An improvement in technology is linearly related to time and time-relevant problems. It has been seen that as time progresses, the number of problems humans face also increases. However, technology to resolve these problems tends to improve as well. One of the earliest existing problems which started with the invention of vehicles was parking. The ease of resolving this problem using technology has evolved over the years but the problem of parking still remains unsolved. The main reason behind this is that parking does not only involve one problem but it consists of a set of problems within itself. One of these problems is the occupancy detection of the parking slots in a distributed parking ecosystem. In a distributed system, users would find preferable parking spaces as opposed to random parking spaces. In this paper, we propose a web-based application as a solution for parking space detection in different parking spaces. The solution is based on Computer Vision (CV) and is built using the Django framework written in Python 3.0. The solution works to resolve the occupancy detection problem along with providing the user the option to determine the block based on availability and his preference. The evaluation results for our proposed system are promising and efficient. The proposed system can also be integrated with different systems and be used for solving other relevant parking problems.

In this paper, we address the problem of finding a correspondence, or matching, between the functions of two programs in binary form, which is one of the most common task in binary diffing. We introduce a new formulation of this problem as a particular instance of a graph edit problem over the call graphs of the programs. In this formulation, the quality of a mapping is evaluated simultaneously with respect to both function content and call graph similarities. We show that this formulation is equivalent to a network alignment problem. We propose a solving strategy for this problem based on max-product belief propagation. Finally, we implement a prototype of our method, called QBinDiff, and propose an extensive evaluation which shows that our approach outperforms state of the art diffing tools.

In this paper, we focus on the decentralized optimization problem over the Stiefel manifold, which is defined on a connected network of $d$ agents. The objective is an average of $d$ local functions, and each function is privately held by an agent and encodes its data. The agents can only communicate with their neighbors in a collaborative effort to solve this problem. In existing methods, multiple rounds of communications are required to guarantee the convergence, giving rise to high communication costs. In contrast, this paper proposes a decentralized algorithm, called DESTINY, which only invokes a single round of communications per iteration. DESTINY combines gradient tracking techniques with a novel approximate augmented Lagrangian function. The global convergence to stationary points is rigorously established. Comprehensive numerical experiments demonstrate that DESTINY has a strong potential to deliver a cutting-edge performance in solving a variety of testing problems.

We study a multivariate version of trend filtering, called Kronecker trend filtering or KTF, for the case in which the design points form a lattice in $d$ dimensions. KTF is a natural extension of univariate trend filtering (Steidl et al., 2006; Kim et al., 2009; Tibshirani, 2014), and is defined by minimizing a penalized least squares problem whose penalty term sums the absolute (higher-order) differences of the parameter to be estimated along each of the coordinate directions. The corresponding penalty operator can be written in terms of Kronecker products of univariate trend filtering penalty operators, hence the name Kronecker trend filtering. Equivalently, one can view KTF in terms of an $\ell_1$-penalized basis regression problem where the basis functions are tensor products of falling factorial functions, a piecewise polynomial (discrete spline) basis that underlies univariate trend filtering. This paper is a unification and extension of the results in Sadhanala et al. (2016, 2017). We develop a complete set of theoretical results that describe the behavior of $k^{\mathrm{th}}$ order Kronecker trend filtering in $d$ dimensions, for every $k \geq 0$ and $d \geq 1$. This reveals a number of interesting phenomena, including the dominance of KTF over linear smoothers in estimating heterogeneously smooth functions, and a phase transition at $d=2(k+1)$, a boundary past which (on the high dimension-to-smoothness side) linear smoothers fail to be consistent entirely. We also leverage recent results on discrete splines from Tibshirani (2020), in particular, discrete spline interpolation results that enable us to extend the KTF estimate to any off-lattice location in constant-time (independent of the size of the lattice $n$).

In dynamic programming (DP) and reinforcement learning (RL), an agent learns to act optimally in terms of expected long-term return by sequentially interacting with its environment modeled by a Markov decision process (MDP). More generally in distributional reinforcement learning (DRL), the focus is on the whole distribution of the return, not just its expectation. Although DRL-based methods produced state-of-the-art performance in RL with function approximation, they involve additional quantities (compared to the non-distributional setting) that are still not well understood. As a first contribution, we introduce a new class of distributional operators, together with a practical DP algorithm for policy evaluation, that come with a robust MDP interpretation. Indeed, our approach reformulates through an augmented state space where each state is split into a worst-case substate and a best-case substate, whose values are maximized by safe and risky policies respectively. Finally, we derive distributional operators and DP algorithms solving a new control task: How to distinguish safe from risky optimal actions in order to break ties in the space of optimal policies?

