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Lagrangian relaxation stands among the most efficient approaches for solving a Mixed Integer Linear Programs (MILP) with difficult constraints. Given any duals for these constraints, called Lagrangian Multipliers (LMs), it returns a bound…
Stochastic variance-reduced gradient (SVRG) algorithms have been shown to work favorably in solving large-scale learning problems. Despite the remarkable success, the stochastic gradient complexity of SVRG-type algorithms usually scales…
We study convex optimization problems under differential privacy (DP). With heavy-tailed gradients, existing works achieve suboptimal rates. The main obstacle is that existing gradient estimators have suboptimal tail properties, resulting…
This paper considers optimization problems on Riemannian manifolds and analyzes iteration-complexity for gradient and subgradient methods on manifolds with non-negative curvature. By using tools from the Riemannian convex analysis and…
In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…
Datalogo is an extension of Datalog that allows for aggregation and recursion over an arbitrary commutative semiring. Like Datalog, Datalogo programs can be evaluated via the natural iterative algorithm until a fixed point is reached.…
Policy gradient (PG) methods are a class of effective reinforcement learning algorithms, particularly when dealing with continuous control problems. They rely on fresh on-policy data, making them sample-inefficient and requiring…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
The analysis of the solving complexity of random 3-SAT instances using the Davis-Putnam-Loveland-Logemann (DPLL) algorithm slightly below threshold is presented. While finding a solution for such instances demands exponential effort with…
Algorithms for bilevel optimization often encounter Hessian computations, which are prohibitive in high dimensions. While recent works offer first-order methods for unconstrained bilevel problems, the constrained setting remains relatively…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
The low-rank matrix recovery problem seeks to reconstruct an unknown $n_1 \times n_2$ rank-$r$ matrix from $m$ linear measurements, where $m\ll n_1n_2$. This problem has been extensively studied over the past few decades, leading to a…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
In this paper, we analyze the generalization performance of the Iterative Hard Thresholding (IHT) algorithm widely used for sparse recovery problems. The parameter estimation and sparsity recovery consistency of IHT has long been known in…
This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…
In distributed stochastic optimization, where parallel and asynchronous methods are employed, we establish optimal time complexities under virtually any computation behavior of workers/devices/CPUs/GPUs, capturing potential disconnections…
This article presents a numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming (LP) problem. Each iteration of the proposed algorithm consists of two Gauss-Jordan pivoting…
We propose a sampling algorithm that achieves superior complexity bounds in all the classical settings (strongly log-concave, log-concave, Logarithmic-Sobolev inequality (LSI), Poincar\'e inequality) as well as more general settings with…
We study the $(\varepsilon, \delta)$-PAC policy identification problem in finite-horizon episodic Markov Decision Processes. Existing approaches provide finite-time guarantees for approximate settings ($\varepsilon>0$) but suffer from high…