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Deep Active Inference for Pixel-Based Discrete Control: Evaluation on the Car Racing Problem

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Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD 2021)


Despite the potential of active inference for visual-based control, learning the model and the preferences (priors) while interacting with the environment is challenging. Here, we study the performance of a deep active inference (dAIF) agent on OpenAI’s car racing benchmark, where there is no access to the car’s state. The agent learns to encode the world’s state from high-dimensional input through unsupervised representation learning. State inference and control are learned end-to-end by optimizing the expected free energy. Results show that our model achieves comparable performance to deep Q-learning. However, vanilla dAIF does not reach state-of-the-art performance compared to other world model approaches. Hence, we discuss the current model implementation’s limitations and potential architectures to overcome them.

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  1. 1.

    The code can be found at

  2. 2.

    The full derivation can be found in Appendix D.


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Correspondence to N. T. A. van Hoeffelen .

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A Model Parameters

Table 2. General parameters
Table 3. DQN parameters
Table 4. dAIF parameters

B DQN: Policy Network

Table 5. Layers DQN policy network


Table 6. VAE layers

D Derivations

Derivation for the EFE for a single time step:

$$\begin{aligned} \begin{aligned} G(s_k, o_k)&= \mathbf {KL}[q(s_k) \mid \mid p(s_k, o_k)] \\&= \int q(s_k) \ln \frac{q(s_k)}{p(s_k,o_k)} \\&= \int q(s_k) \ln {q(s_k)} - \ln {p(s_k,o_k)} \\&= \int q(s_k) \ln {q(s_k)} - \ln {p(s_k|o_k)} - \ln {p(o_k)} \\&\approx \int q(s_k) \ln {q(s_k)} - \ln {q(s_k|o_k)} - \ln {p(o_k)} \\&\approx - \ln {p(o_k)} + \int q(s_k) \ln {q(s_k)} - \ln {q(s_k|o_k)} \\&\approx - \ln {p(o_k)} + \int q(s_k) \ln {\frac{q(s_k)}{q(s_k|o_k)}} \\&\approx - \ln {p(o_k)} + \mathbf {KL}[q(s_k) \mid \mid q(s_k|o_k)] \ \\&\approx -r(o_k) + \mathbf {KL}[q(s_k) \mid \mid q(s_k|o_k)] \end{aligned} \end{aligned}$$

E Average Reward Over 100 Episodes

Fig. 5.
figure 5

Average reward test over 100 episodes for DQN and dAIF. The bright lines show the mean over episodes. The transparent lines show the reward that was obtained in a particular episode.

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van Hoeffelen, N.T.A., Lanillos, P. (2021). Deep Active Inference for Pixel-Based Discrete Control: Evaluation on the Car Racing Problem. In: Kamp, M., et al. Machine Learning and Principles and Practice of Knowledge Discovery in Databases. ECML PKDD 2021. Communications in Computer and Information Science, vol 1524. Springer, Cham.

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