A Unified Perspective on Multiple Shooting In Differential Dynamic Programming

Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. It was originally designed as a single shooting method and thus is sensitive to the initial guess supplied. This work considers the extension of DDP to multiple shooting (MS), improving its robustness to initial guesses. A novel derivation is proposed that accounts for the defect between shooting segments during the DDP backward pass, while still maintaining quadratic convergence locally. The derivation enables unifying multiple previous MS algorithms, and opens the door to many smaller algorithmic improvements. A penalty method is introduced to strategically control the step size, further improving the convergence performance. An adaptive merit function and a more reliable acceptance condition are employed for globalization. The effects of these improvements are benchmarked for trajectory optimization with a quadrotor, an acrobot, and a manipulator. MS-DDP is also demonstrated for use in Model Predictive Control (MPC) for dynamic jumping with a quadruped robot, showing its benefits over a single shooting approach

Mixed Arlequin method for multiscale poromechanics problems

An Arlequin poromechanics model is introduced to simulate the hydro-mechanical coupling effects of fluid-infiltrated porous media across different spatial scales within a concurrent computational framework. A two-field poromechanics problem is first recast as the twofold saddle point of an incremental energy functional. We then introduce Lagrange multipliers and compatibility energy functionals to enforce the weak compatibility of hydro-mechanical responses in the overlapped domain. To examine the numerical stability of this hydro-mechanical Arlequin model, we derive a necessary condition for stability, the twofold inf–sup condition for multi-field problems, and establish a modified inf–sup test formulated in the product space of the solution field. We verify the implementation of the Arlequin poromechanics model through benchmark problems covering the entire range of drainage conditions. Through these numerical examples, we demonstrate the performance, robustness, and numerical stability of the Arlequin poromechanics model

Incorporating spatial characteristics in travel demand models

The goal of this study was to address one of the major weaknesses of the ubiquitous four-step procedure for travel demand modeling: omission of spatial interactions between the variables. While contiguity of the analysis zones is commonly used to define spatial interaction of the variables in spatial analysis, it might not capture the interactions of travel demand variables. In this study, the efficacies of four alternative methods for defining spatial relationships: contiguity, separation, a combination of contiguity and separation, and economic linkages (accessibility), were evaluated. The home-based-work (HBW) spatial models and non-spatial models for trip attraction, and trip production were developed. For the destination choice, the spatial models were developed by using separation and accessibility alternatives for defining spatial relationship. Comparison of the trip attraction models indicated that the model estimated using the separation spatial relationship had the best fit. Furthermore, comparison of the best spatial model and the non spatial model indicated that the spatial model outperforms the non spatial model by increasing the prediction accuracy by 14%. For the trip production model, the results indicated that the spatial variable is unnecessary. For destination choice, the spatial model developed using separation spatial relationship was found to he the best based on statistical tests. To compare the spatial model and the non-spatial model, the forecasted alternative destination shares were used. The results indicated that the difference between the forecasted alternative shares by using spatial and non-spatial models is small when there is a small percentage increase in casino/hotel and retail jobs. In order to use the developed destination choice models for long-term forecasting, additional variables such as housing location should be included. Also, since the design of the analysis zones used in this study may not be optimal, an attempt to design new analysis zones through a careful aggregation process in which homogeneity is carefully controlled, is recommended

Tensor Learning for Recovering Missing Information: Algorithms and Applications on Social Media

Real-time social systems like Facebook, Twitter, and Snapchat have been growing rapidly, producing exabytes of data in different views or aspects. Coupled with more and more GPS-enabled sharing of videos, images, blogs, and tweets that provide valuable information regarding “who”, “where”, “when” and “what”, these real-time human sensor data promise new research opportunities to uncover models of user behavior, mobility, and information sharing. These real-time dynamics in social systems usually come in multiple aspects, which are able to help better understand the social interactions of the underlying network. However, these multi-aspect datasets are often raw and incomplete owing to various unpredictable or unavoidable reasons; for instance, API limitations and data sampling policies can lead to an incomplete (and often biased) perspective on these multi-aspect datasets. This missing data could raise serious concerns such as biased estimations on structural properties of the network and properties of information cascades in social networks. In order to recover missing values or information in social systems, we identify “4S” challenges: extreme sparsity of the observed multi-aspect datasets, adoption of rich side information that is able to describe the similarities of entities, generation of robust models rather than limiting them on specific applications, and scalability of models to handle real large-scale datasets (billions of observed entries). With these challenges in mind, this dissertation aims to develop scalable and interpretable tensor-based frameworks, algorithms and methods for recovering missing information on social media. In particular, this dissertation research makes four unique contributions: _ The first research contribution of this dissertation research is to propose a scalable framework based on low-rank tensor learning in the presence of incomplete information. Concretely, we formally define the problem of recovering the spatio-temporal dynamics of online memes and tackle this problem by proposing a novel tensor-based factorization approach based on the alternative direction method of multipliers (ADMM) with the integration of the latent relationships derived from contextual information among locations, memes, and times. _ The second research contribution of this dissertation research is to evaluate the generalization of the proposed tensor learning framework and extend it to the recommendation problem. In particular, we develop a novel tensor-based approach to solve the personalized expert recommendation by integrating both the latent relationships between homogeneous entities (e.g., users and users, experts and experts) and the relationships between heterogeneous entities (e.g., users and experts, topics and experts) from the geo-spatial, topical, and social contexts. _ The third research contribution of this dissertation research is to extend the proposed tensor learning framework to the user topical profiling problem. Specifically, we propose a tensor-based contextual regularization model embedded into a matrix factorization framework, which leverages the social, textual, and behavioral contexts across users, in order to overcome identified challenges. _ The fourth research contribution of this dissertation research is to scale up the proposed tensor learning framework to be capable of handling real large-scale datasets that are too big to fit in the main memory of a single machine. Particularly, we propose a novel distributed tensor completion algorithm with the trace-based regularization of the auxiliary information based on ADMM under the proposed tensor learning framework, which is designed to scale up to real large-scale tensors (e.g., billions of entries) by efficiently computing auxiliary variables, minimizing intermediate data, and reducing the workload of updating new tensors

