The recent promotion of sustainable urban planning combined with a growing need for public interventions to improve well-being and health have led to an increased collective interest for green spaces in and around cities. In particular, parks have proven a wide range of benefits in urban areas. This also means inequities in park accessibility may contribute to health inequities. In this work, we showcase the application of classic tools from Operations Research to assist decision-makers to improve parks' accessibility, distribution and design. Given the context of public decision-making, we are particularly concerned with equity and environmental justice, and are focused on an advanced assessment of users' behavior through a spatial interaction model. We present a two-stage fair facility location and design model, which serves as a template model to assist public decision-makers at the city-level for the planning of urban green spaces. The first-stage of the optimization model is about the optimal city-budget allocation to neighborhoods based on a data exposing inequality attributes. The second-stage seeks the optimal location and design of parks for each neighborhood, and the objective consists of maximizing the total expected probability of individuals visiting parks. We show how to reformulate the latter as a mixed-integer linear program. We further introduce a clustering method to reduce the size of the problem and determine a close to optimal solution within reasonable time. The model is tested using the case study of the city of Montreal and comparative results are discussed in detail to justify the performance of the model.

Combining machine learning and constrained optimization, Predict+Optimize tackles optimization problems containing parameters that are unknown at the time of solving. Prior works focus on cases with unknowns only in the objectives. A new framework was recently proposed to cater for unknowns also in constraints by introducing a loss function, called Post-hoc Regret, that takes into account the cost of correcting an unsatisfiable prediction. Since Post-hoc Regret is non-differentiable, the previous work computes only its approximation. While the notion of Post-hoc Regret is general, its specific implementation is applicable to only packing and covering linear programming problems. In this paper, we first show how to compute Post-hoc Regret exactly for any optimization problem solvable by a recursive algorithm satisfying simple conditions. Experimentation demonstrates substantial improvement in the quality of solutions as compared to the earlier approximation approach. Furthermore, we show experimentally the empirical behavior of different combinations of correction and penalty functions used in the Post-hoc Regret of the same benchmarks. Results provide insights for defining the appropriate Post-hoc Regret in different application scenarios.

In this work, we present the Bregman Alternating Projected Gradient (BAPG) method, a single-loop algorithm that offers an approximate solution to the Gromov-Wasserstein (GW) distance. We introduce a novel relaxation technique that balances accuracy and computational efficiency, albeit with some compromises in the feasibility of the coupling map. Our analysis is based on the observation that the GW problem satisfies the Luo-Tseng error bound condition, which relates to estimating the distance of a point to the critical point set of the GW problem based on the optimality residual. This observation allows us to provide an approximation bound for the distance between the fixed-point set of BAPG and the critical point set of GW. Moreover, under a mild technical assumption, we can show that BAPG converges to its fixed point set. The effectiveness of BAPG has been validated through comprehensive numerical experiments in graph alignment and partition tasks, where it outperforms existing methods in terms of both solution quality and wall-clock time. The GW distance provides a flexible way to compare and couple probability distributions supported on different metric spaces. Although the GW distance has gained a lot of attention in the machine learning and data science communities, most existing algorithms for computing the GW distance are double-loop algorithms that require another iterative algorithm as a subroutine, making them not ideal for practical use. Recently, an entropy-regularized iterative sinkhorn projection algorithm called eBPG was proposed by Solomon et al. (2016), which has been proven to converge under the Kurdyka-Łojasiewicz framework.

-- We consider the open federated learning (FL) systems, where clients may join and/or leave the system during the FL process. Given the variability of the number of present clients, convergence to a fixed model cannot be guaranteed in open systems. Instead, we resort to a new performance metric that we term the stability of open FL systems, which quantifies the magnitude of the learned model in open systems. Under the assumption that local clients' functions are strongly convex and smooth, we theoretically quantify the radius of stability for two FL algorithms, namely local SGD and local Adam. We observe that this radius relies on several key parameters, including the function condition number as well as the variance of the stochastic gradient. Our theoretical results are further verified by numerical simulations on synthetic data. Federated learning (FL) [1] is a machine learning setup where a group of clients work cooperatively to learn a statistical model. The learning process is coordinated by a central server which facilitates the exchange of model updates. FL algorithms enjoy the benefits of model sharing among clients while preserving data privacy, and they also reduce the number of communications without making too much sacrifice on the performance [2]. In a canonical FL algorithm, the central server broadcasts the initial model to all clients, and then, each client performs several steps of local updates before sending the model to the server.

Robust Markov decision processes (MDPs) aim to handle changing or partially known system dynamics. To solve them, one typically resorts to robust optimization methods. However, this significantly increases computational complexity and limits scalability in both learning and planning. On the other hand, regularized MDPs show more stability in policy learning without impairing time complexity. Yet, they generally do not encompass uncertainty in the model dynamics. In this work, we aim to learn robust MDPs using regularization. We first show that regularized MDPs are a particular instance of robust MDPs with uncertain reward. We thus establish that policy iteration on reward-robust MDPs can have the same time complexity as on regularized MDPs. We further extend this relationship to MDPs with uncertain transitions: this leads to a regularization term with an additional dependence on the value function. We then generalize regularized MDPs to twice regularized MDPs ($\text{R}^2$ MDPs), i.e., MDPs with $\textit{both}$ value and policy regularization. The corresponding Bellman operators enable us to derive planning and learning schemes with convergence and generalization guarantees, thus reducing robustness to regularization. We numerically show this two-fold advantage on tabular and physical domains, highlighting the fact that $\text{R}^2$ preserves its efficacy in continuous environments.

