Gaussian process regression is often applied for learning unknown systems and specifying the uncertainty of the learned model. When using Gaussian process regression to learn unknown systems, a commonly considered approach consists of learning the residual dynamics after applying some standard discretization, which might however not be appropriate for the system at hand. Variational integrators are a less common yet promising approach to discretization, as they retain physical properties of the underlying system, such as energy conservation or satisfaction of explicit constraints. In this work, we propose the combination of a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty. The simulative evaluation of the proposed method shows desirable energy conservation properties in accordance with the theoretical results and demonstrates the capability of treating constrained dynamical systems.
相關內容
Obreshkov-like numerical integrators have been widely applied to power system transient simulation. Misuse of the numerical integrators as numerical differentiators may lead to numerical oscillation or bias. Criteria for Obreshkov-like numerical integrators to be used as numerical differentiators are proposed in this paper to avoid these misleading phenomena. The coefficients of a numerical integrator for the highest order derivative turn out to determine its suitability. Some existing Obreshkov-like numerical integrators are examined under the proposed criteria. It is revealed that the notorious numerical oscillations induced by the implicit trapezoidal method cannot always be eliminated by using the backward Euler method for a few time steps. Guided by the proposed criteria, a frequency response optimized integrator considering second order derivative is put forward which is suitable to be used as a numerical differentiator. Theoretical observations are demonstrated in time domain via case studies. The paper points out how to properly select the numerical integrators for power system transient simulation and helps to prevent their misuse.
When evaluating and comparing models using leave-one-out cross-validation (LOO-CV), the uncertainty of the estimate is typically assessed using the variance of the sampling distribution. Considering the uncertainty is important, as the variability of the estimate can be high in some cases. An important result by Bengio and Grandvalet (2004) states that no general unbiased variance estimator can be constructed, that would apply for any utility or loss measure and any model. We show that it is possible to construct an unbiased estimator considering a specific predictive performance measure and model. We demonstrate an unbiased sampling distribution variance estimator for the Bayesian normal model with fixed model variance using the expected log pointwise predictive density (elpd) utility score. This example demonstrates that it is possible to obtain improved, problem-specific, unbiased estimators for assessing the uncertainty in LOO-CV estimation.
We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points/lines, where three interfaces meet, and at the boundary points/lines, where an interface meets a fixed planar boundary. We propose a parametric finite element method based on a suitable variational formulation. The constructed method is semi-implicit and can be shown to satisfy the volume conservation of each enclosed bubble and the unconditional energy-stability, thus preserving the two fundamental geometric structures of the flow. Besides, the method has very good properties with respect to the distribution of mesh points, thus no mesh smoothing or regularization technique is required. A generalization of the introduced scheme to the case of anisotropic surface energies and non-neutral external boundaries is also considered. Numerical results are presented for the evolution of two-dimensional curve networks and three-dimensional surface clusters in the cases of both isotropic and anisotropic surface energies.
Modern deep reinforcement learning (RL) algorithms are motivated by either the general policy improvement (GPI) or trust-region learning (TRL) frameworks. However, algorithms that strictly respect these theoretical frameworks have proven unscalable. Surprisingly, the only known scalable algorithms violate the GPI/TRL assumptions, e.g. due to required regularisation or other heuristics. The current explanation of their empirical success is essentially "by analogy": they are deemed approximate adaptations of theoretically sound methods. Unfortunately, studies have shown that in practice these algorithms differ greatly from their conceptual ancestors. In contrast, in this paper we introduce a novel theoretical framework, named Mirror Learning, which provides theoretical guarantees to a large class of algorithms, including TRPO and PPO. While the latter two exploit the flexibility of our framework, GPI and TRL fit in merely as pathologically restrictive corner cases thereof. This suggests that the empirical performance of state-of-the-art methods is a direct consequence of their theoretical properties, rather than of aforementioned approximate analogies. Mirror learning sets us free to boldly explore novel, theoretically sound RL algorithms, a thus far uncharted wonderland.
Though remarkable progress has been achieved in various vision tasks, deep neural networks still suffer obvious performance degradation when tested in out-of-distribution scenarios. We argue that the feature statistics (mean and standard deviation), which carry the domain characteristics of the training data, can be properly manipulated to improve the generalization ability of deep learning models. Common methods often consider the feature statistics as deterministic values measured from the learned features and do not explicitly consider the uncertain statistics discrepancy caused by potential domain shifts during testing. In this paper, we improve the network generalization ability by modeling the uncertainty of domain shifts with synthesized feature statistics during training. Specifically, we hypothesize that the feature statistic, after considering the potential uncertainties, follows a multivariate Gaussian distribution. Hence, each feature statistic is no longer a deterministic value, but a probabilistic point with diverse distribution possibilities. With the uncertain feature statistics, the models can be trained to alleviate the domain perturbations and achieve better robustness against potential domain shifts. Our method can be readily integrated into networks without additional parameters. Extensive experiments demonstrate that our proposed method consistently improves the network generalization ability on multiple vision tasks, including image classification, semantic segmentation, and instance retrieval. The code will be released soon at //github.com/lixiaotong97/DSU.
