This work reconsiders the concept of community-based trip sharing proposed by Hasan et al. (2018) that leverages the structure of commuting patterns and urban communities to optimize trip sharing. It aims at quantifying the benefits of autonomous vehicles for community-based trip sharing, compared to a car-pooling platform where vehicles are driven by their owners. In the considered problem, each rider specifies a desired arrival time for her inbound trip (commuting to work) and a departure time for her outbound trip (commuting back home). In addition, her commute time cannot deviate too much from the duration of a direct trip. Prior work motivated by reducing parking pressure and congestion in the city of Ann Arbor, Michigan, showed that a car-pooling platform for community-based trip sharing could reduce the number of vehicles by close to 60%. This paper studies the potential benefits of autonomous vehicles in further reducing the number of vehicles needed to serve all these commuting trips. It proposes a column-generation procedure that generates and assembles mini routes to serve inbound and outbound trips, using a lexicographic objective that first minimizes the required vehicle count and then the total travel distance. The optimization algorithm is evaluated on a large-scale, real-world dataset of commute trips from the city of Ann Arbor, Michigan. The results of the optimization show that it can leverage autonomous vehicles to reduce the daily vehicle usage by 92%, improving upon the results of the original Commute Trip Sharing Problem by 34%, while also reducing daily vehicle miles traveled by approximately 30%. These results demonstrate the significant potential of autonomous vehicles for the shared commuting of a community to a common work destination.

Marketing mix models (MMMs) are statistical models for measuring the effectiveness of various marketing activities such as promotion, media advertisement, etc. In this research, we propose a comprehensive marketing mix model that captures the hierarchical structure and the carryover, shape and scale effects of certain marketing activities, as well as sign restrictions on certain coefficients that are consistent with common business sense. In contrast to commonly adopted approaches in practice, which estimate parameters in a multi-stage process, the proposed approach estimates all the unknown parameters/coefficients simultaneously using a constrained maximum likelihood approach and solved with the Hamiltonian Monte Carlo algorithm. We present results on real datasets to illustrate the use of the proposed solution algorithm.

Markov decision processes (MDPs) are a fundamental mathematical abstraction for sequential decision making under uncertainty and they serve as a basic modeling tool in reinforcement learning (RL) and stochastic control [5, 24, 30]. Two prominent classes of MDPs are average-reward MDPs (AMDPs) and discounted MDPs (DMDPs). Each have been studied extensively; AMDPs are applicable to optimal control, learning automata, and various real-world reinforcement learning settings [17, 3, 22] and DMDPs have a number of nice theoretical properties including reward convergence and operator monotonicity [6]. In this paper we consider the prevalent computational learning problem of finding an approximately optimal policy of an MDP given only restricted access to the model. In particular, we consider the problem of computing an ɛ-optimal policy, i.e. a policy with an additive ɛ error in expected cumulative reward over infinite horizon, under the standard assumption of a generative model [14, 13], which allows one to sample from state-transitions given the current state-action pair. This problem is well-studied and there are multiple known upper and lower bounds on its sample complexity [4, 32, 28, 31]. In this work, we provide a unified framework based on primal-dual stochastic mirror descent (SMD) for learning an ɛ-optimal policies for both AMDPs and DMDPs with a generative model.

The theory and practice of stochastic optimization has focused on stochastic gradient descent (SGD) in recent years, retaining the basic first-order stochastic nature of SGD while aiming to improve it via mechanisms such as averaging, momentum, and variance reduction. Improvement can be measured along various dimensions, however, and it has proved difficult to achieve improvements both in terms of nonasymptotic measures of convergence rate and asymptotic measures of distributional tightness. In this work, we consider first-order stochastic optimization from a general statistical point of view, motivating a specific form of recursive averaging of past stochastic gradients. The resulting algorithm, which we refer to as \emph{Recursive One-Over-T SGD} (ROOT-SGD), matches the state-of-the-art convergence rate among online variance-reduced stochastic approximation methods. Moreover, under slightly stronger distributional assumptions, the rescaled last-iterate of ROOT-SGD converges to a zero-mean Gaussian distribution that achieves near-optimal covariance.

Recommender systems play an important role in modern information and e-commerce applications. While increasing research is dedicated to improving the relevance and diversity of the recommendations, the potential risks of state-of-the-art recommendation models are under-explored, that is, these models could be subject to attacks from malicious third parties, through injecting fake user interactions to achieve their purposes. This paper revisits the adversarially-learned injection attack problem, where the injected fake user `behaviors' are learned locally by the attackers with their own model -- one that is potentially different from the model under attack, but shares similar properties to allow attack transfer. We found that most existing works in literature suffer from two major limitations: (1) they do not solve the optimization problem precisely, making the attack less harmful than it could be, (2) they assume perfect knowledge for the attack, causing the lack of understanding for realistic attack capabilities. We demonstrate that the exact solution for generating fake users as an optimization problem could lead to a much larger impact. Our experiments on a real-world dataset reveal important properties of the attack, including attack transferability and its limitations. These findings can inspire useful defensive methods against this possible existing attack.

