Determinantal point processes (DPPs) are distributions over sets of items that model diversity using kernels. Their applications in machine learning include summary extraction and recommendation systems. Yet, the cost of sampling from a DPP is prohibitive in large-scale applications, which has triggered an effort towards efficient approximate samplers. We build a novel MCMC sampler that combines ideas from combinatorial geometry, linear programming, and Monte Carlo methods to sample from DPPs with a fixed sample cardinality, also called projection DPPs. Our sampler leverages the ability of the hit-and-run MCMC kernel to efficiently move across convex bodies. Previous theoretical results yield a fast mixing time of our chain when targeting a distribution that is close to a projection DPP, but not a DPP in general. Our empirical results demonstrate that this extends to sampling projection DPPs, i.e., our sampler is more sample-efficient than previous approaches which in turn translates to faster convergence when dealing with costly-to-evaluate functions, such as summary extraction in our experiments.

The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the consistency of generic sequential algorithms and formulate the expected minimax rate for their performance. We introduce and analyze a first algorithm called LIPO which assumes the Lipschitz constant to be known. Consistency, minimax rates for LIPO are proved, as well as fast rates under an additional H\"older like condition. An adaptive version of LIPO is also introduced for the more realistic setup where the Lipschitz constant is unknown and has to be estimated along with the optimization. Similar theoretical guarantees are shown to hold for the adaptive LIPO algorithm and a numerical assessment is provided at the end of the paper to illustrate the potential of this strategy with respect to state-of-the-art methods over typical benchmark problems for global optimization.

Due to increased traffic congestion and carbon emissions, Bike Sharing Systems (BSSs) are adopted in various cities for short distance travels, specifically for last mile transportation. The success of a bike sharing system depends on its ability to have bikes available at the "right" base stations at the "right" times. Typically, carrier vehicles are used to perform repositioning of bikes between stations so as to satisfy customer requests. Owing to the uncertainty in customer demand and day-long repositioning, the problem of having bikes available at the right base stations at the right times is a challenging one. In this paper, we propose a multi-stage stochastic formulation, to consider expected future demand over a set of scenarios to find an efficient repositioning strategy for bike sharing systems. Furthermore, we provide a Lagrangian decomposition approach (that decouples the global problem into routing and repositioning slaves and employs a novel DP approach to efficiently solve routing slave) and a greedy online anticipatory heuristic to solve large scale problems effectively and efficiently. Finally, in our experimental results, we demonstrate significant reduction in lost demand provided by our techniques on real world datasets from two bike sharing companies in comparison to existing benchmark approaches.

Bike Sharing System (BSS) is a green mode of transportation that is employed extensively for short distance travels in major cities of the world. Unfortunately, the users behaviour driven by their personal needs can often result in empty or full base stations, thereby resulting in loss of customer demand. To counter this loss in customer demand, BSS operators typically utilize a fleet of carrier vehicles for repositioning the bikes between stations. However, this fuel burning mode of repositioning incurs a significant amount of routing, labor cost and further increases carbon emissions. Therefore, we propose a potentially self-sustaining and environment friendly system of dynamic repositioning, that moves idle bikes during the day with the help of bike trailers. A bike trailer is an add-on to a bike that can help with carrying 3-5 bikes at once. Specifically, we make the following key contributions: (i) We provide an optimization formulation that generates “repositioning” tasks so as to minimize the expected lost demand over past demand scenarios; (ii) Within the budget constraints of the operator, we then design a mechanism to crowdsource the tasks among potential users who intend to execute repositioning tasks; (iii) Finally, we provide extensive results on a wide range of demand scenarios from a real-world data set to demonstrate that our approach is highly competitive to the existing fuel burning mode of repositioning while being green.

Stability of the policy update is a major issue for these methods, rendering them hard to apply for highly nonlinear systems. Recent approaches combine classical Stochastic Optimal Control methods with information-theoretic bounds to control the step-size of the policy update and could even be used to train nonlinear deep control policies. These methods bound the relative entropy between the new and the old policy to ensure a stable policy update. However, despite the bound in policy space, the state distributions of two consecutive policies can still differ significantly, rendering the used local approximate models invalid. To alleviate this issue we propose enforcing a relative entropy constraint not only on the policy update, but also on the update of the state distribution, around which the dynamics and cost are being approximated. We present a derivation of the closed-form policy update and show that our approach outperforms related methods on two nonlinear and highly dynamic simulated systems.

