This paper proposes a novel Decentralized Spike-based Learning (DSL) framework for the discrete Perimeter Defense Problem (d-PDP). A team of defenders is operating on the perimeter to protect the circular territory from radially incoming intruders. At first, the d-PDP is formulated as a spatio-temporal multi-task assignment problem (STMTA). The problem of STMTA is then converted into a multi-label learning problem to obtain labels of segments that defenders have to visit in order to protect the perimeter. The DSL framework uses a Multi-Label Classifier using Synaptic Efficacy Function spiking neuRON (MLC-SEFRON) network for deterministic multi-label learning. Each defender contains a single MLC-SEFRON network. Each MLC-SEFRON network is trained independently using input from its own perspective for decentralized operations. The input spikes to the MLC-SEFRON network can be directly obtained from the spatio-temporal information of defenders and intruders without any extra pre-processing step. The output of MLC-SEFRON contains the labels of segments that a defender has to visit in order to protect the perimeter. Based on the multi-label output from the MLC-SEFRON a trajectory is generated for a defender using a Consensus-Based Bundle Algorithm (CBBA) in order to capture the intruders. The target multi-label output for training MLC-SEFRON is obtained from an expert policy. Also, the MLC-SEFRON trained for a defender can be directly used for obtaining labels of segments assigned to another defender without any retraining. The performance of MLC-SEFRON has been evaluated for full observation and partial observation scenarios of the defender. The overall performance of the DSL framework is then compared with expert policy along with other existing learning algorithms. The scalability of the DSL has been evaluated using an increasing number of defenders.

We investigate the optimization aspects of personalized Federated Learning (FL). We propose general optimizers that can be applied to numerous existing personalized FL objectives, specifically a tailored variant of Local SGD and variants of accelerated coordinate descent/accelerated SVRCD. By examining a general personalized objective capable of recovering many existing personalized FL objectives as special cases, we develop a comprehensive optimization theory applicable to a wide range of strongly convex personalized FL models in the literature. We showcase the practicality and/or optimality of our methods in terms of communication and local computation. Remarkably, our general optimization solvers and theory can recover the best-known communication and computation guarantees for addressing specific personalized FL objectives. Consequently, our proposed methods can serve as universal optimizers, rendering the design of task-specific optimizers unnecessary in many instances.

Most MPC (Model Predictive Control) algorithms used in industries and studied in the control academia use a two-term QP (quadratic programming), where the first term is the weighted norm of the output errors, and the second term is that of the input increments. In this work, a DMC (Dynamic Matrix Control) algorithm that uses three-term QP is studied, where the third term is the weighted norm of the output increments. In the analysis, a relationship between the three-term DMC and the two-term DMC is established; based on that, the closed-loop response curves are derived. Based on the analysis, two controller tuning procedures are developed for the three-term DMC, one for closed-loop step response and one for disturbance reduction. Finally, it will be proven that the three-term DMC can achieve a higher performance and robustness than the two-term DMC can. Simulation studies are used to demonstrate the findings and the tuning methods.

We revisit the online dynamic acknowledgment problem. In the problem, a sequence of requests arrive over time to be acknowledged, and all outstanding requests can be satisfied simultaneously by one acknowledgement. The goal of the problem is to minimize the total request delay plus acknowledgement cost. This elegant model studies the trade-off between acknowledgement cost and waiting experienced by requests. The problem has been well studied and the tight competitive ratios have been determined. For this well-studied problem, we focus on how to effectively use machine-learned predictions to have better performance. We develop algorithms that perform arbitrarily close to the optimum with accurate predictions while concurrently having the guarantees arbitrarily close to what the best online algorithms can offer without access to predictions, thereby achieving simultaneous optimum consistency and robustness. This new result is enabled by our novel prediction error measure. No error measure was defined for the problem prior to our work, and natural measures failed due to the challenge that requests with different arrival times have different effects on the objective. We hope our ideas can be used for other online problems with temporal aspects that have been resisting proper error measures.

