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Hierarchical Task Networks

Hierarchical Task Networks (HTNs)

A hierarchical reinforcement learning approach that decomposes complex tasks into hierarchical structures of subtasks for planning and execution.

Family: Hierarchical Reinforcement Learning Status: 📋 Planned

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Overview

Hierarchical Task Networks (HTNs) represent a powerful approach to reinforcement learning that

decomposes complex tasks into hierarchical structures of subtasks. The algorithm learns to plan and execute tasks at multiple levels of abstraction, where high-level tasks are broken down into simpler subtasks that can be learned and executed independently.

This hierarchical approach enables agents to solve complex, long-horizon problems by leveraging task decomposition and temporal abstraction. HTNs are particularly effective in domains where tasks have natural hierarchical structure, such as robotics manipulation, autonomous navigation, and complex game playing scenarios.

Mathematical Formulation

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Problem Definition

Given:

  • Task hierarchy: T = {T_1, T_2, ..., T_n}
  • Subtask decomposition: T_i = {t_{i1}, t_{i2}, ..., t_{im}}
  • State space: S
  • Action space: A
  • Reward function: R(s,a,s')

Find hierarchical task policies that maximize expected cumulative reward:

V(T_i) = max_π E_{τ ~ π}[∑_{t=0}^H γ^t r_t]

Where π is the policy for executing the task decomposition, and H is the horizon.

Key Properties

Task Decomposition

T_i = {t_{i1}, t_{i2}, ..., t_{im}}

Complex tasks broken into simpler subtasks

Hierarchical Value Function

V(T_i) = max_π E_{τ ~ π}[∑_{t=0}^H γ^t r_t]

Value function for composite tasks

Subtask Policy

π_{t_{ij}}(a|s) = argmax_a Q_{t_{ij}}(s, a)

Policy for executing individual subtasks

Key Properties

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  • Task Decomposition

    Complex tasks broken into manageable subtasks

  • Temporal Abstraction

    Different levels operate at different time scales

  • Modular Learning

    Subtasks can be learned independently

  • Reusability

    Learned subtasks can be applied to different composite tasks

Implementation Approaches

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Standard HTN implementation with task hierarchy and subtask policies

Complexity:

  • Time: O(|T| × |S| × |A| × episodes)
  • Space: O(|T| × |S| × |A|)

Advantages

  • Natural task decomposition for complex problems

  • Modular learning allows independent subtask training

  • Temporal abstraction enables planning at different levels

  • Reusable subtasks can be applied to different composite tasks

Disadvantages

  • Requires manual design of task hierarchy

  • Task decomposition can be challenging

  • Coordination between subtasks can be complex

  • May not discover optimal task decompositions automatically

Complete Implementation

The full implementation with error handling, comprehensive testing, and additional variants is available in the source code:

Complexity Analysis

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Time & Space Complexity Comparison

Approach Time Complexity Space Complexity Notes
Basic HTN O( T ×

Use Cases & Applications

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Application Categories

Robotics and Control

  • Robot Manipulation: Complex manipulation tasks with hierarchical subtasks

  • Autonomous Navigation: Multi-level navigation with waypoint and obstacle avoidance subtasks

  • Industrial Automation: Process control with hierarchical task decomposition

  • Swarm Robotics: Coordinated behavior with hierarchical task networks

Game AI and Strategy

  • Strategy Games: Multi-level decision making with hierarchical task planning

  • Puzzle Games: Complex puzzles with hierarchical solution strategies

  • Adventure Games: Quest completion with hierarchical task networks

  • Simulation Games: Resource management with hierarchical task planning

Real-World Applications

  • Autonomous Vehicles: Multi-level driving with hierarchical task decomposition

  • Healthcare: Treatment planning with hierarchical medical task networks

  • Finance: Portfolio management with hierarchical investment task networks

  • Network Control: Traffic management with hierarchical routing task networks

Educational Value

  • Task Decomposition: Understanding how to break complex problems into simpler parts

  • Hierarchical Planning: Learning to plan at multiple levels of abstraction

  • Modular Learning: Understanding how to learn components independently

  • Transfer Learning: Learning reusable skills across different composite tasks

Educational Value

  • Task Decomposition: Perfect introduction to breaking complex problems into simpler parts

  • Hierarchical Planning: Shows how to plan at multiple levels of abstraction

  • Modular Learning: Demonstrates learning components independently

  • Transfer Learning: Illustrates how skills can be reused across different tasks

References & Further Reading

:material-library: Core Papers

:material-file-document:
Modular multitask reinforcement learning with policy sketches
:material-file-document:
Foundational work on hierarchical reinforcement learning

:material-book: Hierarchical RL Textbooks

:material-file-document:
Comprehensive introduction to reinforcement learning including hierarchical methods
:material-file-document:
Algorithms for reinforcement learning with hierarchical approaches

:material-web: Online Resources

:material-link:
Hierarchical Task Networks
Wikipedia article on hierarchical task networks
:material-link:
Task Decomposition in AI
Task decomposition and hierarchical planning in AI

:material-code-tags: Implementation & Practice

:material-link:
OpenAI Gym
RL environments for testing hierarchical task networks
:material-link:
Stable Baselines3
High-quality RL algorithm implementations
:material-link:
Ray RLlib
Scalable RL library for production use

Interactive Learning

Try implementing the different approaches yourself! This progression will give you deep insight into the algorithm's principles and applications.

Pro Tip: Start with the simplest implementation and gradually work your way up to more complex variants.

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Related Algorithms in Hierarchical Reinforcement Learning:

  • Hierarchical Q-Learning - Extends traditional Q-Learning to handle temporal abstraction and hierarchical task decomposition with multi-level Q-functions.

  • Option-Critic - A hierarchical reinforcement learning algorithm that learns options (temporally extended actions) end-to-end using policy gradient methods.

  • Hierarchical Actor-Critic (HAC) - An advanced hierarchical reinforcement learning algorithm that extends the actor-critic framework with temporal abstraction and hierarchical structure.

  • Hierarchical Policy Gradient - Extends traditional policy gradient methods to handle temporal abstraction and hierarchical task decomposition with multi-level policies.

  • Feudal Networks (FuN) - A hierarchical reinforcement learning algorithm that implements a manager-worker architecture for temporal abstraction and goal-based learning.