Related papers: Smoothed Analysis of the Minimum-Mean Cycle Cancel…
We present several new results about smoothed analysis of multiobjective optimization problems. Motivated by the discrepancy between worst-case analysis and practical experience, this line of research has gained a lot of attention in the…
We show that the smoothed complexity of the FLIP algorithm for local Max-Cut is at most $\smash{\phi n^{O(\sqrt{\log n})}}$, where $n$ is the number of nodes in the graph and $\phi$ is a parameter that measures the magnitude of…
In the present paper, we apply the network simplex algorithm for solving the minimum cost flow problem, to the maximum flow problem. Then we prove that the cycling phenomenon which causes the infinite loop in the algorithm, does not occur…
This paper looks at two problems, minimum constrained input selection and minimum cost constrained input selection for state space structured systems. The input matrix is constrained in the sense that the set of states that each input can…
We consider the task of minimizing the sum of convex functions stored in a decentralized manner across the nodes of a communication network. This problem is relatively well-studied in the scenario when the objective functions are smooth, or…
Machine learning (ML) algorithms are remarkably good at approximating complex non-linear relationships. Most ML training processes, however, are designed to deliver ML tools with good average performance, but do not offer any guarantees…
We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics,…
Narrowing the gap between theory and practice is a longstanding goal of the algorithm analysis community. To further progress our understanding of how algorithms work in practice, we propose a new algorithm analysis framework that we call…
The minimum cost flow problem is one of the most studied network optimization problems and appears in numerous applications. Some efficient algorithms exist for this problem, which are freely available in the form of libraries or software…
We study a class of stochastic nonconvex optimization in the form of $\min_{x\in\mathcal{X}} F(x):=\mathbb{E}_\xi [f(\phi(x,\xi))]$, i.e., $F$ is a composition of a convex function $f$ and a random function $\phi$. Leveraging an (implicit)…
We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy…
Secure multi-party computation (SMC) techniques are increasingly becoming more efficient and practical thanks to many recent novel improvements. The recent work have shown that different protocols that are implemented using different…
We consider the CONGEST model on a network with $n$ nodes, $m$ edges, diameter $D$, and integer costs and capacities bounded by $\text{poly} n$. In this paper, we show how to find an exact solution to the minimum cost flow problem in…
We initiate the study of smoothed analysis for the sequential probability assignment problem with contexts. We study information-theoretically optimal minmax rates as well as a framework for algorithmic reduction involving the maximum…
The approximation ratio has become one of the dominant measures in mechanism design problems. In light of analysis of algorithms, we define the \emph{smoothed approximation ratio} to compare the performance of the optimal mechanism and a…
We investigate the complexity and approximability of the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total value…
Minimum Weight Cycle (MWC) is the problem of finding a simple cycle of minimum weight in a graph $G=(V,E)$. This is a fundamental graph problem with classical sequential algorithms that run in $\tilde{O}(n^3)$ and $\tilde{O}(mn)$ time where…
Bayesian modelling and computational inference by Markov chain Monte Carlo (MCMC) is a principled framework for large-scale uncertainty quantification, though is limited in practice by computational cost when implemented in the simplest…
Motivated by the emergence of federated learning (FL), we design and analyze federated methods for addressing: (i) Nondifferentiable nonconvex optimization; (ii) Bilevel optimization; (iii) Minimax problems; and (iv) Two-stage stochastic…
Inexact methods for model predictive control (MPC), such as real-time iterative schemes or time-distributed optimization, alleviate the computational burden of exact MPC by providing suboptimal solutions. While the asymptotic stability of…