A Constructive Approach to Function Realization by Neural Stochastic Differential Equations

The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given architecture. This can lead to high-complexity controls which are impractical in applications. In this paper, we take the opposite, constructive approach: We impose various structural restrictions on system dynamics and consequently characterize the class of functions that can be realized by such a system. The systems are implemented as a cascade interconnection of a neural stochastic differential equation (Neural SDE), a deterministic dynamical system, and a readout map. Both probabilistic and geometric (Lie-theoretic) methods are used to characterize the classes of functions realized by such systems.

Nonlinear controllability and function representation by neural stochastic differential equations

There has been a great deal of recent interest in learning and approximation of functions that can be expressed as expectations of a given nonlinearity with respect to its random internal parameters. Examples of such representations include "infinitely wide" neural nets, where the underlying nonlinearity is given by the activation function of an individual neuron. In this paper, we bring this perspective to function representation by neural stochastic differential equations (SDEs). A neural SDE is an It\^o diffusion process whose drift and diffusion matrix are elements of some parametric families. We show that the ability of a neural SDE to realize nonlinear functions of its initial condition can be related to the problem of optimally steering a certain deterministic dynamical system between two given points in finite time. This auxiliary system is obtained by formally replacing the Brownian motion in the SDE by a deterministic control input. We derive upper and lower bounds on the minimum control effort needed to accomplish this steering; these bounds may be of independent interest in the context of motion planning and deterministic optimal control.

Design, Benchmarking and Explainability Analysis of a Game-Theoretic Framework towards Energy Efficiency in Smart Infrastructure

In this paper, we propose a gamification approach as a novel framework for smart building infrastructure with the goal of motivating human occupants to reconsider personal energy usage and to have positive effects on their environment. Human interaction in the context of cyber-physical systems is a core component and consideration in the implementation of any smart building technology. Research has shown that the adoption of human-centric building services and amenities leads to improvements in the operational efficiency of these cyber-physical systems directed towards controlling building energy usage. We introduce a strategy in form of a game-theoretic framework that incorporates humans-in-the-loop modeling by creating an interface to allow building managers to interact with occupants and potentially incentivize energy efficient behavior. Prior works on game theoretic analysis typically rely on the assumption that the utility function of each individual agent is known a priori. Instead, we propose novel utility learning framework for benchmarking that employs robust estimations of occupant actions towards energy efficiency. To improve forecasting performance, we extend the utility learning scheme by leveraging deep bi-directional recurrent neural networks. Using the proposed methods on data gathered from occupant actions for resources such as room lighting, we forecast patterns of energy resource usage to demonstrate the prediction performance of the methods. The results of our study show that we can achieve a highly accurate representation of the ground truth for occupant energy resource usage. We also demonstrate the explainable nature on human decision making towards energy usage inherent in the dataset using graphical lasso and granger causality algorithms. Finally, we open source the de-identified, high-dimensional data pertaining to the energy game-theoretic framework.

A Novel Graphical Lasso based approach towards Segmentation Analysis in Energy Game-Theoretic Frameworks

Energy game-theoretic frameworks have emerged to be a successful strategy to encourage energy efficient behavior in large scale by leveraging human-in-the-loop strategy. A number of such frameworks have been introduced over the years which formulate the energy saving process as a competitive game with appropriate incentives for energy efficient players. However, prior works involve an incentive design mechanism which is dependent on knowledge of utility functions for all the players in the game, which is hard to compute especially when the number of players is high, common in energy game-theoretic frameworks. Our research proposes that the utilities of players in such a framework can be grouped together to a relatively small number of clusters, and the clusters can then be targeted with tailored incentives. The key to above segmentation analysis is to learn the features leading to human decision making towards energy usage in competitive environments. We propose a novel graphical lasso based approach to perform such segmentation, by studying the feature correlations in a real-world energy social game dataset. To further improve the explainability of the model, we perform causality study using grangers causality. Proposed segmentation analysis results in characteristic clusters demonstrating different energy usage behaviors. We also present avenues to implement intelligent incentive design using proposed segmentation method.

Segmentation Analysis in Human Centric Cyber-Physical Systems using Graphical Lasso

A generalized gamification framework is introduced as a form of smart infrastructure with potential to improve sustainability and energy efficiency by leveraging humans-in-the-loop strategy. The proposed framework enables a Human-Centric Cyber-Physical System using an interface to allow building managers to interact with occupants. The interface is designed for occupant engagement-integration supporting learning of their preferences over resources in addition to understanding how preferences change as a function of external stimuli such as physical control, time or incentives. Towards intelligent and autonomous incentive design, a noble statistical learning algorithm performing occupants energy usage behavior segmentation is proposed. We apply the proposed algorithm, Graphical Lasso, on energy resource usage data by the occupants to obtain feature correlations--dependencies. Segmentation analysis results in characteristic clusters demonstrating different energy usage behaviors. The features--factors characterizing human decision-making are made explainable.

A Deep Learning and Gamification Approach to Energy Conservation at Nanyang Technological University

The implementation of smart building technology in the form of smart infrastructure applications has great potential to improve sustainability and energy efficiency by leveraging humans-in-the-loop strategy. However, human preference in regard to living conditions is usually unknown and heterogeneous in its manifestation as control inputs to a building. Furthermore, the occupants of a building typically lack the independent motivation necessary to contribute to and play a key role in the control of smart building infrastructure. Moreover, true human actions and their integration with sensing/actuation platforms remains unknown to the decision maker tasked with improving operational efficiency. By modeling user interaction as a sequential discrete game between non-cooperative players, we introduce a gamification approach for supporting user engagement and integration in a human-centric cyber-physical system. We propose the design and implementation of a large-scale network game with the goal of improving the energy efficiency of a building through the utilization of cutting-edge Internet of Things (IoT) sensors and cyber-physical systems sensing/actuation platforms. A benchmark utility learning framework that employs robust estimations for classical discrete choice models provided for the derived high dimensional imbalanced data. To improve forecasting performance, we extend the benchmark utility learning scheme by leveraging Deep Learning end-to-end training with Deep bi-directional Recurrent Neural Networks. We apply the proposed methods to high dimensional data from a social game experiment designed to encourage energy efficient behavior among smart building occupants in Nanyang Technological University (NTU) residential housing. Using occupant-retrieved actions for resources such as lighting and A/C, we simulate the game defined by the estimated utility functions.