Trajectory optimization using a learned model of the environment is one of the core elements of model-based reinforcement learning. This procedure often suffers from exploiting inaccuracies of the learned model. We propose to regularize trajectory optimization by means of a denoising autoencoder that is trained on the same trajectories as the model of the environment. We show that the proposed regularization leads to improved planning with both gradient-based and gradient-free optimizers. We also demonstrate that using regularized trajectory optimization leads to rapid initial learning in a set of popular motor control tasks, which suggests that the proposed approach can be a useful tool for improving sample efficiency.

We propose a recurrent extension of the Ladder networks whose structure is motivated by the inference required in hierarchical latent variable models. We demonstrate that the recurrent Ladder is able to handle a wide variety of complex learning tasks that benefit from iterative inference and temporal modeling. The architecture shows close-to-optimal results on temporal modeling of video data, competitive results on music modeling, and improved perceptual grouping based on higher order abstractions, such as stochastic textures and motion cues. We present results for fully supervised, semi-supervised, and unsupervised tasks. The results suggest that the proposed architecture and principles are powerful tools for learning a hierarchy of abstractions, learning iterative inference and handling temporal information.

We present a framework for efficient perceptual inference that explicitly reasons about the segmentation of its inputs and features. Rather than being trained for any specific segmentation, our framework learns the grouping process in an unsupervised manner or alongside any supervised task. We enable a neural network to group the representations of different objects in an iterative manner through a differentiable mechanism. We achieve very fast convergence by allowing the system to amortize the joint iterative inference of the groupings and their representations. In contrast to many other recently proposed methods for addressing multi-object scenes, our system does not assume the inputs to be images and can therefore directly handle other modalities. We evaluate our method on multi-digit classification of very cluttered images that require texture segmentation. Remarkably our method achieves improved classification performance over convolutional networks despite being fully connected, by making use of the grouping mechanism. Furthermore, we observe that our system greatly improves upon the semi-supervised result of a baseline Ladder network on our dataset. These results are evidence that grouping is a powerful tool that can help to improve sample efficiency.

We combine supervised learning with unsupervised learning in deep neural networks. The proposed model is trained to simultaneously minimize the sum of supervised and unsupervised cost functions by backpropagation, avoiding the need for layer-wise pre-training. Our work builds on top of the Ladder network proposed by Valpola (2015) which we extend by combining the model with supervision. We show that the resulting model reaches state-of-the-art performance in semi-supervised MNIST and CIFAR-10 classification in addition to permutation-invariant MNIST classification with all labels.