Despite remarkable successes, Deep Reinforce- ment Learning (DRL) is not robust to hyperparam- eterization, implementation details, or small envi- ronment changes (Henderson et al. 2017, Zhang et al. 2018). Overcoming such sensitivity is key to making DRL applicable to real world problems. In this paper, we identify sensitivity to time dis- cretization in near continuous-time environments as a critical factor; this covers, e.g., changing the number of frames per second, or the action frequency of the controller. Empirically, we find that Q-learning-based approaches such as Deep Q- learning (Mnih et al., 2015) and Deep Determinis- tic Policy Gradient (Lillicrap et al., 2015) collapse with small time steps. Formally, we prove that Q-learning does not exist in continuous time. We detail a principled way to build an off-policy RL algorithm that yields similar performances over a wide range of time discretizations, and confirm this robustness empirically.

Deep learning models often have more parameters than observations, and still perform well. This is sometimes described as a paradox. In this work, we show experimentally that despite their huge number of parameters, deep neural networks can compress the data losslessly even when taking the cost of encoding the parameters into account. Such a compression viewpoint originally motivated the use of variational methods in neural networks. However, we show that these variational methods provide surprisingly poor compression bounds, despite being explicitly built to minimize such bounds. This might explain the relatively poor practical performance of variational methods in deep learning. Better encoding methods, imported from the Minimum Description Length (MDL) toolbox, yield much better compression values on deep networks.