This paper studies the problem of risk-averse receding horizon motion planning for agents with uncertain dynamics, in the presence of stochastic, dynamic obstacles. We propose a model predictive control (MPC) scheme that formulates the obstacle avoidance constraint using coherent risk measures. To handle disturbances, or process noise, in the state dynamics, the state constraints are tightened in a risk-aware manner to provide a disturbance feedback policy. We also propose a waypoint following algorithm that uses the proposed MPC scheme for discrete distributions and prove its risk-sensitive recursive feasibility while guaranteeing finite-time task completion. We further investigate some commonly used coherent risk metrics, namely, conditional value-at-risk (CVaR), entropic value-at-risk (EVaR), and g-entropic risk measures, and propose a tractable incorporation within MPC. We illustrate our framework via simulation studies.

Uncertainty is prevalent in engineering design, statistical learning, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative optimization models expressed using measures of risk and related concepts. We survey the rapid development of risk measures over the last quarter century. From their beginning in financial engineering, we recount the spread to nearly all areas of engineering and applied mathematics. Solidly rooted in convex analysis, risk measures furnish a general framework for handling uncertainty with significant computational and theoretical advantages. We describe the key facts, list several concrete algorithms, and provide an extensive list of references for further reading. The survey recalls connections with utility theory and distributionally robust optimization, points to emerging applications areas such as fair machine learning, and defines measures of reliability.

Orbital-free density functional theory (OFDFT) is a quantum chemistry formulation that has a lower cost scaling than the prevailing Kohn-Sham DFT, which is increasingly desired for contemporary molecular research. However, its accuracy is limited by the kinetic energy density functional, which is notoriously hard to approximate for non-periodic molecular systems. In this work, we propose M-OFDFT, an OFDFT approach capable of solving molecular systems using a deep-learning functional model. We build the essential nonlocality into the model, which is made affordable by the concise density representation as expansion coefficients under an atomic basis. With techniques to address unconventional learning challenges therein, M-OFDFT achieves a comparable accuracy with Kohn-Sham DFT on a wide range of molecules untouched by OFDFT before. More attractively, M-OFDFT extrapolates well to molecules much larger than those in training, which unleashes the appealing scaling for studying large molecules including proteins, representing an advancement of the accuracy-efficiency trade-off frontier in quantum chemistry.

Safety in dynamic systems with prevalent uncertainties is crucial. Current robust safe controllers, designed primarily for uni-modal uncertainties, may be either overly conservative or unsafe when handling multi-modal uncertainties. To address the problem, we introduce a novel framework for robust safe control, tailored to accommodate multi-modal Gaussian dynamics uncertainties and control limits. We first present an innovative method for deriving the least conservative robust safe control under additive multi-modal uncertainties. Next, we propose a strategy to identify a locally least-conservative robust safe control under multiplicative uncertainties. Following these, we introduce a unique safety index synthesis method. This provides the foundation for a robust safe controller that ensures a high probability of realizability under control limits and multi-modal uncertainties. Experiments on a simulated Segway validate our approach, showing consistent realizability and less conservatism than controllers designed using uni-modal uncertainty methods. The framework offers significant potential for enhancing safety and performance in robotic applications.

We study how to safely control nonlinear control-affine systems that are corrupted with bounded non-stochastic noise, i.e., noise that is unknown a priori and that is not necessarily governed by a stochastic model. We focus on safety constraints that take the form of time-varying convex constraints such as collision-avoidance and control-effort constraints. We provide an algorithm with bounded dynamic regret, i.e., bounded suboptimality against an optimal clairvoyant controller that knows the realization of the noise a prior. We are motivated by the future of autonomy where robots will autonomously perform complex tasks despite real-world unpredictable disturbances such as wind gusts. To develop the algorithm, we capture our problem as a sequential game between a controller and an adversary, where the controller plays first, choosing the control input, whereas the adversary plays second, choosing the noise's realization. The controller aims to minimize its cumulative tracking error despite being unable to know the noise's realization a prior. We validate our algorithm in simulated scenarios of (i) an inverted pendulum aiming to stay upright, and (ii) a quadrotor aiming to fly to a goal location through an unknown cluttered environment.

Genetic Algorithms (GAs) are known for their efficiency in solving combinatorial optimization problems, thanks to their ability to explore diverse solution spaces, handle various representations, exploit parallelism, preserve good solutions, adapt to changing dynamics, handle combinatorial diversity, and provide heuristic search. However, limitations such as premature convergence, lack of problem-specific knowledge, and randomness of crossover and mutation operators make GAs generally inefficient in finding an optimal solution. To address these limitations, this paper proposes a new metaheuristic algorithm called the Genetic Engineering Algorithm (GEA) that draws inspiration from genetic engineering concepts. GEA redesigns the traditional GA while incorporating new search methods to isolate, purify, insert, and express new genes based on existing ones, leading to the emergence of desired traits and the production of specific chromosomes based on the selected genes. Comparative evaluations against state-of-the-art algorithms on benchmark instances demonstrate the superior performance of GEA, showcasing its potential as an innovative and efficient solution for combinatorial optimization problems.