This paper proposes a Generalized Power Method (GPM) to tackle the problem of community detection and group synchronization simultaneously in a direct non-convex manner. Under the stochastic group block model (SGBM), theoretical analysis indicates that the algorithm is able to exactly recover the ground truth in $O(n\log^2n)$ time, sharply outperforming the benchmark method of semidefinite programming (SDP) in $O(n^{3.5})$ time. Moreover, a lower bound of parameters is given as a necessary condition for exact recovery of GPM. The new bound breaches the information-theoretic threshold for pure community detection under the stochastic block model (SBM), thus demonstrating the superiority of our simultaneous optimization algorithm over the trivial two-stage method which performs the two tasks in succession. We also conduct numerical experiments on GPM and SDP to evidence and complement our theoretical analysis.

Several widely-used first-order saddle point optimization methods yield an identical continuous-time ordinary differential equation (ODE) to that of the Gradient Descent Ascent (GDA) method when derived naively. However, their convergence properties are very different even on simple bilinear games. We use a technique from fluid dynamics called High-Resolution Differential Equations (HRDEs) to design ODEs of several saddle point optimization methods. On bilinear games, the convergence properties of the derived HRDEs correspond to that of the starting discrete methods. Using these techniques, we show that the HRDE of Optimistic Gradient Descent Ascent (OGDA) has last-iterate convergence for general monotone variational inequalities. To our knowledge, this is the first continuous-time dynamics shown to converge for such a general setting. Moreover, we provide the rates for the best-iterate convergence of the OGDA method, relying solely on the first-order smoothness of the monotone operator.

A swarm intelligence-based optimization algorithm, named Duck Swarm Algorithm (DSA), is proposed in this paper. This algorithm is inspired by the searching for food sources and foraging behaviors of the duck swarm. The performance of DSA is verified by using eighteen benchmark functions, where it is statistical (best, mean, standard deviation, and average running time) results are compared with seven well-known algorithms like Particle swarm optimization (PSO), Firefly algorithm (FA), Chicken swarm optimization (CSO), Grey wolf optimizer (GWO), Sine cosine algorithm (SCA), and Marine-predators algorithm (MPA), and Archimedes optimization algorithm (AOA). Moreover, the Wilcoxon rank-sum test, Friedman test, and convergence curves of the comparison results are used to prove the superiority of the DSA against other algorithms. The results demonstrate that DSA is a high-performance optimization method in terms of convergence speed and exploration-exploitation balance for solving high-dimension optimization functions. Also, DSA is applied for the optimal design of two constrained engineering problems (the Three-bar truss problem, and the Sawmill operation problem). Additionally, four engineering constraint problems have also been used to analyze the performance of the proposed DSA. Overall, the comparison results revealed that the DSA is a promising and very competitive algorithm for solving different optimization problems.

If you are in the fields of data science or machine learning, chances are you already are doing optimization! For example, training a neural network is an optimization problem, as we want to find the set of model weights that best minimizes the loss function. Finding the set of hyper parameters that results in the best performing model is another optimization problem. Optimization algorithms come in many forms, each created to solve a particular type of problem. In particular, one type of problem commonly faced by scientists in both academia and industry is the optimization of expensive-to-evaluate black box functions.

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees, based on solving large semidefinite programs which are impractical to run, or make strong assumptions such as requiring the factors to be nearly orthogonal. In this paper we introduce a new variant of alternating minimization, which in turn is inspired by understanding how the progress measures that guide convergence of alternating minimization in the matrix setting need to be adapted to the tensor setting. We show strong provable guarantees, including showing that our algorithm converges linearly to the true tensors even when the factors are highly correlated and can be implemented in nearly linear time. Moreover our algorithm is also highly practical and we show that we can complete third order tensors with a thousand dimensions from observing a tiny fraction of its entries. In contrast, and somewhat surprisingly, we show that the standard version of alternating minimization, without our new twist, can converge at a drastically slower rate in practice.