We develop a second order primal-dual method for optimization problems in which the objective function is given by the sum of a strongly convex twice differentiable term and a possibly nondifferentiable convex regularizer. After introducing an auxiliary variable, we utilize the proximal operator of the nonsmooth regularizer to transform the associated augmented Lagrangian into a function that is once, but not twice, continuously differentiable. The saddle point of this function corresponds to the solution of the original optimization problem. We employ a generalization of the Hessian to define second order updates on this function and prove global exponential stability of the corresponding differential inclusion. Furthermore, we develop a globally convergent customized algorithm that utilizes the primal-dual augmented Lagrangian as a merit function. We show that the search direction can be computed efficiently and prove quadratic/superlinear asymptotic convergence. We use the $\ell_1$-regularized model predictive control problem and the problem of designing a distributed controller for a spatially-invariant system to demonstrate the merits and the effectiveness of our method.

We propose a novel optimization framework to predict clinical severity from resting state fMRI (rs-fMRI) data. Our model consists of two coupled terms. The first term decomposes the correlation matrices into a sparse set of representative subnetworks that define a network manifold. These subnetworks are modeled as rank-one outer-products which correspond to the elemental patterns of co-activation across the brain; the subnetworks are combined via patient-specific non-negative coefficients. The second term is a linear regression model that uses the patient-specific coefficients to predict a measure of clinical severity. We validate our framework on two separate datasets in a ten fold cross validation setting. The first is a cohort of fifty-eight patients diagnosed with Autism Spectrum Disorder (ASD). The second dataset consists of sixty three patients from a publicly available ASD database. Our method outperforms standard semi-supervised frameworks, which employ conventional graph theoretic and statistical representation learning techniques to relate the rs-fMRI correlations to behavior. In contrast, our joint network optimization framework exploits the structure of the rs-fMRI correlation matrices to simultaneously capture group level effects and patient heterogeneity. Finally, we demonstrate that our proposed framework robustly identifies clinically relevant networks characteristic of ASD.

Adam is the important optimization algorithm to guarantee efficiency and accuracy for training many important tasks such as BERT and ImageNet. However, Adam is generally not compatible with information (gradient) compression technology. Therefore, the communication usually becomes the bottleneck for parallelizing Adam. In this paper, we propose a communication efficient {\bf A}DAM {\bf p}reconditioned {\bf M}omentum SGD algorithm-- named APMSqueeze-- through an error compensated method compressing gradients. The proposed algorithm achieves a similar convergence efficiency to Adam in term of epochs, but significantly reduces the running time per epoch. In terms of end-to-end performance (including the full-precision pre-condition step), APMSqueeze is able to provide {sometimes by up to $2-10\times$ speed-up depending on network bandwidth.} We also conduct theoretical analysis on the convergence and efficiency.

We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification models, which act as a surrogate for the optimization goals and allow us to suggest multiple design points at once in each iteration. The proposed acquisition function is intuitively understandable and can be tuned to the demands of the problems at hand. We also present a novel ellipsoid truncation method to speed up the expected hypervolume calculation in a straightforward way for regression models with a normal probability density. We benchmark our approach with an evolutionary algorithm on multiple test problems.

Tasks in multi-task learning often correlate, conflict, or even compete with each other. As a result, a single solution that is optimal for all tasks rarely exists. Recent papers introduced the concept of Pareto optimality to this field and directly cast multi-task learning as multi-objective optimization problems, but solutions returned by existing methods are typically finite, sparse, and discrete. We present a novel, efficient method that generates locally continuous Pareto sets and Pareto fronts, which opens up the possibility of continuous analysis of Pareto optimal solutions in machine learning problems. We scale up theoretical results in multi-objective optimization to modern machine learning problems by proposing a sample-based sparse linear system, for which standard Hessian-free solvers in machine learning can be applied. We compare our method to the state-of-the-art algorithms and demonstrate its usage of analyzing local Pareto sets on various multi-task classification and regression problems. The experimental results confirm that our algorithm reveals the primary directions in local Pareto sets for trade-off balancing, finds more solutions with different trade-offs efficiently, and scales well to tasks with millions of parameters.