Related papers: Path optimization method for the sign problem caus…
In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…
Many optimization problems require balancing multiple conflicting objectives. As gradient descent is limited to single-objective optimization, we introduce its direct generalization: Jacobian descent (JD). This algorithm iteratively updates…
This article provides a comprehensive understanding of optimization in deep learning, with a primary focus on the challenges of gradient vanishing and gradient exploding, which normally lead to diminished model representational ability and…
Simulation of interacting fermionic Hamiltonians is one of the most promising applications of quantum computers. However, the feasibility of analysing fermionic systems with a quantum computer hinges on the efficiency of fermion-to-qubit…
We propose a novel Riemannian method for solving the Extreme multi-label classification problem that exploits the geometric structure of the sparse low-dimensional local embedding models. A constrained optimization problem is formulated as…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
Uncertainty in optimization is often represented as stochastic parameters in the optimization model. In Predict-Then-Optimize approaches, predictions of a machine learning model are used as values for such parameters, effectively…
This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural…
Safe path planning is a crucial component in autonomous robotics. The many approaches to find a collision free path can be categorically divided into trajectory optimisers and sampling-based methods. When planning using occupancy maps, the…
Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
In this paper we address several constrained transportation optimization problems (e.g. vehicle routing, shortest Hamiltonian path), for which we present novel algorithmic solutions and extensions, considering several optimization…
The generalized thimble method to treat field theories with sign problems requires repeatedly solving the computationally-expensive holomorphic flow equations. We present a machine learning technique to bypass this problem. The central idea…
Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem…
An effective numerical method is presented for optimizing model parameters that can be applied to any type of system of non-linear equations and any number of data-points, which does not require explicit formulation of the objective…
Symbolic regression is a machine learning technique, and it has seen many advancements in recent years, especially in genetic programming approaches (GPSR). Furthermore, it has been known for many years that constant optimization of…
This study presents a robust optimization algorithm for automated highway merge. The merging scenario is one of the challenging scenes in automated driving, because it requires adjusting ego vehicle's speed to match other vehicles before…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Thimble regularisation of lattice field theories has been proposed as a solution to the infamous sign problem. It is conceptually very clean and powerful, but it is in practice limited by a potentially very serious issue: in general many…