Majorana zero modes in superconductor-nanowire hybrid structures are a promising candidate for topologically protected qubits with the potential to be used in scalable structures. Currently, disorder in such Majorana wires is a major challenge, as it can destroy the topological phase and thus reduce the yield in the fabrication of Majorana devices. We study machine learning optimization of a gate array in proximity to a grounded Majorana wire, which allows us to reliably compensate even strong disorder. We propose a metric for optimization that is inspired by the topological gap protocol, and which can be implemented based on measurements of the non-local conductance through the wire.

Ensuring fairness is a crucial aspect of Federated Learning (FL), which enables the model to perform consistently across all clients. However, designing an FL algorithm that simultaneously improves global model performance and promotes fairness remains a formidable challenge, as achieving the latter often necessitates a trade-off with the former. To address this challenge, we propose a new FL algorithm, FedEBA+, which enhances fairness while simultaneously improving global model performance. FedEBA+ incorporates a fair aggregation scheme that assigns higher weights to underperforming clients and an alignment update method. In addition, we provide theoretical convergence analysis and show the fairness of FedEBA+. Extensive experiments demonstrate that FedEBA+ outperforms other SOTA fairness FL methods in terms of both fairness and global model performance.

We propose SING (StabIlized and Normalized Gradient), a plug-and-play technique that improves the stability and generalization of the Adam(W) optimizer. SING is straightforward to implement and has minimal computational overhead, requiring only a layer-wise standardization of the gradients fed to Adam(W) without introducing additional hyper-parameters. We support the effectiveness and practicality of the proposed approach by showing improved results on a wide range of architectures, problems (such as image classification, depth estimation, and natural language processing), and in combination with other optimizers. We provide a theoretical analysis of the convergence of the method, and we show that by virtue of the standardization, SING can escape local minima narrower than a threshold that is inversely proportional to the network's depth.

We present a novel perspective and algorithm for learning directed acyclic graphs (DAGs) from data generated by a linear structural equation model (SEM). First, we show that a linear SEM can be viewed as a linear transform that, in prior work, computes the data from a dense input vector of random valued root causes (as we will call them) associated with the nodes. Instead, we consider the case of (approximately) few root causes and also introduce noise in the measurement of the data. Intuitively, this means that the DAG data is produced by few data-generating events whose effect percolates through the DAG. We prove identifiability in this new setting and show that the true DAG is the global minimizer of the $L^0$-norm of the vector of root causes. For data with few root causes, with and without noise, we show superior performance compared to prior DAG learning methods.

Integrating renewable energy into the power grid while balancing supply and demand is a complex issue, given its intermittent nature. Demand side management (DSM) offers solutions to this challenge. We propose a new method for DSM, in particular the problem of controlling a large population of electrical devices to follow a desired consumption signal. We model it as a finite horizon Markovian mean field control problem. We develop a new algorithm, MD-MFC, which provides theoretical guarantees for convex and Lipschitz objective functions. What distinguishes MD-MFC from the existing load control literature is its effectiveness in directly solving the target tracking problem without resorting to regularization techniques on the main problem. A non-standard Bregman divergence on a mirror descent scheme allows dynamic programming to be used to obtain simple closed-form solutions. In addition, we show that general mean-field game algorithms can be applied to this problem, which expands the possibilities for addressing load control problems. We illustrate our claims with experiments on a realistic data set.

Constrained $k$-submodular maximization is a general framework that captures many discrete optimization problems such as ad allocation, influence maximization, personalized recommendation, and many others. In many of these applications, datasets are large or decisions need to be made in an online manner, which motivates the development of efficient streaming and online algorithms. In this work, we develop single-pass streaming and online algorithms for constrained $k$-submodular maximization with both monotone and general (possibly non-monotone) objectives subject to cardinality and knapsack constraints. Our algorithms achieve provable constant-factor approximation guarantees which improve upon the state of the art in almost all settings. Moreover, they are combinatorial and very efficient, and have optimal space and running time. We experimentally evaluate our algorithms on instances for ad allocation and other applications, where we observe that our algorithms are efficient and scalable, and construct solutions that are comparable in value to offline greedy algorithms.