Learning and inference movement is a very challenging problem due to its high dimensionality and dependency to varied environments or tasks. In this paper, we propose an effective probabilistic method for learning and inference of basic movements. The motion planning problem is formulated as learning on a directed graphic model and deep generative model is used to perform learning and inference from demonstrations. An important characteristic of this method is that it flexibly incorporates the task descriptors and context information for long-term planning and it can be combined with dynamic systems for robot control. The experimental validations on robotic approaching path planning tasks show the advantages over the base methods with limited training data.
In @cite_3 , researchers try to use a forward neural network to learn the parameters of movement primitives directly from condition input(image of working scene). This model is exactly the same as the NN baseline we used in experiments. As we discussed in Section , a trajectory is inherently to be stochastic instead of deterministic. Thus we believe that a stochastic model may be more appropriate for learning and inference the trajectory, and will lead to a better performance. The results of our experiments also support our intuition.
@cite_3
2424778531 2242818861 2951446714 1583776211
Pedestrians follow different trajectories to avoid obstacles and accommodate fellow pedestrians. Any autonomous vehicle navigating such a scene should be able to foresee the future positions of pedestrians and accordingly adjust its path to avoid collisions. This problem of trajectory prediction can be viewed as a sequence generation task, where we are interested in predicting the future trajectory of people based on their past positions. Following the recent success of Recurrent Neural Network (RNN) models for sequence prediction tasks, we propose an LSTM model which can learn general human movement and predict their future trajectories. This is in contrast to traditional approaches which use hand-crafted functions such as Social forces. We demonstrate the performance of our method on several public datasets. Our model outperforms state-of-the-art methods on some of these datasets. We also analyze the trajectories predicted by our model to demonstrate the motion behaviour learned by our model. Stochastic neurons and hard non-linearities can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such stochastic or non-smooth neurons? I.e., can we "back-propagate" through these stochastic neurons? We examine this question, existing approaches, and compare four families of solutions, applicable in different settings. One of them is the minimum variance unbiased gradient estimator for stochatic binary neurons (a special case of the REINFORCE algorithm). A second approach, introduced here, decomposes the operation of a binary stochastic neuron into a stochastic binary part and a smooth differentiable part, which approximates the expected effect of the pure stochatic binary neuron to first order. A third approach involves the injection of additive or multiplicative noise in a computational graph that is otherwise differentiable. A fourth approach heuristically copies the gradient with respect to the stochastic output directly as an estimator of the gradient with respect to the sigmoid argument (we call this the straight-through estimator). To explore a context where these estimators are useful, we consider a small-scale version of conditional computation , where sparse stochastic units form a distributed representation of gaters that can turn off in combinatorially many ways large chunks of the computation performed in the rest of the neural network. In this case, it is important that the gating units produce an actual 0 most of the time. The resulting sparsity can be potentially be exploited to greatly reduce the computational cost of large deep networks for which conditional computation would be useful. We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose stationary distribution estimates the data distribution. The transition distribution of the Markov chain is conditional on the previous state, generally involving a small move, so this conditional distribution has fewer dominant modes, being unimodal in the limit of small moves. Thus, it is easier to learn because it is easier to approximate its partition function, more like learning to perform supervised function approximation, with gradients that can be obtained by backprop. We provide theorems that generalize recent work on the probabilistic interpretation of denoising autoencoders and obtain along the way an interesting justification for dependency networks and generalized pseudolikelihood, along with a definition of an appropriate joint distribution and sampling mechanism even when the conditionals are not consistent. GSNs can be used with missing inputs and can be used to sample subsets of variables given the rest. We validate these theoretical results with experiments on two image datasets using an architecture that mimics the Deep Boltzmann Machine Gibbs sampler but allows training to proceed with simple backprop, without the need for layerwise pretraining. Stochastic neurons can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such s tochastic neurons, i.e., can we “back-propagate” through these stochastic neurons? We examine this question, existing approaches, and present two novel families of solutions, applicable in different settings. In particular, it is demonstrate d that a simple biologically plausible formula gives rise to an an unbiased (but noisy) estimator of the gradient with respect to a binary stochastic neuron firing proba bility. Unlike other estimators which view the noise as a small perturbation in order to estimate gradients by finite differences, this estimator is unbiased even w ithout assuming that the stochastic perturbation is small. This estimator is also in teresting because it can be applied in very general settings which do not allow gradient back-propagation, including the estimation of the gradient with respect to futur e rewards, as required in reinforcement learning setups. We also propose an approach to approximating this unbiased but high-variance estimator by learning to predict it using a biased estimator. The second approach we propose assumes that an estimator of the gradient can be back-propagated and it provides an unbiased estimator of the gradient, but can only work with non-linearities unlike the hard threshold, but like the rectifier, that are not flat for all of their range. This is similar to trad itional sigmoidal units but has the advantage that for many inputs, a hard decision (e.g., a 0 output) can be produced, which would be convenient for conditional computation and achieving sparse representations and sparse gradients.