Related papers: Moduli space of optimization algorithms

We present a parallelized primal-dual algorithm for solving constrained convex optimization problems. The algorithm is "block-based," in that vectors of primal and dual variables are partitioned into blocks, each of which is updated only by…

Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime…

Variational quantum algorithms are a leading candidate for early applications on noisy intermediate-scale quantum computers. These algorithms depend on a classical optimization outer-loop that minimizes some function of a parameterized…

A fundamental task underlying many important optimization problems, from influence maximization to sensor placement to content recommendation, is to select the optimal group of $k$ items from a larger set. Submodularity has been very…

The sliding cubes model is a well-established theoretical framework that supports the analysis of reconfiguration algorithms for modular robots consisting of face-connected cubes. The best algorithm currently known for the reconfiguration…

We investigate the convergence properties of a class of iterative algorithms designed to minimize a potentially non-smooth and noisy objective function, which may be algebraically intractable and whose values may be obtained as the output…

Robust optimization (RO) is one of the key paradigms for solving optimization problems affected by uncertainty. Two principal approaches for RO, the robust counterpart method and the adversarial approach, potentially lead to excessively…

Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

In data-driven optimization, solution feasibility is often ensured through a "safe" reformulation of the uncertain constraints, such that an obtained data-driven solution is guaranteed to be feasible for the oracle formulation with high…

Submodularity is one of the most well-studied properties of problem classes in combinatorial optimization and many applications of machine learning and data mining, with strong implications for guaranteed optimization. In this thesis, we…

Convex optimization problems with staged structure appear in several contexts, including optimal control, verification of deep neural networks, and isotonic regression. Off-the-shelf solvers can solve these problems but may scale poorly. We…

Feedback optimization has emerged as a promising approach for regulating dynamical systems to optimal steady states that are implicitly defined by underlying optimization problems. Despite their effectiveness, existing methods face two key…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…

This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an…

In this paper, we focus on applications in machine learning, optimization, and control that call for the resilient selection of a few elements, e.g. features, sensors, or leaders, against a number of adversarial denial-of-service attacks or…

Classes of set functions along with a choice of ground set are a bedrock to determine and develop corresponding variants of greedy algorithms to obtain efficient solutions for combinatorial optimization problems. The class of approximate…

This work addresses the instability in asynchronous data parallel optimization. It does so by introducing a novel distributed optimizer which is able to efficiently optimize a centralized model under communication constraints. The optimizer…

In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on…