A longstanding goal of reinforcement learning is to develop non- parametric representations of policies and value functions that support rapid learning without suffering from interference or the curse of di- mensionality. We have developed a trajectory-based approach, in which policies and value functions are represented nonparametrically along tra- jectories. These trajectories, policies, and value functions are updated as the value function becomes more accurate or as a model of the task is up- dated. We have applied this approach to periodic tasks such as hopping and walking, which required handling discount factors and discontinu- ities in the task dynamics, and using function approximation to represent value functions at discontinuities. We also describe extensions of the ap- proach to make the policies more robust to modeling error and sensor noise.

Kernel methods are powerful tools to capture nonlinear patterns behind data. They implicitly learn high (even infinite) dimensional nonlinear features in the Reproducing Kernel Hilbert Space (RKHS) while making the computation tractable by leveraging the kernel trick. Classic kernel methods learn a single layer of nonlinear features, whose representational power may be limited. Motivated by recent success of deep neural networks (DNNs) that learn multi-layer hierarchical representations, we propose a Stacked Kernel Network (SKN) that learns a hierarchy of RKHS-based nonlinear features. SKN interleaves several layers of nonlinear transformations (from a linear space to a RKHS) and linear transformations (from a RKHS to a linear space). Similar to DNNs, a SKN is composed of multiple layers of hidden units, but each parameterized by a RKHS function rather than a finite-dimensional vector. We propose three ways to represent the RKHS functions in SKN: (1)nonparametric representation, (2)parametric representation and (3)random Fourier feature representation. Furthermore, we expand SKN into CNN architecture called Stacked Kernel Convolutional Network (SKCN). SKCN learning a hierarchy of RKHS-based nonlinear features by convolutional operation with each filter also parameterized by a RKHS function rather than a finite-dimensional matrix in CNN, which is suitable for image inputs. Experiments on various datasets demonstrate the effectiveness of SKN and SKCN, which outperform the competitive methods.

The ability to automatically discover patterns and perform extrapolation is an essential quality of intelligent systems. Kernel methods, such as Gaussian processes, have great potential for pattern extrapolation, since the kernel flexibly and interpretably controls the generalisation properties of these methods. However, automatically extrapolating large scale multidimensional patterns is in general difficult, and developing Gaussian process models for this purpose involves several challenges. A vast majority of kernels, and kernel learning methods, currently only succeed in smoothing and interpolation. This difficulty is compounded by the fact that Gaussian processes are typically only tractable for small datasets, and scaling an expressive kernel learning approach poses different challenges than scaling a standard Gaussian process model. One faces additional computational constraints, and the need to retain significant model structure for expressing the rich information available in a large dataset. In this paper, we propose a Gaussian process approach for large scale multidimensional pattern extrapolation. We recover sophisticated out of class kernels, perform texture extrapolation, inpainting, and video extrapolation, and long range forecasting of land surface temperatures, all on large multidimensional datasets, including a problem with 383,400 training points. The proposed method significantly outperforms alternative scalable and flexible Gaussian process methods, in speed and accuracy. Moreover, we show that a distinct combination of expressive kernels, a fully non-parametric representation, and scalable inference which exploits existing model structure, are critical for large scale multidimensional pattern extrapolation.

A longstanding goal of reinforcement learning is to develop nonparametric representations of policies and value functions that support rapid learning without suffering from interference or the curse of dimensionality. We have developed a trajectory-based approach, in which policies and value functions are represented nonparametrically along trajectories. These trajectories, policies, and value functions are updated as the value function becomes more accurate or as a model of the task is updated. We have applied this approach to periodic tasks such as hopping and walking, which required handling discount factors and discontinuities in the task dynamics, and using function approximation to represent value functions at discontinuities. We also describe extensions of the approach to make the policies more robust to modeling error and sensor noise.

A longstanding goal of reinforcement learning is to develop nonparametric representations of policies and value functions that support rapid learning without suffering from interference or the curse of dimensionality. We have developed a trajectory-based approach, in which policies and value functions are represented nonparametrically along trajectories. These trajectories, policies, and value functions are updated as the value function becomes more accurate or as a model of the task is updated. We have applied this approach to periodic tasks such as hopping and walking, which required handling discount factors and discontinuities in the task dynamics, and using function approximation to represent value functions at discontinuities. We also describe extensions of the approach to make the policies more robust to modeling error and sensor noise.

A longstanding goal of reinforcement learning is to develop nonparametric representationsof policies and value functions that support rapid learning without suffering from interference or the curse of dimensionality. Wehave developed a trajectory-based approach, in which policies and value functions are represented nonparametrically along trajectories. Thesetrajectories, policies, and value functions are updated as the value function becomes more accurate or as a model of the task is updated. Wehave applied this approach to periodic tasks such as hopping and walking, which required handling discount factors and discontinuities inthe task dynamics, and using function approximation to represent value functions at discontinuities. We also describe extensions of the approach tomake the policies more robust to modeling error and sensor noise.