In structure learning, the output is generally a structure that is used as supervision information to achieve good performance. Considering the interpretation of deep learning models has raised extended attention these years, it will be beneficial if we can learn an interpretable structure from deep learning models. In this paper, we focus on Recurrent Neural Networks (RNNs) whose inner mechanism is still not clearly understood. We find that Finite State Automaton (FSA) that processes sequential data has more interpretable inner mechanism and can be learned from RNNs as the interpretable structure. We propose two methods to learn FSA from RNN based on two different clustering methods. We first give the graphical illustration of FSA for human beings to follow, which shows the interpretability. From the FSA's point of view, we then analyze how the performance of RNNs are affected by the number of gates, as well as the semantic meaning behind the transition of numerical hidden states. Our results suggest that RNNs with simple gated structure such as Minimal Gated Unit (MGU) is more desirable and the transitions in FSA leading to specific classification result are associated with corresponding words which are understandable by human beings.
Recent studies have shown the vulnerability of reinforcement learning (RL) models in noisy settings. The sources of noises differ across scenarios. For instance, in practice, the observed reward channel is often subject to noise (e.g., when observed rewards are collected through sensors), and thus observed rewards may not be credible as a result. Also, in applications such as robotics, a deep reinforcement learning (DRL) algorithm can be manipulated to produce arbitrary errors. In this paper, we consider noisy RL problems where observed rewards by RL agents are generated with a reward confusion matrix. We call such observed rewards as perturbed rewards. We develop an unbiased reward estimator aided robust RL framework that enables RL agents to learn in noisy environments while observing only perturbed rewards. Our framework draws upon approaches for supervised learning with noisy data. The core ideas of our solution include estimating a reward confusion matrix and defining a set of unbiased surrogate rewards. We prove the convergence and sample complexity of our approach. Extensive experiments on different DRL platforms show that policies based on our estimated surrogate reward can achieve higher expected rewards, and converge faster than existing baselines. For instance, the state-of-the-art PPO algorithm is able to obtain 67.5% and 46.7% improvements in average on five Atari games, when the error rates are 10% and 30% respectively.
We consider the exploration-exploitation trade-off in reinforcement learning and we show that an agent imbued with a risk-seeking utility function is able to explore efficiently, as measured by regret. The parameter that controls how risk-seeking the agent is can be optimized exactly, or annealed according to a schedule. We call the resulting algorithm K-learning and show that the corresponding K-values are optimistic for the expected Q-values at each state-action pair. The K-values induce a natural Boltzmann exploration policy for which the `temperature' parameter is equal to the risk-seeking parameter. This policy achieves an expected regret bound of $\tilde O(L^{3/2} \sqrt{S A T})$, where $L$ is the time horizon, $S$ is the number of states, $A$ is the number of actions, and $T$ is the total number of elapsed time-steps. This bound is only a factor of $L$ larger than the established lower bound. K-learning can be interpreted as mirror descent in the policy space, and it is similar to other well-known methods in the literature, including Q-learning, soft-Q-learning, and maximum entropy policy gradient, and is closely related to optimism and count based exploration methods. K-learning is simple to implement, as it only requires adding a bonus to the reward at each state-action and then solving a Bellman equation. We conclude with a numerical example demonstrating that K-learning is competitive with other state-of-the-art algorithms in practice.
Zero shot learning in Image Classification refers to the setting where images from some novel classes are absent in the training data but other information such as natural language descriptions or attribute vectors of the classes are available. This setting is important in the real world since one may not be able to obtain images of all the possible classes at training. While previous approaches have tried to model the relationship between the class attribute space and the image space via some kind of a transfer function in order to model the image space correspondingly to an unseen class, we take a different approach and try to generate the samples from the given attributes, using a conditional variational autoencoder, and use the generated samples for classification of the unseen classes. By extensive testing on four benchmark datasets, we show that our model outperforms the state of the art, particularly in the more realistic generalized setting, where the training classes can also appear at the test time along with the novel classes.
Amortized inference has led to efficient approximate inference for large datasets. The quality of posterior inference is largely determined by two factors: a) the ability of the variational distribution to model the true posterior and b) the capacity of the recognition network to generalize inference over all datapoints. We analyze approximate inference in variational autoencoders in terms of these factors. We find that suboptimal inference is often due to amortizing inference rather than the limited complexity of the approximating distribution. We show that this is due partly to the generator learning to accommodate the choice of approximation. Furthermore, we show that the parameters used to increase the expressiveness of the approximation play a role in generalizing inference rather than simply improving the complexity of the approximation.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191