We investigate the benefits of feature selection, nonlinear modelling and online learning when forecasting in financial time series. We consider the sequential and continual learning sub-genres of online learning. The experiments we conduct show that there is a benefit to online transfer learning, beyond the sequential updating of recursive least-squares models. We show that feature representation transfer via radial basis function networks, which make use of clustering algorithms to construct a kernel Gram matrix, are more beneficial than treating each training vector as separate basis functions, as occurs with kernel Ridge regression. We also demonstrate quantitative procedures to determine the very structure of the networks. Finally, we conduct experiments on the log returns of financial time series and show that these online transfer learning models are able to outperform a random walk baseline, whereas the offline learning models struggle to do so.
相關內容
With rising uncertainty in the real world, online Reinforcement Learning (RL) has been receiving increasing attention due to its fast learning capability and improving data efficiency. However, online RL often suffers from complex Value Function Approximation (VFA) and catastrophic interference, creating difficulty for the deep neural network to be applied to an online RL algorithm in a fully online setting. Therefore, a simpler and more adaptive approach is introduced to evaluate value function with the kernel-based model. Sparse representations are superior at handling interference, indicating that competitive sparse representations should be learnable, non-prior, non-truncated and explicit when compared with current sparse representation methods. Moreover, in learning sparse representations, attention mechanisms are utilized to represent the degree of sparsification, and a smooth attentive function is introduced into the kernel-based VFA. In this paper, we propose an Online Attentive Kernel-Based Temporal Difference (OAKTD) algorithm using two-timescale optimization and provide convergence analysis of our proposed algorithm. Experimental evaluations showed that OAKTD outperformed several Online Kernel-based Temporal Difference (OKTD) learning algorithms in addition to the Temporal Difference (TD) learning algorithm with Tile Coding on public Mountain Car, Acrobot, CartPole and Puddle World tasks.
With the help of special neuromorphic hardware, spiking neural networks (SNNs) are expected to realize artificial intelligence with less energy consumption. It provides a promising energy-efficient way for realistic control tasks by combing SNNs and deep reinforcement learning (RL). There are only a few existing SNN-based RL methods at present. Most of them either lack generalization ability or employ Artificial Neural Networks (ANNs) to estimate value function in training. The former needs to tune numerous hyper-parameters for each scenario, and the latter limits the application of different types of RL algorithm and ignores the large energy consumption in training. To develop a robust spike-based RL method, we draw inspiration from non-spiking interneurons found in insects and propose the deep spiking Q-network (DSQN), using the membrane voltage of non-spiking neurons as the representation of Q-value, which can directly learn robust policies from high-dimensional sensory inputs using end-to-end RL. Experiments conducted on 17 Atari games demonstrate the effectiveness of DSQN by outperforming the ANN-based deep Q-network (DQN) in most games. Moreover, the experimental results show superior learning stability and robustness to adversarial attacks of DSQN.
In this monograph, I introduce the basic concepts of Online Learning through a modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order and second-order algorithms for online learning with convex losses, in Euclidean and non-Euclidean settings. All the algorithms are clearly presented as instantiation of Online Mirror Descent or Follow-The-Regularized-Leader and their variants. Particular attention is given to the issue of tuning the parameters of the algorithms and learning in unbounded domains, through adaptive and parameter-free online learning algorithms. Non-convex losses are dealt through convex surrogate losses and through randomization. The bandit setting is also briefly discussed, touching on the problem of adversarial and stochastic multi-armed bandits. These notes do not require prior knowledge of convex analysis and all the required mathematical tools are rigorously explained. Moreover, all the proofs have been carefully chosen to be as simple and as short as possible.
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, very much in the spirit of classical numerical analysis and statistical physics. We demonstrate that conventional machine learning models and algorithms, such as the random feature model, the shallow neural network model and the residual neural network model, can all be recovered as particular discretizations of different continuous formulations. We also present examples of new models, such as the flow-based random feature model, and new algorithms, such as the smoothed particle method and spectral method, that arise naturally from this continuous formulation. We discuss how the issues of generalization error and implicit regularization can be studied under this framework.
Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough formulates the problem as a continuous optimization with a structural constraint that ensures acyclicity (Zheng et al., 2018). The authors apply the approach to the linear structural equation model (SEM) and the least-squares loss function that are statistically well justified but nevertheless limited. Motivated by the widespread success of deep learning that is capable of capturing complex nonlinear mappings, in this work we propose a deep generative model and apply a variant of the structural constraint to learn the DAG. At the heart of the generative model is a variational autoencoder parameterized by a novel graph neural network architecture, which we coin DAG-GNN. In addition to the richer capacity, an advantage of the proposed model is that it naturally handles discrete variables as well as vector-valued ones. We demonstrate that on synthetic data sets, the proposed method learns more accurate graphs for nonlinearly generated samples; and on benchmark data sets with discrete variables, the learned graphs are reasonably close to the global optima. The code is available at \url{//github.com/fishmoon1234/DAG-GNN}.
This paper proposes a model-free Reinforcement Learning (RL) algorithm to synthesise policies for an unknown Markov Decision Process (MDP), such that a linear time property is satisfied. We convert the given property into a Limit Deterministic Buchi Automaton (LDBA), then construct a synchronized MDP between the automaton and the original MDP. According to the resulting LDBA, a reward function is then defined over the state-action pairs of the product MDP. With this reward function, our algorithm synthesises a policy whose traces satisfies the linear time property: as such, the policy synthesis procedure is "constrained" by the given specification. Additionally, we show that the RL procedure sets up an online value iteration method to calculate the maximum probability of satisfying the given property, at any given state of the MDP - a convergence proof for the procedure is provided. Finally, the performance of the algorithm is evaluated via a set of numerical examples. We observe an improvement of one order of magnitude in the number of iterations required for the synthesis compared to existing approaches.
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.
Deep learning (DL) is a high dimensional data reduction technique for constructing high-dimensional predictors in input-output models. DL is a form of machine learning that uses hierarchical layers of latent features. In this article, we review the state-of-the-art of deep learning from a modeling and algorithmic perspective. We provide a list of successful areas of applications in Artificial Intelligence (AI), Image Processing, Robotics and Automation. Deep learning is predictive in its nature rather then inferential and can be viewed as a black-box methodology for high-dimensional function estimation.
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.
Metric learning learns a metric function from training data to calculate the similarity or distance between samples. From the perspective of feature learning, metric learning essentially learns a new feature space by feature transformation (e.g., Mahalanobis distance metric). However, traditional metric learning algorithms are shallow, which just learn one metric space (feature transformation). Can we further learn a better metric space from the learnt metric space? In other words, can we learn metric progressively and nonlinearly like deep learning by just using the existing metric learning algorithms? To this end, we present a hierarchical metric learning scheme and implement an online deep metric learning framework, namely ODML. Specifically, we take one online metric learning algorithm as a metric layer, followed by a nonlinear layer (i.e., ReLU), and then stack these layers modelled after the deep learning. The proposed ODML enjoys some nice properties, indeed can learn metric progressively and performs superiorly on some datasets. Various experiments with different settings have been conducted to verify these properties of the proposed ODML.
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