The DeeP-Mod framework builds an environment model using features from a Deep Dynamic Programming Network (DDPN), trained via a Deep Q-Network (DQN). While Deep Q-Learning is effective in decision-making, state information is lost in deeper DQN layers due to mixed state-action representations. We address this by using Dynamic Programming (DP) to train a DDPN, where Value Iteration ensures the output represents state values, not state-action pairs. Extracting features from the DDPN preserves state information, enabling task and action set independence. We show that a reduced DDPN can be trained using features extracted from the original DDPN trained on an identical problem. This reduced DDPN achieves faster convergence under noise and outperforms the original DDPN. Finally, we introduce the DeeP-Mod framework, which creates an environment model using the evolution of features extracted from a DDPN in response to actions. A second DDPN, which learns directly from this feature model rather than raw states, can learn an effective feature-value representation and thus optimal policy. A key advantage of DeeP-Mod is that an externally defined environment model is not needed at any stage, making DDPN applicable to a wide range of environments.

Neural networks that can produce accurate, input-conditional uncertainty representations are critical for real-world applications. Recent progress on heteroscedastic continuous regression has shown great promise for calibrated uncertainty quantification on complex tasks, like image regression. However, when these methods are applied to discrete regression tasks, such as crowd counting, ratings prediction, or inventory estimation, they tend to produce predictive distributions with numerous pathologies. We propose to address these issues by training a neural network to output the parameters of a Double Poisson distribution, which we call the Deep Double Poisson Network (DDPN). In contrast to existing methods that are trained to minimize Gaussian negative log likelihood (NLL), DDPNs produce a proper probability mass function over discrete output. Additionally, DDPNs naturally model under-, over-, and equi-dispersion, unlike networks trained with the more rigid Poisson and Negative Binomial parameterizations. We show DDPNs 1) vastly outperform existing discrete models; 2) meet or exceed the accuracy and flexibility of networks trained with Gaussian NLL; 3) produce proper predictive distributions over discrete counts; and 4) exhibit superior out-of-distribution detection. DDPNs can easily be applied to a variety of count regression datasets including tabular, image, point cloud, and text data.