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Demonstrating the Continual Learning Capabilities and Practical Application of Discrete-Time Active Inference

Rithvik Prakki

TL;DR

This paper derives the mathematical formulations of variational and expected free energy and applies them to the design of a self-learning research agent, demonstrating the agent's ability to relearn and refine its models efficiently, making it suitable for complex domains like finance and healthcare.

Abstract

Active inference is a mathematical framework for understanding how agents (biological or artificial) interact with their environments, enabling continual adaptation and decision-making. It combines Bayesian inference and free energy minimization to model perception, action, and learning in uncertain and dynamic contexts. Unlike reinforcement learning, active inference integrates exploration and exploitation seamlessly by minimizing expected free energy. In this paper, we present a continual learning framework for agents operating in discrete time environments, using active inference as the foundation. We derive the mathematical formulations of variational and expected free energy and apply them to the design of a self-learning research agent. This agent updates its beliefs and adapts its actions based on new data without manual intervention. Through experiments in changing environments, we demonstrate the agent's ability to relearn and refine its models efficiently, making it suitable for complex domains like finance and healthcare. The paper concludes by discussing how the proposed framework generalizes to other systems, positioning active inference as a flexible approach for adaptive AI.

Demonstrating the Continual Learning Capabilities and Practical Application of Discrete-Time Active Inference

TL;DR

This paper derives the mathematical formulations of variational and expected free energy and applies them to the design of a self-learning research agent, demonstrating the agent's ability to relearn and refine its models efficiently, making it suitable for complex domains like finance and healthcare.

Abstract

Active inference is a mathematical framework for understanding how agents (biological or artificial) interact with their environments, enabling continual adaptation and decision-making. It combines Bayesian inference and free energy minimization to model perception, action, and learning in uncertain and dynamic contexts. Unlike reinforcement learning, active inference integrates exploration and exploitation seamlessly by minimizing expected free energy. In this paper, we present a continual learning framework for agents operating in discrete time environments, using active inference as the foundation. We derive the mathematical formulations of variational and expected free energy and apply them to the design of a self-learning research agent. This agent updates its beliefs and adapts its actions based on new data without manual intervention. Through experiments in changing environments, we demonstrate the agent's ability to relearn and refine its models efficiently, making it suitable for complex domains like finance and healthcare. The paper concludes by discussing how the proposed framework generalizes to other systems, positioning active inference as a flexible approach for adaptive AI.
Paper Structure (28 sections, 15 equations, 3 figures)

This paper contains 28 sections, 15 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Active Inference and Free Energy Principle
  3. Mathematical Derivation of Variational Free Energy (VFE)
  4. Expected Free Energy (EFE)
  5. Learning in Active Inference: The Dirichlet-Categorical Model
  6. Learning the A Matrix
  7. Application to Self-Learning Agents
  8. Active Inference as an Agentic Learning Mechanism
  9. Motivating the Problem
  10. Developing the Framework
  11. Definitions
  12. Generative Model
  13. Generative Process
  14. Results
  15. Scoring Mechanism
  16. ...and 13 more sections

Figures (3)

  • Figure 1: Hierarchical POMDP showing research methods and their outcomes. The agent adapts to changes in the research environment by updating the state and observation factors. This structure allows for continual learning as new information becomes available.
  • Figure 2: The results of the first 10 trials in the original environment. The agent quickly learns the dynamics of the environment, reaching a high score for Industry 1 within six iterations, demonstrating that the active inference agent is able to learn environmental dynamics effectively.
  • Figure 3: Learning progress of the active inference agent across all industries in the original environment. After an initial drop due to uncertainty, the agent learns the correct mappings, achieving a higher score over 20 trials.