Learning Merton's Strategies in an Incomplete Market: Recursive Entropy Regularization and Biased Gaussian Exploration

We study Merton's expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. We take the reinforcement learning (RL) approach to learn optimal portfolio policies directly by exploring the unknown market, without attempting to estimate the model parameters. Based on the entropy-regularization framework for general continuous-time RL formulated in Wang et al. (2020), we propose a recursive weighting scheme on exploration that endogenously discounts the current exploration reward by the past accumulative amount of exploration. Such a recursive regularization restores the optimality of Gaussian exploration. However, contrary to the existing results, the optimal Gaussian policy turns out to be biased in general, due to the interwinding needs for hedging and for exploration. We present an asymptotic analysis of the resulting errors to show how the level of exploration affects the learned policies. Furthermore, we establish a policy improvement theorem and design several RL algorithms to learn Merton's optimal strategies. At last, we carry out both simulation and empirical studies with a stochastic volatility environment to demonstrate the efficiency and robustness of the RL algorithms in comparison to the conventional plug-in method.

Multi-Domain Walking with Reduced-Order Models of Locomotion

Drawing inspiration from human multi-domain walking, this work presents a novel reduced-order model based framework for realizing multi-domain robotic walking. At the core of our approach is the viewpoint that human walking can be represented by a hybrid dynamical system, with continuous phases that are fully-actuated, under-actuated, and over-actuated and discrete changes in actuation type occurring with changes in contact. Leveraging this perspective, we synthesize a multi-domain linear inverted pendulum (MLIP) model of locomotion. Utilizing the step-to-step dynamics of the MLIP model, we successfully demonstrate multi-domain walking behaviors on the bipedal robot Cassie -- a high degree of freedom 3D bipedal robot. Thus, we show the ability to bridge the gap between multi-domain reduced order models and full-order multi-contact locomotion. Additionally, our results showcase the ability of the proposed method to achieve versatile speed-tracking performance and robust push recovery behaviors.

A Fast Fourier Convolutional Deep Neural Network For Accurate and Explainable Discrimination Of Wheat Yellow Rust And Nitrogen Deficiency From Sentinel-2 Time-Series Data

Accurate and timely detection of plant stress is essential for yield protection, allowing better-targeted intervention strategies. Recent advances in remote sensing and deep learning have shown great potential for rapid non-invasive detection of plant stress in a fully automated and reproducible manner. However, the existing models always face several challenges: 1) computational inefficiency and the misclassifications between the different stresses with similar symptoms; and 2) the poor interpretability of the host-stress interaction. In this work, we propose a novel fast Fourier Convolutional Neural Network (FFDNN) for accurate and explainable detection of two plant stresses with similar symptoms (i.e. Wheat Yellow Rust And Nitrogen Deficiency). Specifically, unlike the existing CNN models, the main components of the proposed model include: 1) a fast Fourier convolutional block, a newly fast Fourier transformation kernel as the basic perception unit, to substitute the traditional convolutional kernel to capture both local and global responses to plant stress in various time-scale and improve computing efficiency with reduced learning parameters in Fourier domain; 2) Capsule Feature Encoder to encapsulate the extracted features into a series of vector features to represent part-to-whole relationship with the hierarchical structure of the host-stress interactions of the specific stress. In addition, in order to alleviate over-fitting, a photochemical vegetation indices-based filter is placed as pre-processing operator to remove the non-photochemical noises from the input Sentinel-2 time series.

Meta contrastive label correction for financial time series

Financial applications such as stock price forecasting, usually face an issue that under the predefined labeling rules, it is hard to accurately predict the directions of stock movement. This is because traditional ways of labeling, taking Triple Barrier Method, for example, usually gives us inaccurate or even corrupted labels. To address this issue, we focus on two main goals. One is that our proposed method can automatically generate correct labels for noisy time series patterns, while at the same time, the method is capable of boosting classification performance on this new labeled dataset. Based on the aforementioned goals, our approach has the following three novelties: First, we fuse a new contrastive learning algorithm into the meta-learning framework to estimate correct labels iteratively when updating the classification model inside. Moreover, we utilize images generated from time series data through Gramian angular field and representative learning. Most important of all, we adopt multi-task learning to forecast temporal-variant labels. In the experiments, we work on 6% clean data and the rest unlabeled data. It is shown that our method is competitive and outperforms a lot compared with benchmarks.

