Related papers: When Gravity Fails: Local Search Topology
Variational quantum algorithms are viewed as promising candidates for demonstrating quantum advantage on near-term devices. These approaches typically involve the training of parameterized quantum circuits through a classical optimization…
A variety of strategies have been proposed for overcoming local optimality in metaheuristic search. This paper examines characteristics of moves that can be exploited to make good decisions about steps that lead away from a local optimum…
In this paper, we study the complexity of computing locally optimal solutions for weighted versions of standard set problems such as SetCover, SetPacking, and many more. For our investigation, we use the framework of PLS, as defined in…
Iteration complexities for optimizing smooth functions with first-order algorithms are typically stated in terms of a global Lipschitz constant of the gradient, and near-optimal results are then achieved using fixed step sizes. But many…
We study the task of finding good local optima in combinatorial optimization problems. Although combinatorial optimization is NP-hard in general, locally optimal solutions are frequently used in practice. Local search methods however…
We propose a family of nonconvex optimization algorithms that are able to save gradient and negative curvature computations to a large extent, and are guaranteed to find an approximate local minimum with improved runtime complexity. At the…
A major obstacle to non-convex optimization is the problem of getting stuck in local minima. We introduce a novel metaheuristic to handle this issue, creating an alternate Hamiltonian that shares minima with the original Hamiltonian only…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
We study the performance of stochastic local search algorithms for random instances of the $K$-satisfiability ($K$-SAT) problem. We introduce a new stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a…
Solving topological grid puzzles requires reasoning over global spatial invariants such as connectivity, loop closure, and region symmetry and remains challenging for even the most powerful large language models (LLMs). To study these…
Algorithms for computing local minima of smooth objective functions enjoy a mature theory as well as robust and efficient implementations. By comparison, the theory and practice of saddle search is destitute. In this paper we present…
There has been a lot of recent interest in trying to characterize the error surface of deep models. This stems from a long standing question. Given that deep networks are highly nonlinear systems optimized by local gradient methods, why do…
More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…
Local search heuristics for non-convex optimizations are popular in applied machine learning. However, in general it is hard to guarantee that such algorithms even converge to a local minimum, due to the existence of complicated saddle…
Memetic algorithms are popular hybrid search heuristics that integrate local search into the search process of an evolutionary algorithm in order to combine the advantages of rapid exploitation and global optimisation. However, these…
In this paper the approach to solving several combinatorial optimization problems using the local search and the genetic algorithm techniques is proposed. Initially this approach was developed in purpose to overcome some difficulties…
Local Policy Search is a popular reinforcement learning approach for handling large state spaces. Formally, it searches locally in a paramet erized policy space in order to maximize the associated value function averaged over some…
The existence of barren plateaus has recently revealed new training challenges in quantum machine learning (QML). Uncovering the mechanisms behind barren plateaus is essential in understanding the scope of problems that QML can efficiently…
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the…
We present a data mining approach for reducing the search space of local search algorithms in a class of binary integer programs including the set covering and partitioning problems. The quality of locally optimal solutions typically…