Tax-benefit revealed social preferences

This paper inverts the usual logic of applied optimal income taxation. It starts from the observed distribution of income before and after redistribution and corresponding marginal tax rates. Under a set of simplifying assumptions, it is then possible to recover the social welfare function that would make the observed marginal tax rate schedule optimal. In this framework, the issue of the optimality of an existing tax-benefit system is transformed into the issue of the shape of the social welfare function associated with that system and whether it satisfies elementary properties. This method is applied to the French redistribution system with the interesting implication that the French redistribution authority may appear, under some plausible scenario concerning the size of the labor supply behavioral reactions, non Paretian (e.g. giving negative marginal social weights to the richest class of tax payers).Cet article renverse la logique classique de la littérature de la fiscalité optimale. On part de la distribution observée des revenus bruts et des revenus disponibles d'une population et des taux d'imposition marginaux observés calculés par un modèle de microsimulation. On montre alors que, sous certaines conditions simplificatrices, il est possible d'identifier la fonction de bien-être social qui rendrait optimal le schéma des taux marginaux observés sous certaines hypothèses sur les préférences consommation-loisir. Dans ce cadre, la question de l'optimalité d'un système tax-benefit concret peut être analysée en vérifiant si la fonction de bien-être social associée satisfait certaines propriétés. Cette méthode est appliquée au système de redistribution français. On observe que, ou l'autorité fiscale assigne des valeurs peu élevées aux élasticités de l'offre de travail, ou bien elle assigne des poids sociaux négatifs aux agents les plus riches

Fast, Distributed Optimization Strategies for Resource Allocation in Networks

Many challenges in network science and engineering today arise from systems composed of many individual agents interacting over a network. Such problems range from humans interacting with each other in social networks to computers processing and exchanging information over wired or wireless networks. In any application where information is spread out spatially, solutions must address information aggregation in addition to the decision process itself. Intelligently addressing the trade off between information aggregation and decision accuracy is fundamental to finding solutions quickly and accurately. Network optimization challenges such as these have generated a lot of interest in distributed optimization methods. The field of distributed optimization deals with iterative methods which perform calculations using locally available information. Early methods such as subgradient descent suffer very slow convergence rates because the underlying optimization method is a first order method. My work addresses problems in the area of network optimization and control with an emphasis on accelerating the rate of convergence by using a faster underlying optimization method. In the case of convex network flow optimization, the problem is transformed to the dual domain, moving the equality constraints which guarantee flow conservation into the objective. The Newton direction can be computed locally by using a consensus iteration to solve a Poisson equation, but this requires a lot of communication between neighboring nodes. Accelerated Dual Descent (ADD) is an approximate Newton method, which significantly reduces the communication requirement. Defining a stochastic version of the convex network flow problem with edge capacities yields a problem equivalent to the queue stability problem studied in the backpressure literature. Accelerated Backpressure (ABP) is developed to solve the queue stabilization problem. A queue reduction method is introduced by merging ideas from integral control and momentum based optimization

Anomaly Detection Using Robust Principal Component Analysis

In this Major Qualifying Project, we focus on the development of a visualization-enabled anomaly detection system. We examine the 2011 VAST dataset challenge to efficiently generate meaningful features and apply Robust Principal Component Analysis (RPCA) to detect any data points estimated to be anomalous. This is done through an infrastructure that promotes the closing of the loop from feature generation to anomaly detection through RPCA. We enable our user to choose subsets of the data through a web application and learn through visualization systems where problems are within their chosen local data slice. We explore both feature engineering techniques along with optimizing RPCA which ultimately lead to a generalized approach for detecting anomalies within a defined network architecture

The credit-card-services augmented Divisia monetary aggregates

While credit cards provide transactions services, credit cards have never been included in measures of the money supply. The reason is accounting conventions, which do not permit adding liabilities to assets. However, index number theory measures service flows and is based on aggregation theory, not accounting. We derive theory needed to measure the joint services of credit cards and money. We provide and evaluate two such aggregate measures having different objectives. We initially apply to NGDP nowcasting. Both aggregates are being implemented by the Center for Financial Stability, which will provide them to the public monthly, along with Bloomberg Terminals

The credit-card-services augmented Divisia monetary aggregates

While credit cards provide transactions services, credit cards have never been included in measures of the money supply. The reason is accounting conventions, which do not permit adding liabilities to assets. However, index number theory measures service flows and is based on aggregation theory, not accounting. We derive theory needed to measure the joint services of credit cards and money. We provide and evaluate two such aggregate measures having different objectives. We initially apply to NGDP nowcasting. Both aggregates are being implemented by the Center for Financial Stability, which will provide them to the public monthly, along with Bloomberg Terminals