In this work, we investigate a multi-period Home Health Care Scheduling Problem (HHCSP) under stochastic service and travel times. We first model the deterministic problem as an integer linear programming model that incorporates real-world requirements, such as time windows, continuity of care, workload fairness, inter-visit temporal dependencies. We then extend the model to cope with uncertainty in durations, by introducing chance constraints into the formulation. We propose efficient solution approaches, which provide quantifiable near-optimal solutions and further handle the uncertainties by employing a sampling-based strategy. We demonstrate the effectiveness of our proposed approaches on instances synthetically generated by real-world dataset for both deterministic and stochastic scenarios.

For example, we may need to (i) perform inverse learning of the cost parameters of a multi-objective reward based on observed agent behavior; (ii) perform sensitivity analyses of policies to various parameter settings; or (iii) analyze and optimize policy performance as a function of policy parameters. When such problems have mixed discrete and continuous state and/or action spaces, this leads to parameterized hybrid MDPs (PHMDPs) that are often approximately solved via discretization, sampling, and/or local gradient methods (when optimization is involved). In this paper we combine two recent advances that allow for the first exact solution and optimization of PHMDPs. We first show how each of the aforementioned use cases can be formalized as PHMDPs, which can then be solved via an extension of symbolic dynamic programming (SDP) even when the solution is piecewise nonlinear. Secondly, we can leverage recent advances in non-convex solvers that require symbolic forms of the objective function for non-convex global optimization in (i), (ii), and (iii) using SDP to derive symbolic solutions for each PHMDP formalization. We demonstrate the efficacy and scalability of our optimal analytical framework on nonlinear examples of each of the aforementioned use cases.

Energy costs are an increasingly important issue in real-world scheduling, for both economic and environmental reasons. This paper deals with a variant of the well-known job shop scheduling problem, where we consider a bi-objective optimization of both the weighted tardiness and the energy costs. To this end, we design a hybrid metaheuristic that combines a genetic algorithm with a novel local search method and a linear programming approach. We also propose an efficient procedure for improving the energy cost of a given schedule. In the experimental study we analyse our proposal and compare it with the state of the art and also with a constraint programming approach, obtaining competitive results.

The cardinality constraint is an intrinsic way to restrict the solution structure in many domains, for example, sparse learning, feature selection, and compressed sensing. To solve a cardinality constrained problem, the key challenge is to solve the projection onto the cardinality constraint set, which is NP-hard in general when there exist multiple overlapped cardinality constraints. In this paper, we consider the scenario where the overlapped cardinality constraints satisfy a Three-view Cardinality Structure (TVCS), which reflects the natural restriction in many applications, such as identification of gene regulatory networks and task-worker assignment problem. We cast the projection into a linear programming, and show that for TVCS, the vertex solution of this linear programming is the solution for the original projection problem. We further prove that such solution can be found with the complexity proportional to the number of variables and constraints. We finally use synthetic experiments and two interesting applications in bioinformatics and crowdsourcing to validate the proposed TVCS model and method.

We present Deep Generalized Canonical Correlation Analysis (DGCCA) - a method for learning nonlinear transformations of arbitrarily many views of data, such that the resulting transformations are maximally informative of each other. While methods for nonlinear two-view representation learning (Deep CCA, (Andrew et al., 2013)) and linear many-view representation learning (Generalized CCA (Horst, 1961)) exist, DGCCA is the first CCA-style multiview representation learning technique that combines the flexibility of nonlinear (deep) representation learning with the statistical power of incorporating information from many independent sources, or views. We present the DGCCA formulation as well as an efficient stochastic optimization algorithm for solving it. We learn DGCCA representations on two distinct datasets for three downstream tasks: phonetic transcription from acoustic and articulatory measurements, and recommending hashtags and friends on a dataset of Twitter users. We find that DGCCA representations soundly beat existing methods at phonetic transcription and hashtag recommendation, and in general perform no worse than standard linear many-view techniques. Multiview representation learning refers to settings where one has access to many "views" of data, at train time. Views often correspond to different modalities or independent information about examples: a scene represented as a series of audio and image frames, a social media user characterized by the messages they post and who they friend, or a speech utterance and the configuration of the speaker's tongue.