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Recent strides in nonlinear model predictive control (NMPC) underscore a dependence on numerical advancements to efficiently and accurately solve large-scale problems. Given the substantial number of variables characterizing typical whole-body optimal control (OC) problems - often numbering in the thousands - exploiting the sparse structure of the numerical problem becomes crucial to meet computational demands, typically in the range of a few milliseconds. Addressing the linear-quadratic regulator (LQR) problem is a fundamental building block for computing Newton or Sequential Quadratic Programming (SQP) steps in direct optimal control methods. This paper concentrates on equality-constrained problems featuring implicit system dynamics and dual regularization, a characteristic of advanced interiorpoint or augmented Lagrangian solvers. Here, we introduce a parallel algorithm for solving an LQR problem with dual regularization. Leveraging a rewriting of the LQR recursion through block elimination, we first enhanced the efficiency of the serial algorithm and then subsequently generalized it to handle parametric problems. This extension enables us to split decision variables and solve multiple subproblems concurrently. Our algorithm is implemented in our nonlinear numerical optimal control library ALIGATOR. It showcases improved performance over previous serial formulations and we validate its efficacy by deploying it in the model predictive control of a real quadruped robot.

This paper investigates goal-oriented communication for remote estimation of multiple Markov sources in resource-constrained networks. An agent decides the updating times of the sources and transmits the packet to a remote destination over an unreliable channel with delay. The destination is tasked with source reconstruction for actuation. We utilize the metric \textit{cost of actuation error} (CAE) to capture the state-dependent actuation costs. We aim for a sampling policy that minimizes the long-term average CAE subject to an average resource constraint. We formulate this problem as an average-cost constrained Markov Decision Process (CMDP) and relax it into an unconstrained problem by utilizing \textit{Lyapunov drift} techniques. Then, we propose a low-complexity \textit{drift-plus-penalty} (DPP) policy for systems with known source/channel statistics and a Lyapunov optimization-based deep reinforcement learning (LO-DRL) policy for unknown environments. Our policies significantly reduce the number of uninformative transmissions by exploiting the timing of the important information.

Non-fungible tokens (NFTs) are becoming increasingly popular in Play-to-Earn (P2E) Web3 applications as a means of incentivizing user engagement. In Web3, users with NFTs ownership are entitled to monetize them. However, due to lack of objective NFT valuation, which makes NFT value determination challenging, P2E applications ecosystems have experienced inflation. In this paper, we propose a method that enables NFT inflation value management in P2E applications. Our method leverages the contribution-rewards model proposed by Curve Finance and the automated market maker (AMM) of decentralized exchanges. In decentralized systems, P2E Web3 applications inclusive, not all participants contribute in good faith. Therefore, rewards are provided to incentivize contribution. Our mechanism proves that burning NFTs, indicating the permanent removal of NFTs, contributes to managing inflation by reducing the number of NFTs in circulation. As a reward for this contribution, our method mints a compensation (CP) token as an ERC-20 token, which can be exchanged for NFTs once enough tokens have been accumulated. To further increase the value of the CP token, we suggest using governance tokens and CP tokens to create liquidity pools for AMM. The value of the governance token is determined by the market, and the CP token derives its value from the governance token in AMM. The CP token can determine its worth based on the market value of the governance token. Additionally, since CP tokens are used for exchanging NFTs, the value of the NFT is ultimately determined by the value of the CP token. To further illustrate our concept, we show how to adjust burning rewards based on factors such as the probability of upgrading NFTs' rarity or the current swap ratio of governance and CP tokens in AMM.

This paper investigates the optimal selection and fusion of feature encoders across multiple modalities and combines these in one neural network to improve sentiment detection. We compare different fusion methods and examine the impact of multi-loss training within the multi-modality fusion network, identifying surprisingly important findings relating to subnet performance. We have also found that integrating context significantly enhances model performance. Our best model achieves state-of-the-art performance for three datasets (CMU-MOSI, CMU-MOSEI and CH-SIMS). These results suggest a roadmap toward an optimized feature selection and fusion approach for enhancing sentiment detection in neural networks.

