The back-end module of Distributed Collaborative Simultaneous Localization and Mapping (DCSLAM) requires solving a nonlinear Pose Graph Optimization (PGO) under a distributed setting, also known as SE(d)-synchronization. Most existing distributed graph optimization algorithms employ a simple sequential partitioning scheme, which may result in unbalanced subgraph dimensions due to the different geographic locations of each robot, and hence imposes extra communication load. Moreover, the performance of current Riemannian optimization algorithms can be further accelerated. In this letter, we propose a novel distributed pose graph optimization algorithm combining multi-level partitioning with an accelerated Riemannian optimization method. Firstly, we employ the multi-level graph partitioning algorithm to preprocess the naive pose graph to formulate a balanced optimization problem. In addition, inspired by the accelerated coordinate descent method, we devise an Improved Riemannian Block Coordinate Descent (IRBCD) algorithm and the critical point obtained is globally optimal. Finally, we evaluate the effects of four common graph partitioning approaches on the correlation of the inter-subgraphs, and discover that the Highest scheme has the best partitioning performance. Also, we implement simulations to quantitatively demonstrate that our proposed algorithm outperforms the state-of-the-art distributed pose graph optimization protocols.

Community detection, which involves partitioning nodes within a network, has widespread applications across computational sciences. Modularity-based algorithms identify communities by attempting to maximize the modularity function across network node partitions. Our study assesses the performance of various modularity-based algorithms in obtaining optimal partitions. Our analysis utilizes 104 networks, including both real-world instances from diverse contexts and modular graphs from two families of synthetic benchmarks. We analyze ten inexact modularity-based algorithms against the exact integer programming baseline that globally optimizes modularity. Our comparative analysis includes eight heuristics, two variants of a graph neural network algorithm, and nine variations of the Bayan approximation algorithm. Our findings reveal that the average modularity-based heuristic yields optimal partitions in only 43.9% of the 104 networks analyzed. Graph neural networks and approximate Bayan, on average, achieve optimality on 68.7% and 82.3% of the networks respectively. Additionally, our analysis of three partition similarity metrics exposes substantial dissimilarities between high-modularity sub-optimal partitions and any optimal partition of the networks. We observe that near-optimal partitions are often disproportionately dissimilar to any optimal partition. Taken together, our analysis points to a crucial limitation of the commonly used modularity-based methods: they rarely produce an optimal partition or a partition resembling an optimal partition even on networks with modular structures. If modularity is to be used for detecting communities, we recommend approximate optimization algorithms for a more methodologically sound usage of modularity within its applicability limits.

In root finding and optimization, there are many cases where there is a closed set $A$ one likes that the sequence constructed by one's favourite method will not converge to A (here, we do not assume extra properties on $A$ such as being convex or connected). For example, if one wants to find roots, and one chooses initial points in the basin of attraction for 1 root $z^*$ (a fact which one may not know before hand), then one will always end up in that root. In this case, one would like to have a mechanism to avoid this point $z^*$ in the next runs of one's algorithm. Assume that one already has a method IM for optimization (and root finding) for non-constrained optimization. We provide a simple modification IM1 of the method to treat the situation discussed in the previous paragraph. If the method IM has strong theoretical guarantees, then so is IM1. As applications, we prove two theoretical applications: one concerns finding roots of a meromorphic function in an open subset of a Riemann surface, and the other concerns finding local minima of a function in an open subset of a Euclidean space inside it the function has at most countably many critical points. Along the way, we compare with main existing relevant methods in the current literature. We provide several examples in various different settings to illustrate the usefulness of the new approach.

Communication compression is a common technique in distributed optimization that can alleviate communication overhead by transmitting compressed gradients and model parameters. However, compression can introduce information distortion, which slows down convergence and incurs more communication rounds to achieve desired solutions. Given the trade-off between lower per-round communication costs and additional rounds of communication, it is unclear whether communication compression reduces the total communication cost. This paper explores the conditions under which unbiased compression, a widely used form of compression, can reduce the total communication cost, as well as the extent to which it can do so. To this end, we present the first theoretical formulation for characterizing the total communication cost in distributed optimization with communication compression. We demonstrate that unbiased compression alone does not necessarily save the total communication cost, but this outcome can be achieved if the compressors used by all workers are further assumed independent. We establish lower bounds on the communication rounds required by algorithms using independent unbiased compressors to minimize smooth convex functions and show that these lower bounds are tight by refining the analysis for ADIANA. Our results reveal that using independent unbiased compression can reduce the total communication cost by a factor of up to $\Theta(\sqrt{\min\{n, \kappa\}})$ when all local smoothness constants are constrained by a common upper bound, where $n$ is the number of workers and $\kappa$ is the condition number of the functions being minimized. These theoretical findings are supported by experimental results.

As neural networks (NN) are deployed across diverse sectors, their energy demand correspondingly grows. While several prior works have focused on reducing energy consumption during training, the continuous operation of ML-powered systems leads to significant energy use during inference. This paper investigates how the configuration of on-device hardware--elements such as GPU, memory, and CPU frequency, often neglected in prior studies, affects energy consumption for NN inference with regular fine-tuning. We propose PolyThrottle, a solution that optimizes configurations across individual hardware components using Constrained Bayesian Optimization in an energy-conserving manner. Our empirical evaluation uncovers novel facets of the energy-performance equilibrium showing that we can save up to 36 percent of energy for popular models.

