On efficient computation in active inference

Abstract: Despite being recognized as neurobiologically plausible, active inference faces difficulties when employed to simulate intelligent behaviour in complex environments due to its computational cost and the difficulty of specifying an appropriate target distribution for the agent. This paper introduces two solutions that work in concert to address these limitations. First, we present a novel planning algorithm for finite temporal horizons with drastically lower computational complexity. Second, inspired by Z-learning from control theory literature, we simplify the process of setting an appropriate target distribution for new and existing active inference planning schemes. Our first approach leverages the dynamic programming algorithm, known for its computational efficiency, to minimize the cost function used in planning through the Bellman-optimality principle. Accordingly, our algorithm recursively assesses the expected free energy of actions in the reverse temporal order. This improves computational efficiency by orders of magnitude and allows precise model learning and planning, even under uncertain conditions. Our method simplifies the planning process and shows meaningful behaviour even when specifying only the agent's final goal state. The proposed solutions make defining a target distribution from a goal state straightforward compared to the more complicated task of defining a temporally informed target distribution. The effectiveness of these methods is tested and demonstrated through simulations in standard grid-world tasks. These advances create new opportunities for various applications.

• The paper introduces dynamic programming-based planning and a Z-learning inspired target specification to enhance computational efficiency in active inference.
• It leverages backward induction via the Bellman-optimality principle to evaluate expected free energy, streamlining planning in grid-world simulations.
• The approach broadens active inference applications by lowering computational costs and improving model learning in uncertain, dynamic environments.

On Efficient Computation in Active Inference

Introduction

The field of active inference, which posits a framework for understanding intelligent behavior, faces significant computational challenges when applied to complex environments. Specifically, the high computational cost and difficulty in specifying appropriate target distributions for agents present substantive barriers. This paper introduces two novel solutions to address these limitations: a planning algorithm informed by dynamic programming for finite temporal horizons, and the adaptation of Z-learning from control theory literature to streamline target distribution setting in planning schemes.

Active Inference and Dynamic Programming

Active inference models aim at minimizing variational free energy, a statistical measure often linked to biological plausibility. However, complex tasks involve substantial computational resources, hindering the framework's applicability. The paper proposes a more efficient planning algorithm leveraging dynamic programming, significantly improving computational efficiency via recursive assessment of free energy using the Bellman-optimality principle. This backward-in-time planning effectively reduces the planning complexity and supports precise model learning even amid uncertainty.

Evaluating Expected Free Energy

The proposed algorithm evaluates the expected free energy (EFE) by starting at the desired goal state's time horizon and moving backwards. This approach circumvents the traditional tree search by condensing anticipated future free energies into immediate state-action pairs, distinctly reducing computational demand. The practical outcomes are demonstrated through simulations in standard grid-world environments where these methods improved computational efficiency substantially over classical active inference approaches.

Simplified Target Distribution Formation

In addition to planning improvements, the authors propose simplifying the specification of target distributions. Inspired by the Z-learning paradigm, this method allows the derivation of straightforward target distributions from agent-defined goal states. The utility of this simplification manifests in more adept behavioral modeling without the burden of temporally informed distribution settings, which typically require significant manual intervention and computational overhead. This approach allows for broader application of active inference in varied and uncertain environments.

Implications and Future Directions

The advances presented in this paper create a fertile ground for diverse practical applications of active inference, particularly in environments previously deemed intractable due to computational demands. By dramatically improving the efficiency of planning and target specification, the utility of active inference in stochastic control and artificial intelligence domains broadens significantly. Future developments in AI might leverage these enhancements to create more robust, adaptable systems capable of operating autonomously in dynamic, uncertain contexts.

Conclusion

The solutions introduced in this paper represent a significant step forward in making active inference a feasible approach in complex, real-world applications. By harnessing dynamic programming and simplified target distribution frameworks, the computational barriers that once encumbered active inference are substantially lowered, promising greater integration into practical AI systems and fostering continued innovation in understanding and modeling intelligent behavior.