MOPO-LSI is an open-source Multi-Objective Portfolio Optimization Library for Sustainable Investments. This document provides a user guide for MOPO-LSI version 1.0, including problem setup, workflow and the hyper-parameters in configurations.

We study optimality for the safety-constrained Markov decision process which is the underlying framework for safe reinforcement learning. Specifically, we consider a constrained Markov decision process (with finite states and finite actions) where the goal of the decision maker is to reach a target set while avoiding an unsafe set(s) with certain probabilistic guarantees. Therefore the underlying Markov chain for any control policy will be multichain since by definition there exists a target set and an unsafe set. The decision maker also has to be optimal (with respect to a cost function) while navigating to the target set. This gives rise to a multi-objective optimization problem. We highlight the fact that Bellman's principle of optimality may not hold for constrained Markov decision problems with an underlying multichain structure (as shown by the counterexample due to Haviv. We resolve the counterexample by formulating the aforementioned multi-objective optimization problem as a zero-sum game and thereafter construct an asynchronous value iteration scheme for the Lagrangian (similar to Shapley's algorithm). Finally, we consider the reinforcement learning problem for the same and construct a modified $Q$-learning algorithm for learning the Lagrangian from data. We also provide a lower bound on the number of iterations required for learning the Lagrangian and corresponding error bounds.

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components separately, linearizing only the smooth parts. This provides us with new generalizations of the classical Frank-Wolfe method and the Conditional Gradient Sliding algorithm, that cater to a subclass of non-differentiable problems. Our algorithms rely on a stronger version of the linear minimization oracle, which can be efficiently implemented in several practical applications. We provide the basic version of our method with an affine-invariant analysis and prove global convergence rates for both convex and non-convex objectives. Furthermore, in the convex case, we propose an accelerated method with correspondingly improved complexity. Finally, we provide illustrative experiments to support our theoretical results.

Efficient planning of scarce resources in hospitals is a challenging task for which a large variety of Operations Research and Management Science approaches have been developed since the 1950s. While efficient planning of single resources such as operating rooms, beds, or specific types of staff can already lead to enormous efficiency gains, integrated planning of several resources has been shown to hold even greater potential, and a large number of integrated planning approaches have been presented in the literature over the past decades. This paper provides the first literature review that focuses specifically on the Operations Research and Management Science literature related to integrated planning of different resources in hospitals. We collect the relevant literature and analyze it regarding different aspects such as uncertainty modeling and the use of real-life data. Several cross comparisons reveal interesting insights concerning, e.g., relations between the modeling and solution methods used and the practical implementation of the approaches developed. Moreover, we provide a high-level taxonomy for classifying different resource-focused integration approaches and point out gaps in the literature as well as promising directions for future research.

This paper presents a scalable solution with adjustable computation time for the joint problem of scheduling and assigning machines and transporters for missions that must be completed in a fixed order of operations across multiple stages. A battery-operated multi-robot system with a maximum travel range is employed as the transporter between stages and charging them is considered as an operation. Robots are assigned to a single job until its completion. Additionally, The operation completion time is assumed to be dependent on the machine and the type of operation, but independent of the job. This work aims to minimize a weighted multi-objective goal that includes both the required time and energy consumed by the transporters. This problem is a variation of the flexible flow shop with transports, that is proven to be NP-complete. To provide a solution, time is discretized, the solution space is divided temporally, and jobs are clustered into diverse groups. Finally, an integer linear programming solver is applied within a sliding time window to determine assignments and create a schedule that minimizes the objective. The computation time can be reduced depending on the number of jobs selected at each segment, with a trade-off on optimality. The proposed algorithm finds its application in a water sampling project, where water sampling jobs are assigned to robots, sample deliveries at laboratories are scheduled, and the robots are routed to charging stations.

