Author name cluster

Aaron M. Ferber

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

7 papers

2 author rows

AAAI Conference 2026 Conference Paper

Unsupervised Combinatorial Probabilistic Reasoning: Probabilistic Coin Change Problem

Zhongdi Qu
Yingheng Wang
Utku Umur Acikalin
Aaron M. Ferber
Goncalo J. Gouveia
Brandon Bills
Guohui Li
Joshua Kline

We introduce the Probabilistic Coin Change Problem (PCCP), a novel variant of the classical Combination Coin Change Problem (CCCP), motivated by a real-world scientific inverse task. The goal of CCCP is to enumerate all unordered combinations of coin denominations that sum to a given target. In PCCP, each coin type’s value follows a discrete probability distribution, and the aggregate value of a combination of coins is thus stochastic. Given a set of such coin types and noisy observations of total sums, the task is to infer the most likely latent coin combination. To address the combinatorial and probabilistic complexity of PCCP, we propose DeepProReasoner (Deep Combinatorial Probabilistic Reasoning with Embedded Representations), an unsupervised, end-to-end, deep-learning framework that integrates combinatorial reasoning, latent-space modeling, and differentiable probabilistic reasoning. The model is trained using a reconstruction loss between the observed empirical distribution and a decoded probability mass function (PMF), enabling efficient gradient-based search over a continuous relaxation of the combinatorial space. We evaluate DeepProReasoner on two instances of PCCP: (1) a synthetic Candy Mix problem for ablation studies, and (2) a real-world task of molecular formula inference from ultrahigh resolution mass spectrometry (MS) data. Besides the two given instances, PCCP captures a wide range of inverse settings in biology, chemistry, environmental sciences, and medicine, where latent combinatorial structures give rise to noisy aggregate observations through stochastic processes. Our results show that DeepProReasoner achieves high accuracy and robustness, outperforming state-of-the-art methods.

PDF Details DOI

ICLR Conference 2025 Conference Paper

Learning to Explore and Exploit with GNNs for Unsupervised Combinatorial Optimization

Utku Umur Acikalin
Aaron M. Ferber
Carla P. Gomes

Combinatorial optimization (CO) problems are pervasive across various domains, but their NP-hard nature often necessitates problem-specific heuristic algorithms. Recent advancements in deep learning have led to the development of learning-based heuristics, yet these approaches often struggle with limited search capabilities. We introduce Explore-and-Exploit GNN ($X^2$GNN, pronounced x-squared GNN), a novel unsupervised neural framework that combines exploration and exploitation for combinatorial search optimization: i) Exploration - $X^2$GNN generates multiple solutions simultaneously, promoting diversity in the search space; (ii) Exploitation - $X^2$GNN employs neural stochastic iterative refinement to exploit partial existing solutions, guiding the search toward promising regions and helping escape local optima. By balancing exploration and exploitation, $X^2$GNN achieves superior performance and generalization on several graph CO problems including Max Cut, Max Independent Set, and Max Clique. Notably, for large Max Clique problems, $X^2$GNN consistently generates solutions within 1.2\% of optimality, while other state-of-the-art learning-based approaches struggle to reach within 22\% of optimal. Moreover, $X^2$GNN consistently generates better solutions than Gurobi on large graphs for all three problems under reasonable time budgets. Furthermore, $X^2$GNN exhibits exceptional generalization capabilities. For the Maximum Independent Set problem, $X^2$GNN outperforms state-of-the-art methods even when trained on smaller or out-of-distribution graphs compared to the test set. Our framework offers a more effective and flexible approach to neural combinatorial optimization, addressing a key challenge in the field and providing a promising direction for future research in learning-based heuristics for combinatorial optimization.

Details

ICML Conference 2024 Conference Paper

Contrastive Predict-and-Search for Mixed Integer Linear Programs

Taoan Huang
Aaron M. Ferber
Arman Zharmagambetov
Yuandong Tian
Bistra Dilkina

Mixed integer linear programs (MILP) are flexible and powerful tools for modeling and solving many difficult real-world combinatorial optimization problems. In this paper, we propose a novel machine learning (ML)-based framework ConPaS that learns to predict solutions to MILPs with contrastive learning. For training, we collect high-quality solutions as positive samples. We also collect low-quality or infeasible solutions as negative samples using novel optimization-based or sampling approaches. We then learn to make discriminative predictions by contrasting the positive and negative samples. During testing, we predict and fix the assignments for a subset of integer variables and then solve the resulting reduced MILP to find high-quality solutions. Empirically, ConPaS achieves state-of-the-art results compared to other ML-based approaches in terms of the quality of and the speed at which solutions are found.

