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In this paper, we study the computational complexity of the quadratic unconstrained binary optimization (QUBO) problem under the functional problem FP^NP categorization. We focus on four sub-classes: (1) When all coefficients are integers…
Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is…
Efficiently optimizing Nondeterministic Polynomial time (NP) problems in polynomial time has profound implications in many domains. CMOS oscillator networks have been shown to be effective and efficient in approximating certain NP-hard…
Predictive combinatorial optimization, where the parameters of combinatorial optimization (CO) are unknown at the decision-making time, is the precise modeling of many real-world applications, including energy cost-aware scheduling and…
The minimum linear ordering problem (MLOP) generalizes well-known combinatorial optimization problems such as minimum linear arrangement and minimum sum set cover. MLOP seeks to minimize an aggregated cost $f(\cdot)$ due to an ordering…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
In this work we advance the understanding of the fundamental limits of computation for Binary Polynomial Optimization (BPO), which is the problem of maximizing a given polynomial function over all binary points. In our main result we…
Combinatorial Optimisation problems arise in several application domains and are often formulated in terms of graphs. Many of these problems are NP-hard, but exact solutions are not always needed. Several heuristics have been developed to…
Real-world problems of operations research are typically high-dimensional and combinatorial. Linear programs are generally used to formulate and efficiently solve these large decision problems. However, in multi-period decision problems, we…
The OSCAR (octagonal selection and clustering algorithm for regression) regularizer consists of a L_1 norm plus a pair-wise L_inf norm (responsible for its grouping behavior) and was proposed to encourage group sparsity in scenarios where…
We study the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…
Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate complex form over various popular constraint sets including…
Bayesian optimization has been challenged by datasets with large-scale, high-dimensional, and non-stationary characteristics, which are common in real-world scenarios. Recent works attempt to handle such input by applying neural networks…
DPO (Direct Preference Optimization) has become a widely used offline preference optimization algorithm due to its simplicity and training stability. However, DPO is prone to overfitting and collapse. To address these challenges, we propose…
Deep Optimisation (DO) combines evolutionary search with Deep Neural Networks (DNNs) in a novel way - not for optimising a learning algorithm, but for finding a solution to an optimisation problem. Deep learning has been successfully…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
For many applications of reinforcement learning it can be more convenient to specify both a reward function and constraints, rather than trying to design behavior through the reward function. For example, systems that physically interact…
Robust optimization is concerned with constructing solutions that remain feasible also when a limited number of resources is removed from the solution. Most studies of robust combinatorial optimization to date made the assumption that every…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…