In order for reinforcement learning (RL) agents to be deployed in real-world environments, they must be able to generalize to unseen environments. However, RL struggles with out-of-distribution generalization, often due to overfitting the particulars of the training environment. Although regularization techniques from supervised learning can be applied to avoid over-fitting, the differences between supervised learning and RL limit their application. To address this, we propose the Signal-to-Noise Ratio regulated Parameter Uncertainty Network (SNR PUN) for RL. We introduce SNR as a new measure of regularizing the parameter uncertainty of a network and provide a formal analysis explaining why SNR regularization works well for RL. We demonstrate the effectiveness of our proposed method to generalize in several simulated environments; and in a physical system showing the possibility of using SNR PUN for applying RL to real-world applications.

Implicit neural networks including deep equilibrium models have achieved superior task performance with better parameter efficiency in various applications. However, it is often at the expense of higher computation costs during inference. In this work, we identify a phenomenon named $\textbf{heterogeneous convergence}$ that exists in deep equilibrium models and other iterative methods. We observe much faster convergence of state activations in certain dimensions therefore indicating the dimensionality of the underlying dynamics of the forward pass is much lower than the defined dimension of the states. We thereby propose to exploit heterogeneous convergence by storing past linear operation results (e.g., fully connected and convolutional layers) and only propagating the state activation when its change exceeds a threshold. Thus, for the already converged dimensions, the computations can be skipped. We verified our findings and reached 84\% FLOPs reduction on the implicit neural representation task, 73\% on the Sintel and 76\% on the KITTI datasets for the optical flow estimation task while keeping comparable task accuracy with the models that perform the full update.