Recent advances in federated learning (FL) enable collaborative training of machine learning (ML) models from large-scale and widely dispersed clients while protecting their privacy. However, when different clients' datasets are heterogeneous, traditional FL mechanisms produce a global model that does not adequately represent the poorer clients with limited data resources, resulting in lower accuracy and higher bias on their local data. According to the Matthew effect, which describes how the advantaged gain more advantage and the disadvantaged lose more over time, deploying such a global model in client applications may worsen the resource disparity among the clients and harm the principles of social welfare and fairness. To mitigate the Matthew effect, we propose Egalitarian Fairness Federated Learning (EFFL), where egalitarian fairness refers to the global model learned from FL has: (1) equal accuracy among clients; (2) equal decision bias among clients. Besides achieving egalitarian fairness among the clients, EFFL also aims for performance optimality, minimizing the empirical risk loss and the bias for each client; both are essential for any ML model training, whether centralized or decentralized. We formulate EFFL as a constrained multi-constrained multi-objectives optimization (MCMOO) problem, with the decision bias and egalitarian fairness as constraints and the minimization of the empirical risk losses on all clients as multiple objectives to be optimized. We propose a gradient-based three-stage algorithm to obtain the Pareto optimal solutions within the constraint space. Extensive experiments demonstrate that EFFL outperforms other state-of-the-art FL algorithms in achieving a high-performance global model with enhanced egalitarian fairness among all clients.

Daily fantasy sports (DFS) are weekly or daily online contests where real-game performances of individual players are converted to fantasy points (FPTS). Users select players for their lineup to maximize their FPTS within a set player salary cap. This paper focuses on (1) the development of a method to forecast NFL player performance under uncertainty and (2) determining an optimal lineup to maximize FPTS under a set salary limit. A supervised learning neural network was created and used to project FPTS based on past player performance (2018 NFL regular season for this work) prior to the upcoming week. These projected FPTS were used in a mixed integer linear program to find the optimal lineup. The performance of resultant lineups was compared to randomly-created lineups. On average, the optimal lineups outperformed the random lineups. The generated lineups were then compared to real-world lineups from users on DraftKings. The generated lineups generally fell in approximately the 31st percentile (median). The FPTS methods and predictions presented here can be further improved using this study as a baseline comparison.

Leximin is a common approach to multi-objective optimization, frequently employed in fair division applications. In leximin optimization, one first aims to maximize the smallest objective value; subject to this, one maximizes the second-smallest objective; and so on. Often, even the single-objective problem of maximizing the smallest value cannot be solved accurately. What can we hope to accomplish for leximin optimization in this situation? Recently, Henzinger et al. (2022) defined a notion of \emph{approximate} leximin optimality. Their definition, however, considers only an additive approximation. In this work, we first define the notion of approximate leximin optimality, allowing both multiplicative and additive errors. We then show how to compute, in polynomial time, such an approximate leximin solution, using an oracle that finds an approximation to a single-objective problem. The approximation factors of the algorithms are closely related: an $(\alpha,\epsilon)$-approximation for the single-objective problem (where $\alpha \in (0,1]$ and $\epsilon \geq 0$ are the multiplicative and additive factors respectively) translates into an $\left(\frac{\alpha^2}{1-\alpha + \alpha^2}, \frac{\epsilon}{1-\alpha +\alpha^2}\right)$-approximation for the multi-objective leximin problem, regardless of the number of objectives.

Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization Problems (COPs) as Markov Decision Processes (MDPs) that effectively leverages common symmetries of COPs to improve out-of-distribution robustness. Starting from a direct MDP formulation of a constructive method, we introduce a generic way to reduce the state space, based on Bisimulation Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize the bisimulation and show how the reduced state exploits the symmetries of these problems and facilitates MDP solving. Our approach is principled and we prove that an optimal policy for the proposed BQ-MDP actually solves the associated COPs. We illustrate our approach on five classical problems: the Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing, Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce a simple attention-based policy network for the BQ-MDPs, which we train by imitation of (near) optimal solutions of small instances from a single distribution. We obtain new state-of-the-art results for the five COPs on both synthetic and realistic benchmarks. Notably, in contrast to most existing neural approaches, our learned policies show excellent generalization performance to much larger instances than seen during training, without any additional search procedure.