Interest in this research area is also driven by the importance of ensuring an efficient and satisfying client service policy after a product delivery, which substantially contributes to the maintain of the market share [15]. The workforce scheduling problem focuses on the elaboration of models and solution methods for planning in-field personnel activities, including their mobilization between different locations. Moreover, the problem consists in the elaboration of workload allocation and routing of technician crews, as well as the scheduling of their operations at the level of task locations, which include industrial facilities, patient homes, telecommunication infrastructure, etc. In addition, many objectives and challenges may be considered, such as increasing productivity, reducing transportation costs, increasing the number of fulfilled tasks, reducing outsourcing costs, reducing overtime, balancing technician workloads, etc. Furthermore, to have a reliable and satisfactory organization of the workforce in the field, several requirements and constraints have to be met: in addition to the vehicle routing problem classical constraints (capacity and time windows) and work regulations (breaks and workload). Other aspects could be taken into consideration such as skill types and competency levels required by each task, precedence constraints between several tasks for the same customer, priorities, limited crews of technicians, and sometimes the use of specific tools and spare parts. In this paper, we address a variant of the technician routing and scheduling problem (TRSP) presented by Pillac et al.[24]. Given a crew of technicians and a set of tasks to fulfill at their respective locations, the goal is to assign subsets of tasks to individual technicians and construct the routes for each technician in such a way that the total duration of the routes is minimized. Several types of constraints must be respected by each route.

A crucial technology in fully autonomous aerial swarms is collaborative SLAM (CSLAM), which enables the estimation of relative pose and global consistent trajectories of aerial robots. However, existing CSLAM systems do not prioritize relative localization accuracy, critical for close collaboration among UAVs. This paper presents $D^2$SLAM, a novel decentralized and distributed ($D^2$) CSLAM system that covers two scenarios: near-field estimation for high accuracy state estimation in close range and far-field estimation for consistent global trajectory estimation. $D^2$SLAM has a versatile and powerful front-end that can use stereo cameras or omnidirectional cameras as input, the former being easy to obtain and the latter being an excellent solution to the Field of View problem in relative localization. Our experiments verify $D^2$SLAM achieves high accuracy in ego-motion estimation, relative localization, and global consistency. Moreover, distributed optimization algorithms are adopted to achieve the $D^2$ objective to allow the scale-up of the swarm and ensure robustness against network delays. We argue $D^2$SLAM can be applied in a wide range of real-world applications.

The paper proposes two control methods for performing a backflip maneuver with miniature quadcopters. First, an existing feedforward control approach is improved by finding the optimal sequence of motion primitives via Bayesian optimization, using a surrogate Gaussian Process model. To evaluate the cost function, the flip maneuver is performed repeatedly in a simulation environment. The second method is based on closed-loop control and it consists of two main steps: first a novel robust, adaptive controller is designed to provide reliable reference tracking even in case of model uncertainties. The controller is constructed by augmenting the nominal model of the drone with a Gaussian Process that is trained by using measurement data. Second, an efficient trajectory planning algorithm is proposed, which designs feasible trajectories for the flip maneuver by using only quadratic programming. The two approaches are analyzed in simulations and in real experiments using Bitcraze Crazyflie 2.1 quadcopters.

How should we intervene on an unknown structural equation model to maximize a downstream variable of interest? This setting, also known as causal Bayesian optimization (CBO), has important applications in medicine, ecology, and manufacturing. Standard Bayesian optimization algorithms fail to effectively leverage the underlying causal structure. Existing CBO approaches assume noiseless measurements and do not come with guarantees. We propose the model-based causal Bayesian optimization algorithm (MCBO) that learns a full system model instead of only modeling intervention-reward pairs. MCBO propagates epistemic uncertainty about the causal mechanisms through the graph and trades off exploration and exploitation via the optimism principle. We bound its cumulative regret, and obtain the first non-asymptotic bounds for CBO. Unlike in standard Bayesian optimization, our acquisition function cannot be evaluated in closed form, so we show how the reparameterization trick can be used to apply gradient-based optimizers. The resulting practical implementation of MCBO compares favorably with state-of-the-art approaches empirically.

To enable emerging applications such as deep machine learning and graph processing, 3D network-on-chip (NoC) enabled heterogeneous manycore platforms that can integrate many processing elements (PEs) are needed. However, designing such complex systems with multiple objectives can be challenging due to the huge associated design space and long evaluation times. To optimize such systems, we propose a new multi-objective design space exploration framework called MOELA that combines the benefits of evolutionary-based search with a learning-based local search to quickly determine PE and communication link placement to optimize multiple objectives (e.g., latency, throughput, and energy) in 3D NoC enabled heterogeneous manycore systems. Compared to state-of-the-art approaches, MOELA increases the speed of finding solutions by up to 128x, leads to a better Pareto Hypervolume (PHV) by up to 12.14x and improves energy-delay-product (EDP) by up to 7.7% in a 5-objective scenario.