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We present herein a new approach based on the simultaneous application of the deep learning and statistical physics methods to solve the combinatorial optimization problems. The recent modern advanced techniques, such as an artificial…
We study the problem of infinite-horizon average-reward reinforcement learning with linear Markov decision processes (MDPs). The associated Bellman operator of the problem not being a contraction makes the algorithm design challenging.…
The Maximum Cut (Max-Cut) problem could be naturally expressed either in a Quadratic Unconstrained Binary Optimization (QUBO) formulation, or as an Ising model. It has long been known that the Maximum Independent Set (MIS) problem could…
We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…
Combinatorial optimization is regarded as a potentially promising application of near and long-term quantum computers. The best-known heuristic quantum algorithm for combinatorial optimization on gate-based devices, the Quantum Approximate…
Given an edge-weighted graph $G$ on $n$ nodes, the NP-hard Max-Cut problem asks for a node bipartition such that the sum of edge weights joining the different partitions is maximized. We propose a fixed-parameter tractable algorithm…
In this paper, we consider reinforcement learning of nonlinear systems with continuous state and action spaces. We present an episodic learning algorithm, where we for each episode use convex optimization to find a two-layer neural network…
We study MaxCut on 3-regular graphs of minimum girth $g$ for various $g$'s. We obtain new lower bounds on the maximum cut achievable in such graphs by analyzing the Quantum Approximate Optimization Algorithm (QAOA). For $g \geq 16$, at…
Optimizing parameterized quantum circuits promises efficient use of near-term quantum computers to achieve the potential quantum advantage. However, there is a notorious tradeoff between the expressibility and trainability of the parameter…
In recent years, parameterized quantum circuits have become a major tool to design quantum algorithms for optimization problems. The challenge in fully taking advantage of a given family of parameterized circuits lies in finding a good set…
Structured pruning methods are developed to bridge the gap between the massive scale of neural networks and the limited hardware resources. Most current structured pruning methods rely on training datasets to fine-tune the compressed model,…
In a wide range of applications, we are required to rapidly solve a sequence of convex multiparametric quadratic programs (mp-QPs) on resource-limited hardwares. This is a nontrivial task and has been an active topic for decades in control…
Reinforcement Learning (RL) enhances LLM reasoning, yet a paradox emerges as models scale: strong base models saturate standard benchmarks (e.g., MATH), yielding correct but homogeneous solutions. In such environments, the lack of failure…
Decision diagrams (DDs) have emerged as a state-of-the-art method for exact multiobjective integer linear programming. When the DD is too large to fit into memory or the decision-maker prefers a fast approximation to the Pareto frontier,…
We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…
In contrast to the many continuous global optimization methods that assume the objective function and constraints are factorable, we study how to find globally maximal solutions to problems that are not factorable, focusing on a particular…
Generalized Benders decomposition (GBD) is a globally optimal algorithm for mixed integer nonlinear programming (MINLP) problems, which are NP-hard and can be widely found in the area of wireless resource allocation. The main idea of GBD is…
Hyperparameter optimization (HPO) is critical for enhancing the performance of machine learning models, yet it often involves a computationally intensive search across a large parameter space. Traditional approaches such as Grid Search and…
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
We introduce a quantum-inspired approximation algorithm for MaxCut based on low-depth Clifford circuits. We start by showing that the solution unitaries found by the adaptive quantum approximation optimization algorithm (ADAPT-QAOA) for the…