Data-driven Step-to-step Dynamics based Adaptive Control for Robust and Versatile Underactuated Bipedal Robotic Walking

This paper presents a framework for synthesizing bipedal robotic walking that adapts to unknown environment and dynamics error via a data-driven step-to-step (S2S) dynamics model. We begin by synthesizing an S2S controller that stabilizes the walking using foot placement through nominal S2S dynamics from the hybrid linear inverted pendulum (H-LIP) model. Next, a data-driven representation of the S2S dynamics of the robot is learned online via classical adaptive control methods. The desired discrete foot placement on the robot is thereby realized by proper continuous output synthesis capturing the data-driven S2S controller coupled with a low-level tracking controller. The proposed approach is implemented in simulation on an underactuated 3D bipedal robot, Cassie, and improved reference velocity tracking is demonstrated. The proposed approach is also able to realize walking behavior that is robustly adaptive to unknown loads, inaccurate robot models, external disturbance forces, biased velocity estimation, and unknown slopes.

Primitive Graph Learning for Unified Vector Mapping

Large-scale vector mapping is important for transportation, city planning, and survey and census. We propose GraphMapper, a unified framework for end-to-end vector map extraction from satellite images. Our key idea is a novel unified representation of shapes of different topologies named "primitive graph", which is a set of shape primitives and their pairwise relationship matrix. Then, we convert vector shape prediction, regularization, and topology reconstruction into a unique primitive graph learning problem. Specifically, GraphMapper is a generic primitive graph learning network based on global shape context modelling through multi-head-attention. An embedding space sorting method is developed for accurate primitive relationship modelling. We empirically demonstrate the effectiveness of GraphMapper on two challenging mapping tasks, building footprint regularization and road network topology reconstruction. Our model outperforms state-of-the-art methods by 8-10% in both tasks on public benchmarks. All code will be publicly available.

Auto-SDE: Learning effective reduced dynamics from data-driven stochastic dynamical systems

Multiscale stochastic dynamical systems have been widely adopted to scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to investigating the effective reduced dynamics for a slow-fast stochastic dynamical system. Given observation data on a short-term period satisfying some unknown slow-fast stochastic system, we propose a novel algorithm including a neural network called Auto-SDE to learn invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also proved to be accurate, stable and effective through numerical experiments under various evaluation metrics.

Episodic Learning for Safe Bipedal Locomotion with Control Barrier Functions and Projection-to-State Safety

This paper combines episodic learning and control barrier functions in the setting of bipedal locomotion. The safety guarantees that control barrier functions provide are only valid with perfect model knowledge; however, this assumption cannot be met on hardware platforms. To address this, we utilize the notion of projection-to-state safety paired with a machine learning framework in an attempt to learn the model uncertainty as it affects the barrier functions. The proposed approach is demonstrated both in simulation and on hardware for the AMBER-3M bipedal robot in the context of the stepping-stone problem, which requires precise foot placement while walking dynamically.

Bipedal Walking on Constrained Footholds: Momentum Regulation via Vertical COM Control

This paper presents an online walking gait synthesis and a feedback control methodology to enable stable walking on constrained footholds for bipedal robots. For this challenging task, the foot placement and center of pressure cannot be changed, which hinders the application of state-of-art stepping controllers or zero-moment-point (ZMP) based approaches for walking generation. As a result, this paper takes a different approach to modulate the change of the angular momentum about the foot-ground contact pivot at the discrete impact with vertical center of mass (COM) velocity. We utilize the underactuated Linear Inverted Pendulum (LIP) model for approximating the underactuated walking dynamics to provide the desired post-impact angular momentum for each step. Outputs are constructed via online optimization combined with closed-form polynomials and then tracked via a quadratic program based controller. This method is implemented online on two robot models, AMBER and Cassie, for which stable walking behaviors with constrained footholds are realized on flat ground, stairs, and randomly located stepping stones.

Learning Controller Gains on Bipedal Walking Robots via User Preferences

Experimental demonstration of complex robotic behaviors relies heavily on finding the correct controller gains. This painstaking process is often completed by a domain expert, requiring deep knowledge of the relationship between parameter values and the resulting behavior of the system. Even when such knowledge is possessed, it can take significant effort to navigate the nonintuitive landscape of possible parameter combinations. In this work, we explore the extent to which preference-based learning can be used to optimize controller gains online by repeatedly querying the user for their preferences. This general methodology is applied to two variants of control Lyapunov function based nonlinear controllers framed as quadratic programs, which have nice theoretic properties but are challenging to realize in practice. These controllers are successfully demonstrated both on the planar underactuated biped, AMBER, and on the 3D underactuated biped, Cassie. We experimentally evaluate the performance of the learned controllers and show that the proposed method is repeatably able to learn gains that yield stable and robust locomotion.