We seek the best traffic allocation scheme for the edge-cloud computing network that satisfies constraints and minimizes the cost based on burstable billing. First, for a fixed network topology, we formulate a family of integer programming problems with random parameters describing the various traffic demands. Then, to overcome the difficulty caused by the discrete feature of the problem, we generalize the Gumbel-softmax reparameterization method to induce an unconstrained continuous optimization problem as a regularized continuation of the discrete problem. Finally, we introduce the Gumbel-softmax sampling network to solve the optimization problems via unsupervised learning. The network structure reflects the edge-cloud computing topology and is trained to minimize the expectation of the cost function for unconstrained continuous optimization problems. The trained network works as an efficient traffic allocation scheme sampler, remarkably outperforming the random strategy in feasibility and cost function value. Besides testing the quality of the output allocation scheme, we examine the generalization property of the network by increasing the time steps and the number of users. We also feed the solution to existing integer optimization solvers as initial conditions and verify the warm-starts can accelerate the short-time iteration process. The framework is general with solid performance, and the decoupled feature of the random neural networks is adequate for practical implementations.

Despite the rich literature on machine learning fairness, relatively little attention has been paid to remediating complex systems, where the final prediction is the combination of multiple classifiers and where multiple groups are present. In this paper, we first show that natural baseline approaches for improving equal opportunity fairness scale linearly with the product of the number of remediated groups and the number of remediated prediction labels, rendering them impractical. We then introduce two simple techniques, called {\em task-overconditioning} and {\em group-interleaving}, to achieve a constant scaling in this multi-group multi-label setup. Our experimental results in academic and real-world environments demonstrate the effectiveness of our proposal at mitigation within this environment.

In this paper, a green-quantized FL framework, which represents data with a finite precision level in both local training and uplink transmission, is proposed. Here, the finite precision level is captured through the use of quantized neural networks (QNNs) that quantize weights and activations in fixed-precision format. In the considered FL model, each device trains its QNN and transmits a quantized training result to the base station. Energy models for the local training and the transmission with quantization are rigorously derived. To minimize the energy consumption and the number of communication rounds simultaneously, a multi-objective optimization problem is formulated with respect to the number of local iterations, the number of selected devices, and the precision levels for both local training and transmission while ensuring convergence under a target accuracy constraint. To solve this problem, the convergence rate of the proposed FL system is analytically derived with respect to the system control variables. Then, the Pareto boundary of the problem is characterized to provide efficient solutions using the normal boundary inspection method. Design insights on balancing the tradeoff between the two objectives while achieving a target accuracy are drawn from using the Nash bargaining solution and analyzing the derived convergence rate. Simulation results show that the proposed FL framework can reduce energy consumption until convergence by up to 70\% compared to a baseline FL algorithm that represents data with full precision without damaging the convergence rate.

Many real-world optimization problems contain unknown parameters that must be predicted prior to solving. To train the predictive machine learning (ML) models involved, the commonly adopted approach focuses on maximizing predictive accuracy. However, this approach does not always lead to the minimization of the downstream task loss. Decision-focused learning (DFL) is a recently proposed paradigm whose goal is to train the ML model by directly minimizing the task loss. However, state-of-the-art DFL methods are limited by the assumptions they make about the structure of the optimization problem (e.g., that the problem is linear) and by the fact that can only predict parameters that appear in the objective function. In this work, we address these limitations by instead predicting \textit{distributions} over parameters and adopting score function gradient estimation (SFGE) to compute decision-focused updates to the predictive model, thereby widening the applicability of DFL. Our experiments show that by using SFGE we can: (1) deal with predictions that occur both in the objective function and in the constraints; and (2) effectively tackle two-stage stochastic optimization problems.

Bayesian Optimization (BO) is a class of black-box, surrogate-based heuristics that can efficiently optimize problems that are expensive to evaluate, and hence admit only small evaluation budgets. BO is particularly popular for solving numerical optimization problems in industry, where the evaluation of objective functions often relies on time-consuming simulations or physical experiments. However, many industrial problems depend on a large number of parameters. This poses a challenge for BO algorithms, whose performance is often reported to suffer when the dimension grows beyond 15 variables. Although many new algorithms have been proposed to address this problem, it is not well understood which one is the best for which optimization scenario. In this work, we compare five state-of-the-art high-dimensional BO algorithms, with vanilla BO and CMA-ES on the 24 BBOB functions of the COCO environment at increasing dimensionality, ranging from 10 to 60 variables. Our results confirm the superiority of BO over CMA-ES for limited evaluation budgets and suggest that the most promising approach to improve BO is the use of trust regions. However, we also observe significant performance differences for different function landscapes and budget exploitation phases, indicating improvement potential, e.g., through hybridization of algorithmic components.