melee} => 0.251

    • Ranged Weapon: No {Melee, Retreat}, Yes {Melee} => 0.251

    • All three have equal gain, so randomly select Mana.

    • Mana = Enough: Melee Attack

    • Mana = Low: Remaining data {1, 2}. Recalculate and repeat the process.

      • HP or Ranged Weapon has equal gain, randomly select Ranged Weapon.
      • Ranged Weapon = No: Melee Attack
      • Ranged Weapon = Yes: Melee Attack

  • Branch: Distance = Medium: {5, 6, 9, 10} = {2x Spellcasting, 2x Ranged}. Calculate the gain for HP, Mana, and Ranged Weapon.

    • HP: Low, High => 0, which means we can split this to the nodes.
      • Mana = Low: Ranged Attack
      • Mana = Enough: Spellcasting

  • Branch: Distance = Far: {3, 4, 8} = {Ranged, Spellcasting, Retreat}. Calculate the gain for HP, Mana, and Ranged Weapon.

    • All three have equal gain, so randomly select Mana.
      • Mana = Enough: Spellcasting
      • Mana = Low: Calculate the gain for HP and Ranged Weapon.
        • HP = Low: Retreat
        • HP = High: Ranged Attack

Why ID3 for Behavior Trees?

ID3 is a great choice for this because it's easy to understand and implement. It helps us break down complex decisions into a series of simple questions. Each node in the tree represents a question about a feature (like distance), and each branch represents a possible answer. The leaves of the tree are the actions the monster will take. It’s perfect for creating a structured, rule-based system that's easy to adjust as we gather more data. Plus, it gives us insights into which features are most important for the monster's decision-making process. The best part is that you can implement it and train it rather quickly, which makes it an excellent choice for iterating and testing.

Why CAL2 Isn't Ideal

Now, let's talk about why CAL2 isn't a good fit. CAL2 is a different algorithm that's often used for classification, but it's not well-suited for building behavior trees. CAL2 (and algorithms like it) focuses more on the statistical relationships between features and classes, rather than the hierarchical decision-making process that ID3 offers. Behavior trees need a structured approach to decision-making, where the monster's actions depend on a series of conditions. CAL2 might not provide the interpretable, step-by-step logic we need for a behavior tree.

CAL2 is also designed to find the best overall classification, which isn't always what we need in a game. We want the monster to react in a believable and dynamic way, based on its current situation. CAL2's focus on overall accuracy might lead to less flexible or predictable behavior. We need a system that can adapt to changing situations, and CAL2's focus on statistical patterns might not be as responsive to these changes as a decision tree built with ID3.

Conclusion

There you have it! We've seen how to build a behavior tree for our monster using ID3. It's a great way to make our game characters smarter. By analyzing data and creating a hierarchical decision-making process, we can give our monsters the ability to make intelligent choices, all while keeping things understandable and adaptable. ID3 provides the clarity and flexibility needed to give your monsters a realistic and engaging way to behave.

Now go forth and create some intelligent monsters! Keep experimenting, and see how you can refine their behavior even further. Good luck, and happy coding!