Intrinsic motivation as constrained entropy maximization

The evolution of autonomous AI has shifted from reward-centric reinforcement learning towards models inspired by biological intrinsic motivation, such as curiosity, empowerment, and active inference. Early works like Schmidhuber's artificial curiosity, Friston's free energy principle, and Baranes & Oudeyer’s empowerment laid foundational concepts. These approaches aim to emulate biological behaviors like exploration, self-organization, and goal-seeking without explicit external rewards. Despite progress, a unified theoretical framework that captures the common principles underlying these models remains lacking, limiting their scalability and interpretability in complex environments.

The core challenge is to develop a comprehensive theoretical framework that unifies diverse intrinsic motivation models—active inference, empowerment, and maximum occupancy—under a common principle. Existing models are often isolated, focusing on specific mechanisms without addressing their fundamental connections. This fragmentation hampers the understanding of how intrinsic drives can be systematically harnessed for scalable, goal-directed autonomous behavior, especially in high-dimensional, uncertain environments. The problem involves formalizing the relationships among information-theoretic measures, model evidence, and behavioral objectives within a single, scalable framework.

This paper's innovation lies in proposing a unified constrained maximum entropy inference framework that encapsulates active inference, empowerment, and maximum occupancy. It introduces a variational Bayesian approach that explicitly incorporates model evidence constraints, linking information gain, free energy minimization, and path entropy maximization. This integration offers a new theoretical lens to understand intrinsic motivation, emphasizing the role of implicit model evidence constraints in stabilizing exploration and goal-directed behaviors. The framework advances the state-of-the-art by providing a scalable, interpretable, and theoretically grounded approach to autonomous motivation.

• �� Construct a Bayesian generative model defining state and observation spaces. • Formulate active inference as variational free energy minimization, incorporating model evidence constraints. • Integrate empowerment by maximizing mutual information between actions and observations, using variational bounds. • Extend to maximum occupancy by maximizing path entropy, balancing exploration and control. • Employ iterative optimization of free energy, mutual information, and path entropy using stochastic gradient methods. • Validate through simulations in continuous state spaces, comparing exploration efficiency and robustness against baseline methods.

Simulations involve continuous state-space environments with varying complexity. Baselines include traditional empowerment, active inference, and random exploration. Metrics focus on exploration coverage, path diversity, and goal achievement. Hyperparameters such as β (path occupancy weight) and γ (discount factor) are tuned for optimal performance. Results show maximum occupancy agents achieve 20% higher exploration coverage, demonstrate goal-directed behaviors without explicit rewards, and maintain stability across different environment complexities. Ablation studies confirm the importance of model evidence constraints and the balance between exploration and control.

The experiments reveal that the unified framework enables agents to explore more broadly and adaptively, outperforming traditional methods in complex scenarios. The implicit model evidence constraint enhances stability and information efficiency, reducing the risk of degenerate behaviors. The approach successfully produces goal-like behaviors solely driven by intrinsic drives, validating the theoretical claims. Quantitative improvements include increased exploration coverage, reduced variance in behavior, and higher robustness to environmental noise, demonstrating the framework's practical viability.

Potential applications include autonomous robotics, adaptive control systems, and intelligent exploration in uncertain environments. The framework supports self-driven learning without external rewards, suitable for exploration in unknown terrains, autonomous navigation, and complex decision-making tasks. Its scalability and robustness make it promising for real-world deployment in robotics, autonomous vehicles, and adaptive AI agents, especially where external supervision is limited or unavailable.

The approach assumes accurate models of environment dynamics, which may be challenging in real-world scenarios with high-dimensional, noisy data. Computational complexity increases with state space size, requiring further optimization for real-time applications. Most validation is in simulation; real-world tests are needed to assess robustness. Additionally, integrating multi-modal sensory data and multi-task learning remains an open challenge, requiring future research to enhance scalability and practical deployment.