Related papers: Characterizing finite-dimensional quantum behavior
The Moment/Sum-of-squares hierarchy provides a way to compute the global minimizers of polynomial optimization problems (POP), at the cost of solving a sequence of increasingly large semidefinite programs (SDPs). We consider large-scale…
This paper introduces algorithms for problems where a decision maker has to control a system composed of several components and has access to only partial information on the state of each component. Such problems are difficult because of…
In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA). Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case…
Chordal and factor-width decomposition methods for semidefinite programming and polynomial optimization have recently enabled the analysis and control of large-scale linear systems and medium-scale nonlinear systems. Chordal decomposition…
The disorder parameter, defined as the expectation value of the symmetry transformation acting on a subsystem, can be used to characterize symmetric phases as an analogy to detecting spontaneous symmetry breaking (SSB) phases using local…
Automated hyperparameter optimization (HPO) can support practitioners to obtain peak performance in machine learning models. However, there is often a lack of valuable insights into the effects of different hyperparameters on the final…
The unconstrained binary quadratic programming (UBQP) problem is a class of problems of significant importance in many practical applications, such as in combinatorial optimization, circuit design, and other fields. The positive…
In this paper, we study a class of fractional semi-infinite polynomial programming (FSIPP) problems, in which the objective is a fraction of a convex polynomial and a concave polynomial, and the constraints consist of infinitely many convex…
An important problem in quantum information theory is that of bounding sets of correlations that arise from making local measurements on entangled states of arbitrary dimension. Currently, the best-known method to tackle this problem is the…
We provide a new hierarchy of semidefinite programming relaxations, called NCTSSOS, to solve large-scale sparse noncommutative polynomial optimization problems. This hierarchy features the exploitation of term sparsity hidden in the input…
A major obstacle for quantum optimizers is the reformulation of constraints as a quadratic unconstrained binary optimization (QUBO). Current QUBO translators exaggerate the weight $M$ of the penalty terms. Classically known as the "Big-$M$"…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
This paper investigates the minimization of the expectation of piecewise polynomial loss functions over Wasserstein balls. This optimization problem often appears as a key sub-problem of distributionally robust optimization problems. We…
We introduce a quantum dynamic programming framework that allows us to directly extend to the quantum realm a large body of classical dynamic programming algorithms. The corresponding quantum dynamic programming algorithms retain the same…
Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to…
Search-based software engineering (SBSE) addresses critical optimization challenges in software engineering, including the next release problem (NRP) and feature selection problem (FSP). While traditional heuristic approaches and integer…
Sequential Quantum State Discrimination (SQSD) can be naturally framed as a sequential decision-making problem: at each time step, an agent must decide whether to perform an additional measurement to gather more information or to conclude…
Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit…
Many statistical learning problems have recently been shown to be amenable to Semi-Definite Programming (SDP), with community detection and clustering in Gaussian mixture models as the most striking instances [javanmard et al., 2016]. Given…
Decoders are a critical component of fault-tolerant quantum computing. They must identify errors based on syndrome measurements to correct quantum states. While finding the optimal correction is NP-hard and thus extremely difficult,…