In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted redundant constraints are required to obtain tight relaxations and thus global optimality. These constraints are formulation-dependent and typically require a lengthy manual process to find. Instead, the present paper suggests an automatic method to find a set of sufficient redundant constraints to obtain tightness, if they exist. We first propose an efficient feasibility check to determine if a given set of variables can lead to a tight formulation. Secondly, we show how to scale the method to problems of bigger size. At no point of the process do we have to manually find redundant constraints. We showcase the effectiveness of the approach, in simulation and on real datasets, for range-based localization and stereo-based pose estimation. Finally, we reproduce semidefinite relaxations presented in recent literature and show that our automatic method finds a smaller set of constraints sufficient for tightness than previously considered.

Federated learning (FL) has drawn increasing attention owing to its potential use in large-scale industrial applications. Existing federated learning works mainly focus on model homogeneous settings. However, practical federated learning typically faces the heterogeneity of data distributions, model architectures, network environments, and hardware devices among participant clients. Heterogeneous Federated Learning (HFL) is much more challenging, and corresponding solutions are diverse and complex. Therefore, a systematic survey on this topic about the research challenges and state-of-the-art is essential. In this survey, we firstly summarize the various research challenges in HFL from five aspects: statistical heterogeneity, model heterogeneity, communication heterogeneity, device heterogeneity, and additional challenges. In addition, recent advances in HFL are reviewed and a new taxonomy of existing HFL methods is proposed with an in-depth analysis of their pros and cons. We classify existing methods from three different levels according to the HFL procedure: data-level, model-level, and server-level. Finally, several critical and promising future research directions in HFL are discussed, which may facilitate further developments in this field. A periodically updated collection on HFL is available at https://github.com/marswhu/HFL_Survey.

Markov games model interactions among multiple players in a stochastic, dynamic environment. Each player in a Markov game maximizes its expected total discounted reward, which depends upon the policies of the other players. We formulate a class of Markov games, termed affine Markov games, where an affine reward function couples the players' actions. We introduce a novel solution concept, the soft-Bellman equilibrium, where each player is boundedly rational and chooses a soft-Bellman policy rather than a purely rational policy as in the well-known Nash equilibrium concept. We provide conditions for the existence and uniqueness of the soft-Bellman equilibrium and propose a nonlinear least-squares algorithm to compute such an equilibrium in the forward problem. We then solve the inverse game problem of inferring the players' reward parameters from observed state-action trajectories via a projected-gradient algorithm. Experiments in a predator-prey OpenAI Gym environment show that the reward parameters inferred by the proposed algorithm outperform those inferred by a baseline algorithm: they reduce the Kullback-Leibler divergence between the equilibrium policies and observed policies by at least two orders of magnitude.

Social insects such as ants communicate via pheromones which allows them to coordinate their activity and solve complex tasks as a swarm, e.g. foraging for food. This behavior was shaped through evolutionary processes. In computational models, self-coordination in swarms has been implemented using probabilistic or simple action rules to shape the decision of each agent and the collective behavior. However, manual tuned decision rules may limit the behavior of the swarm. In this work we investigate the emergence of self-coordination and communication in evolved swarms without defining any explicit rule. We evolve a swarm of agents representing an ant colony. We use an evolutionary algorithm to optimize a spiking neural network (SNN) which serves as an artificial brain to control the behavior of each agent. The goal of the evolved colony is to find optimal ways to forage for food and return it to the nest in the shortest amount of time. In the evolutionary phase, the ants are able to learn to collaborate by depositing pheromone near food piles and near the nest to guide other ants. The pheromone usage is not manually encoded into the network; instead, this behavior is established through the optimization procedure. We observe that pheromone-based communication enables the ants to perform better in comparison to colonies where communication via pheromone did not emerge. We assess the foraging performance by comparing the SNN based model to a rule based system. Our results show that the SNN based model can efficiently complete the foraging task in a short amount of time. Our approach illustrates self coordination via pheromone emerges as a result of the network optimization. This work serves as a proof of concept for the possibility of creating complex applications utilizing SNNs as underlying architectures for multi-agent interactions where communication and self-coordination is desired.

In addition to maximizing the total revenue, decision-makers in lots of industries would like to guarantee balanced consumption across different resources. For instance, in the retailing industry, ensuring a balanced consumption of resources from different suppliers enhances fairness and helps main a healthy channel relationship; in the cloud computing industry, resource-consumption balance helps increase customer satisfaction and reduce operational costs. Motivated by these practical needs, this paper studies the price-based network revenue management (NRM) problem with both demand learning and fair resource-consumption balancing. We introduce the regularized revenue, i.e., the total revenue with a balancing regularization, as our objective to incorporate fair resource-consumption balancing into the revenue maximization goal. We propose a primal-dual-type online policy with the Upper-Confidence-Bound (UCB) demand learning method to maximize the regularized revenue. We adopt several innovative techniques to make our algorithm a unified and computationally efficient framework for the continuous price set and a wide class of balancing regularizers. Our algorithm achieves a worst-case regret of $\widetilde O(N^{5/2}\sqrt{T})$, where $N$ denotes the number of products and $T$ denotes the number of time periods. Numerical experiments in a few NRM examples demonstrate the effectiveness of our algorithm in simultaneously achieving revenue maximization and fair resource-consumption balancing

