Abstract
This paper proposes a dynamic model of the limit order book to derive conditions to test if a trading algorithm will learn to spoof the order book. The testable conditions are simple and easy to implement because they depend only on the parameters of the model. We test the conditions with order book data from Nasdaq and show that market conditions are conducive for an algorithm to learn to spoof the order book.
Abstract
Despite the success of data driven approaches in transfer learning, the theoretical understanding of transfer learning from statistics or information theory is somewhat behind. A key challenge when conducting theoretical analyses for transfer learning problems is that the statistical correlation between source and target tasks are often unknown, and hence traditional mathematical tools in statistics and estimation theory are difficult to be applied. In this talk, we address this issue by formulating the transfer learning as an optimization problem for the testing loss over certain similarity constraints of the source and target tasks. Specifically, we first show that when the similarity between both tasks measured by a certain distance metric is given, the optimal linear transfer model can be computed. The optimal coefficient in such a model reveals how the sample complexity, model complexity, and the task similarity affect the knowledge transferring in transfer learning. Moreover, when the task similarity cannot be well estimated due to insufficient samples, we propose a minimax formulation, which only requires the similarity being bounded, and the resulting distribution estimator is robust against sample insufficiency. We show an approximately optimal distribution estimator for the minimax problem from the bounded normal mean problem, and develop similar knowledge transferring insights as in the linear transferring model. Finally, some experimental results validate the algorithms led by our theoretical approach.
Abstract
We develop and analyze a principled approach to kernel ridge regression under covariate shift. The goal is to learn a regression function with small mean squared error over a target distribution, based on unlabeled data from there and labeled data that may have a different feature distribution. We propose to split the labeled data into two subsets and conduct kernel ridge regression on them separately to obtain a collection of candidate models and an imputation model. We use the latter to fill the missing labels and then select the best candidate model accordingly. Our non-asymptotic excess risk bounds show that in quite general scenarios, our estimator adapts to the structure of the target distribution and the covariate shift. It achieves the minimax optimal error rate up to a logarithmic factor. The use of pseudo-labels in model selection does not have major negative impacts.
Abstract
TBD
Abstract
We propose and analyze two policy learning methods: regularized policy gradient (RPG) and iterative policy optimization (IPO), for a class of discounted linear-quadratic regulator (LQR) problems over an infinite time horizon with entropy regularization. Assuming access to the exact policy evaluation, both proposed approaches are shown to converge linearly in finding optimal policies of the regularized LQR. Moreover, the IPO method can achieve a super-linear convergence rate once it enters a local region around the optimal policy. Finally, when the optimal policy from a well-known environment in an RL problem is appropriately transferred as the initial policy to an RL problem with an unknown environment, the IPO method is shown to enable a super-linear convergence rate if the latter is sufficiently close to the former.
Abstract
Transfer learning is an emerging and popular paradigm for utilizing existing knowledge from previous learning tasks to improve the performance of new ones. In this paper, we propose a novel concept of transfer risk and and analyze its properties to evaluate transferability of transfer learning. We apply transfer learning techniques and this concept of transfer risk to stock return prediction and portfolio optimization problems. Numerical results demonstrate a strong correlation between transfer risk and overall transfer learning performance, where transfer risk provides a computationally efficient way to identify appropriate source tasks in transfer learning, including cross-continent, cross-sector, and cross-frequency transfer for portfolio optimization.