相关论文: Q-curve and area rules for choosing heuristic para…

Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and…

Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate algorithm for solving combinatorial optimization problems on quantum computers. However, in many cases QAOA requires computationally intensive parameter optimization.…

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…

We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…

For a generic set of Markovian noise models, the estimation precision of a parameter associated with the Hamiltonian is limited by the $1/\sqrt{t}$ scaling where $t$ is the total probing time, in which case the maximal possible quantum…

In a Hilbert framework, we consider an inertial Tikhonov regularized dynamical system governed by a maximally comonotone operator, where the damping coefficient is proportional to the square root of the Tikhonov regularization parameter.…

Quantum annealing (QA) holds promise for optimization problems in quantum computing, especially for combinatorial optimization. This analog framework attracts attention for its potential to address complex problems. Its gate-based…

We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression. More precisely, we analyze estimators arising from a linear regularization scheme $g_\lam$. In practical applications, an…

As robots are being integrated into our daily lives, it becomes necessary to provide guarantees on the safe and provably correct operation. Such guarantees can be provided using automata theoretic task and mission planning where the…

High-order tensor methods for solving both convex and nonconvex optimization problems have generated significant research interest, leading to algorithms with optimal global rates of convergence and local rates that are faster than Newton's…

We study a Q learning algorithm for continuous time stochastic control problems. The proposed algorithm uses the sampled state process by discretizing the state and control action spaces under piece-wise constant control processes. We show…

The minimum accuracy heuristic evaluates quantum feature maps without requiring full quantum support vector machine (QSVM) training. However, the original formulation is computationally expensive, restricted to balanced datasets, and lacks…

We describe a measure quantization procedure i.e., an algorithm which finds the best approximation of a target probability law (and more generally signed finite variation measure) by a sum of $Q$ Dirac masses ($Q$ being the quantization…

This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…

Regularized Markov Decision Processes serve as models of sequential decision making under uncertainty wherein the decision maker has limited information processing capacity and/or aversion to model ambiguity. With functional approximation,…

Conditional stability estimates are a popular tool for the regularization of ill-posed problems. A drawback in particular under nonlinear operators is that additional regularization is needed for obtaining stable approximate solutions if…

This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: minimize f(x):=h(c(x)), where h is an infinite-valued proper convex function and c is C^2-smooth. We focus on the case…

We address the inverse problem of local volatility surface calibration from market given option prices. We integrate the ever-increasing flow of option price information into the well-accepted local volatility model of Dupire. This leads to…

Further studies on the corner singularity of GS reconstruction are are compiled in this paper. It's focused on solution of the Data Completion (DC) problem with the Extended Hilbert Transform (EHT) over plane rectangular region. Optimal…

To deal with the ill-posed nature of the inverse heat conduction problem (IHCP), the regularization parameter alpha can be incorporated into a minimization problem, which is known as Tikhonov regularization method, a popular technique to…