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, has been recently extended to exploit prior knowledge on the cardinality of each cluster. Such knowledge is used to increase performance as well as solution quality. In this paper, we propose a global optimization approach based on the branch-and-cut technique to solve the cardinality-constrained MSSC. For the lower bound routine, we use the semidefinite programming (SDP) relaxation recently proposed by Rujeerapaiboon et al. [SIAM J. Optim. 29(2), 1211-1239, (2019)]. However, this relaxation can be used in a branch-and-cut method only for small-size instances. Therefore, we derive a new SDP relaxation that scales better with the instance size and the number of clusters. In both cases, we strengthen the bound by adding polyhedral cuts. Benefiting from a tailored branching strategy which enforces pairwise constraints, we reduce the complexity of the problems arising in the children nodes. For the upper bound, instead, we present a local search procedure that exploits the solution of the SDP relaxation solved at each node. Computational results show that the proposed algorithm globally solves, for the first time, real-world instances of size 10 times larger than those solved by state-of-the-art exact methods.

In this work, we introduce GraPhSyM, a Graph Attention Network (GATv2) model for fast and accurate estimation of post-physical synthesis circuit delay and area metrics from pre-physical synthesis circuit netlists. Once trained, GraPhSyM provides accurate visibility of final design metrics to early EDA stages, such as logic synthesis, without running the slow physical synthesis flow, enabling global co-optimization across stages. Additionally, the swift and precise feedback provided by GraPhSyM is instrumental for machine-learning-based EDA optimization frameworks. Given a gate-level netlist of a circuit represented as a graph, GraPhSyM utilizes graph structure, connectivity, and electrical property features to predict the impact of physical synthesis transformations such as buffer insertion and gate sizing. When trained on a dataset of 6000 prefix adder designs synthesized at an aggressive delay target, GraPhSyM can accurately predict the post-synthesis delay (98.3%) and area (96.1%) metrics of unseen adders with a fast 0.22s inference time. Furthermore, we illustrate the compositionality of GraPhSyM by employing the model trained on a fixed delay target to accurately anticipate post-synthesis metrics at a variety of unseen delay targets. Lastly, we report promising generalization capabilities of the GraPhSyM model when it is evaluated on circuits different from the adders it was exclusively trained on. The results show the potential for GraPhSyM to serve as a powerful tool for advanced optimization techniques and as an oracle for EDA machine learning frameworks.

We present a novel optimization algorithm, element-wise relaxed scalar auxiliary variable (E-RSAV), that satisfies an unconditional energy dissipation law and exhibits improved alignment between the modified and the original energy. Our algorithm features rigorous proofs of linear convergence in the convex setting. Furthermore, we present a simple accelerated algorithm that improves the linear convergence rate to super-linear in the univariate case. We also propose an adaptive version of E-RSAV with Steffensen step size.

In recent years, there is a growing interest in combining techniques attributed to the areas of Statistics and Machine Learning in order to obtain the benefits of both approaches. In this article, the statistical technique lasso for variable selection is represented through a neural network. It is observed that, although both the statistical approach and its neural version have the same objective function, they differ due to their optimization. In particular, the neural version is usually optimized in one-step using a single validation set, while the statistical counterpart uses a two-step optimization based on cross-validation. The more elaborated optimization of the statistical method results in more accurate parameter estimation, especially when the training set is small. For this reason, a modification of the standard approach for training neural networks, that mimics the statistical framework, is proposed. During the development of the above modification, a new optimization algorithm for identifying the significant variables emerged. Experimental results, using synthetic and real data sets, show that this new optimization algorithm achieves better performance than any of the three previous optimization approaches.

This work introduces a novel control strategy called Iterative Linear Quadratic Regulator for Iterative Tasks (i2LQR), which aims to improve closed-loop performance with local trajectory optimization for iterative tasks in a dynamic environment. The proposed algorithm is reference-free and utilizes historical data from previous iterations to enhance the performance of the autonomous system. Unlike existing algorithms, the i2LQR computes the optimal solution in an iterative manner at each timestamp, rendering it well-suited for iterative tasks with changing constraints at different iterations. To evaluate the performance of the proposed algorithm, we conduct numerical simulations for an iterative task aimed at minimizing completion time. The results show that i2LQR achieves an optimized performance with respect to learning-based MPC (LMPC) as the benchmark in static environments, and outperforms LMPC in dynamic environments with both static and dynamics obstacles.