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We are interested in the intersection of approximation algorithms and complexity theory, in particular focusing on the complexity class APX. Informally, APX $\subseteq$ NPO is the complexity class comprising optimization problems where the…
Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…
Learning to optimize (L2O) has recently emerged as a promising approach to solving optimization problems by exploiting the strong prediction power of neural networks and offering lower runtime complexity than conventional solvers. While L2O…
Solving NP-hard/complete combinatorial problems with neural networks is a challenging research area that aims to surpass classical approximate algorithms. The long-term objective is to outperform hand-designed heuristics for…
Assigning jobs onto identical machines with the objective to minimize the maximal load is one of the most basic problems in combinatorial optimization. Motivated by product planing and data placement, we study a natural extension called…
Nonconvex optimization problems with an L1-constraint are ubiquitous, and are found in many application domains including: optimal control of hybrid systems, machine learning and statistics, and operations research. This paper shows that…
Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require…
Neural Combinatorial Optimization (NCO) has emerged as a promising approach for NP-hard problems. However, prevailing RL-based methods suffer from low sample efficiency due to sparse rewards and underused solutions. We propose Best-anchored…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
Optimization problems pervade essentially every scientific discipline and industry. Many such problems require finding a solution that maximizes the number of constraints satisfied. Often, these problems are particularly difficult to solve…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
Combinatorial optimization (CO) is the fundamental problem at the intersection of computer science, applied mathematics, etc. The inherent hardness in CO problems brings up challenge for solving CO exactly, making deep-neural-network-based…
Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with…
We give a unified treatment to optimization problems that can be expressed in the form of nonnegative-real-weighted Boolean constraint satisfaction problems. Creignou, Khanna, Sudan, Trevisan, and Williamson studied the complexity of…
Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…
Nonlinear robust optimization (NRO) is widely used in different applications, including energy, control, and economics, to make robust decisions under uncertainty. One of the classical solution methods in NRO is an outer approximation…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
In neural combinatorial optimization (CO), reinforcement learning (RL) can turn a deep neural net into a fast, powerful heuristic solver of NP-hard problems. This approach has a great potential in practical applications because it allows…
The proximal policy optimization (PPO) algorithm stands as one of the most prosperous methods in the field of reinforcement learning (RL). Despite its success, the theoretical understanding of PPO remains deficient. Specifically, it is…
Proximal Policy Optimization (PPO) dominates reinforcement learning and LLM alignment but relies on a "hard clipping" mechanism that discards valuable gradients. Conversely, unconstrained methods like SPO expose the optimization to…