The objective of this paper is to provide an introduction to the principles of Bayesian joint modeling of longitudinal measurements and time-to-event outcomes, as well as model implementation using the BUGS language syntax. This syntax can be executed directly using OpenBUGS or by utilizing convenient functions to invoke OpenBUGS and JAGS from R software. In this paper, all details of joint models are provided, ranging from simple to more advanced models. The presentation started with the joint modeling of a Gaussian longitudinal marker and time-to-event outcome. The implementation of the Bayesian paradigm of the model is reviewed. The strategies for simulating data from the JM are also discussed. A proportional hazard model with various forms of baseline hazards, along with the discussion of all possible association structures between the two sub-models are taken into consideration. The paper covers joint models with multivariate longitudinal measurements, zero-inflated longitudinal measurements, competing risks, and time-to-event with cure fraction. The models are illustrated by the analyses of several real data sets. All simulated and real data and code are available at \url{//github.com/tbaghfalaki/JM-with-BUGS-and-JAGS}.

This paper explores the distance-based relative state estimation problem in large-scale systems, which is hard to solve effectively due to its high-dimensionality and non-convexity. In this paper, we alleviate this inherent hardness to simultaneously achieve scalability and robustness of inference on this problem. Our idea is launched from a universal geometric formulation, called \emph{generalized graph realization}, for the distance-based relative state estimation problem. Based on this formulation, we introduce two collaborative optimization models, one of which is convex and thus globally solvable, and the other enables fast searching on non-convex landscapes to refine the solution offered by the convex one. Importantly, both models enjoy \emph{multiconvex} and \emph{decomposable} structures, allowing efficient and safe solutions using \emph{block coordinate descent} that enjoys scalability and a distributed nature. The proposed algorithms collaborate to demonstrate superior or comparable solution precision to the current centralized convex relaxation-based methods, which are known for their high optimality. Distinctly, the proposed methods demonstrate scalability beyond the reach of previous convex relaxation-based methods. We also demonstrate that the combination of the two proposed algorithms achieves a more robust pipeline than deploying the local search method alone in a continuous-time scenario.

Communication efficiency has garnered significant attention as it is considered the main bottleneck for large-scale decentralized Machine Learning applications in distributed and federated settings. In this regime, clients are restricted to transmitting small amounts of quantized information to their neighbors over a communication graph. Numerous endeavors have been made to address this challenging problem by developing algorithms with compressed communication for decentralized non-convex optimization problems. Despite considerable efforts, the current results suffer from various issues such as non-scalability with the number of clients, requirements for large batches, or bounded gradient assumption. In this paper, we introduce MoTEF, a novel approach that integrates communication compression with Momentum Tracking and Error Feedback. Our analysis demonstrates that MoTEF achieves most of the desired properties, and significantly outperforms existing methods under arbitrary data heterogeneity. We provide numerical experiments to validate our theoretical findings and confirm the practical superiority of MoTEF.

This work investigates the performance of intelligent reflective surfaces (IRSs) assisted uplink non-orthogonal multiple access (NOMA) in energy-constrained networks. Specifically, we formulate and solve two optimization problems; the first aims at minimizing the sum of users' transmit power, while the second targets maximizing the system level energy efficiency (EE). The two problems are solved by jointly optimizing the users' transmit powers and the beamforming coefficients at IRS subject to the users' individual uplink rate and transmit power constraints. A novel and low complexity algorithm is developed to optimize the IRS beamforming coefficients by optimizing the objective function over a \textit{complex circle manifold} (CCM). To efficiently optimize the IRS phase shifts over the manifold, the optimization problem is reformulated into a feasibility expansion problem which is reduced to a max-min signal-plus-interference-ratio (SINR). Then, with the aid of a smoothing technique, the exact penalty method is applied to transform the problem from constrained to unconstrained. The proposed solution is compared against three semi-definite programming (SDP)-based benchmarks which are semi-definite relaxation (SDR), SDP-difference of convex (SDP-DC) and sequential rank-one constraint relaxation (SROCR). The results show that the manifold algorithm provides better performance than the SDP-based benchmarks, and at a much lower computational complexity for both the transmit power minimization and EE maximization problems. The results also reveal that IRS-NOMA is only superior to orthogonal multiple access (OMA) when the users' target achievable rate requirements are relatively high.

The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN) based models generate richer and more expressive feature embeddings and hence also perform well on relation prediction. However, we observe that these KG embeddings treat triples independently and thus fail to cover the complex and hidden information that is inherently implicit in the local neighborhood surrounding a triple. To this effect, our paper proposes a novel attention based feature embedding that captures both entity and relation features in any given entity's neighborhood. Additionally, we also encapsulate relation clusters and multihop relations in our model. Our empirical study offers insights into the efficacy of our attention based model and we show marked performance gains in comparison to state of the art methods on all datasets.