Related papers: When Gravity Fails: Local Search Topology

A recent development in Bayesian optimization is the use of local optimization strategies, which can deliver strong empirical performance on high-dimensional problems compared to traditional global strategies. The "folk wisdom" in the…

We investigate the landscape of the negative log-likelihood function of Gaussian Mixture Models (GMMs) with a general number of components in the population limit. As the objective function is non-convex, there can be multiple local minima…

This is a survey of "Iterated Local Search", a general purpose metaheuristic for finding good solutions of combinatorial optimization problems. It is based on building a sequence of (locally optimal) solutions by: (1) perturbing the current…

We propose a novel optimization algorithm for continuous functions using geodesics and contours under conformal mapping.The algorithm can find multiple optima by first following a geodesic curve to a local optimum then traveling to the next…

In this paper, we present a method using AI techniques to solve a case of pure mathematics applications for finding narrow admissible tuples. The original problem is formulated into a combinatorial optimization problem. In particular, we…

We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle…

We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to…

Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they…

We propose a new Pareto Local Search Algorithm for the many-objective combinatorial optimization. Pareto Local Search proved to be a very effective tool in the case of the bi-objective combinatorial optimization and it was used in a number…

A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…

Online algorithms make decisions based on past inputs. In general, the decision may depend on the entire history of inputs. If many computers run the same online algorithm with the same input stream but are started at different times, they…

The properties of local optimal solutions in multi-objective combinatorial optimization problems are crucial for the effectiveness of local search algorithms, particularly when these algorithms are based on Pareto dominance. Such local…

Low-rank matrix sensing is a fundamental yet challenging nonconvex problem whose optimization landscape typically contains numerous spurious local minima, making it difficult for gradient-based optimizers to converge to the global optimum.…

Local search algorithms applied to optimization problems often suffer from getting trapped in a local optimum. The common solution for this deficiency is to restart the algorithm when no progress is observed. Alternatively, one can start…

We show a principled way of deriving online learning algorithms from a minimax analysis. Various upper bounds on the minimax value, previously thought to be non-constructive, are shown to yield algorithms. This allows us to seamlessly…

Despite the fact that the loss functions of deep neural networks are highly non-convex, gradient-based optimization algorithms converge to approximately the same performance from many random initial points. One thread of work has focused on…

We elaborate on the principle that for gapped quantum spin systems with local interaction "local perturbations [in the Hamiltonian] perturb locally [the ground state]". This principle was established in [Bachmann et al. 2012], relying on…

Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…

To deal with the complexity of the new bigger and more complex generation of data, machine learning (ML) techniques are probably the first and foremost used. For ML algorithms to produce results in a reasonable amount of time, they need to…

Machine learning models have prevalent applications in many real-world problems, which increases the importance of correctness in the behaviour of these trained models. Finding a good test case that can reveal the potential failure in these…