With the scaling up of crude oil scheduling in modern refineries, large-scale crude oil scheduling problems (LSCOSPs) emerge with thousands of binary variables and non-linear constraints, which are challenging to be optimized by traditional optimization methods. To solve LSCOSPs, we take the practical crude oil scheduling from a marine-access refinery as an example and start with modeling LSCOSPs from crude unloading, transportation, crude distillation unit processing, and inventory management of intermediate products. On the basis of the proposed model, a dual-stage evolutionary algorithm driven by heuristic rules (denoted by DSEA/HR) is developed, where the dual-stage search mechanism consists of global search and local refinement. In the global search stage, we devise several heuristic rules based on the empirical operating knowledge to generate a well-performing initial population and accelerate convergence in the mixed variables space. In the local refinement stage, a repair strategy is proposed to move the infeasible solutions towards feasible regions by further optimizing the local continuous variables. During the whole evolutionary process, the proposed dual-stage framework plays a crucial role in balancing exploration and exploitation. Experimental results have shown that DSEA/HR outperforms the state-of-the-art and widely-used mathematical programming methods and metaheuristic algorithms on LSCOSP instances within a reasonable time.

Decision making and planning have long relied heavily on AI-driven forecasts. The government and the general public are working to minimize the risks while maximizing benefits in the face of potential future public health uncertainties. This study used an improved method of forecasting utilizing the Random Descending Velocity Inertia Weight (RDV IW) technique to improve the convergence of Particle Swarm Optimization (PSO) and the accuracy of Artificial Neural Network (ANN). The IW technique, inspired by the motions of a golf ball, modified the particles' velocities as they approached the solution point to a parabolically descending structure. Simulation results revealed that the proposed forecasting model with [0.4, 0.9] combination of alpha and alpha_dump exhibits a 6.36% improvement in position error and 11.75% improvement in computational time compared to the old model, thus, improving its convergence. It reached the optimum level at minimal steps with 12.50% improvement as against the old model since it provides better velocity averages when speed stabilization occurs at the 24th iteration. Meanwhile, the computed p-values for NRMSE (0.04889174), MAE (0.02829063), MAPE (0.02226053), WAPE (0.01701545), and R2 (0.00000021) of the proposed algorithm are less than the set 0.05 level of significance, thus the values indicated a significant result in terms of accuracy performance. Applying the modified ANN-PSO using RDV IW technique greatly improved the new HIV/AIDS forecasting model compared with the two models.

This paper develops a graph reinforcement learning approach to online planning of the schedule and destinations of electric aircraft that comprise an urban air mobility (UAM) fleet operating across multiple vertiports. This fleet scheduling problem is formulated to consider time-varying demand, constraints related to vertiport capacity, aircraft capacity and airspace safety guidelines, uncertainties related to take-off delay, weather-induced route closures, and unanticipated aircraft downtime. Collectively, such a formulation presents greater complexity, and potentially increased realism, than in existing UAM fleet planning implementations. To address these complexities, a new policy architecture is constructed, primary components of which include: graph capsule conv-nets for encoding vertiport and aircraft-fleet states both abstracted as graphs; transformer layers encoding time series information on demand and passenger fare; and a Multi-head Attention-based decoder that uses the encoded information to compute the probability of selecting each available destination for an aircraft. Trained with Proximal Policy Optimization, this policy architecture shows significantly better performance in terms of daily averaged profits on unseen test scenarios involving 8 vertiports and 40 aircraft, when compared to a random baseline and genetic algorithm-derived optimal solutions, while being nearly 1000 times faster in execution than the latter.

We propose new algorithms with provable performance for online binary optimization subject to general constraints and in dynamic settings. We consider the subset of problems in which the objective function is submodular. We propose the online submodular greedy algorithm (OSGA) which solves to optimality an approximation of the previous round loss function to avoid the NP-hardness of the original problem. We extend OSGA to a generic approximation function. We show that OSGA has a dynamic regret bound similar to the tightest bounds in online convex optimization with respect to the time horizon and the cumulative round optimum variation. For instances where no approximation exists or a computationally simpler implementation is desired, we design the online submodular projected gradient descent (OSPGD) by leveraging the Lova\'sz extension. We obtain a regret bound that is akin to the conventional online gradient descent (OGD). Finally, we numerically test our algorithms in two power system applications: fast-timescale demand response and real-time distribution network reconfiguration.

Humans can leverage physical interaction to teach robot arms. This physical interaction takes multiple forms depending on the task, the user, and what the robot has learned so far. State-of-the-art approaches focus on learning from a single modality, or combine multiple interaction types by assuming that the robot has prior information about the human's intended task. By contrast, in this paper we introduce an algorithmic formalism that unites learning from demonstrations, corrections, and preferences. Our approach makes no assumptions about the tasks the human wants to teach the robot; instead, we learn a reward model from scratch by comparing the human's inputs to nearby alternatives. We first derive a loss function that trains an ensemble of reward models to match the human's demonstrations, corrections, and preferences. The type and order of feedback is up to the human teacher: we enable the robot to collect this feedback passively or actively. We then apply constrained optimization to convert our learned reward into a desired robot trajectory. Through simulations and a user study we demonstrate that our proposed approach more accurately learns manipulation tasks from physical human interaction than existing baselines, particularly when the robot is faced with new or unexpected objectives. Videos of our user study are available at: https://youtu.be/FSUJsTYvEKU