Details

ICML Conference 2024 Conference Paper

GenCO: Generating Diverse Designs with Combinatorial Constraints

Aaron M. Ferber
Arman Zharmagambetov
Taoan Huang
Bistra Dilkina
Yuandong Tian

Deep generative models like GAN and VAE have shown impressive results in generating unconstrained objects like images. However, many design settings arising in industrial design, material science, computer graphics and more require that the generated objects satisfy hard combinatorial constraints or meet objectives in addition to modeling a data distribution. To address this, we propose GenCO, a generative framework that guarantees constraint satisfaction throughout training by leveraging differentiable combinatorial solvers to enforce feasibility. GenCO imposes the generative loss on provably feasible solutions rather than intermediate soft solutions, meaning that the deep generative network can focus on ensuring the generated objects match the data distribution without having to also capture feasibility. This shift enables practitioners to enforce hard constraints on the generated outputs during end-to-end training, enabling assessments of their feasibility and introducing additional combinatorial loss components to deep generative training. We demonstrate the effectiveness of our approach on a variety of generative combinatorial tasks, including game level generation, map creation for path planning, and photonic device design, consistently demonstrating its capability to yield diverse, high-quality solutions that verifiably adhere to user-specified combinatorial properties.

Details

ICML Conference 2023 Conference Paper

Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning

Taoan Huang
Aaron M. Ferber
Yuandong Tian
Bistra Dilkina
Benoit Steiner

Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high-quality solutions to ILPs faster than Branch and Bound. However, how to find the right heuristics to maximize the performance of LNS remains an open problem. In this paper, we propose a novel approach, CL-LNS, that delivers state-of-the-art anytime performance on several ILP benchmarks measured by metrics including the primal gap, the primal integral, survival rates and the best performing rate. Specifically, CL-LNS collects positive and negative solution samples from an expert heuristic that is slow to compute and learns a more efficient one with contrastive learning. We use graph attention networks and a richer set of features to further improve its performance.

Details

ICML Conference 2023 Conference Paper

SurCo: Learning Linear SURrogates for COmbinatorial Nonlinear Optimization Problems

Aaron M. Ferber
Taoan Huang
Daochen Zha
Martin Schubert
Benoit Steiner
Bistra Dilkina
Yuandong Tian

Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose $\textbf{\emph{\texttt{SurCo}}}$ that learns linear $\underline{\text{Sur}}$rogate costs which can be used in existing $\underline{\text{Co}}$mbinatorial solvers to output good solutions to the original nonlinear combinatorial optimization problem. The surrogate costs are learned end-to-end with nonlinear loss by differentiating through the linear surrogate solver, combining the flexibility of gradient-based methods with the structure of linear combinatorial optimization. We propose three $\texttt{SurCo}$ variants: $\texttt{SurCo}-\texttt{zero}$ for individual nonlinear problems, $\texttt{SurCo}-\texttt{prior}$ for problem distributions, and $\texttt{SurCo}-\texttt{hybrid}$ to combine both distribution and problem-specific information. We give theoretical intuition motivating $\texttt{SurCo}$, and evaluate it empirically. Experiments show that $\texttt{SurCo}$ finds better solutions faster than state-of-the-art and domain expert approaches in real-world optimization problems such as embedding table sharding, inverse photonic design, and nonlinear route planning.

Details

SoCS Conference 2021 Conference Paper

Learning Pseudo-Backdoors for Mixed Integer Programs

Aaron M. Ferber
Jialin Song
Bistra Dilkina
Yisong Yue

We propose a machine learning approach for quickly solving Mixed Integer Programs (MIP) by learning to prioritize a set of decision variables, which we call pseudo-backdoors, for branching that results in faster solution times. Learning-based approaches have seen success in the area of solving combinatorial optimization problems by being able to flexibly leverage common structures in a given distribution of problems. Our approach takes inspiration from the concept of strong backdoors, which corresponds to a small set of variables such that only branching on these variables yields an optimal integral solution and a proof of optimality. Our notion of pseudo-backdoors corresponds to a small set of variables such that only branching on them leads to faster solve time (which can be solver dependent). A key advantage of pseudo-backdoors over strong backdoors is that they are much amenable to data-driven identification or prediction. Our proposed method learns to estimate the solver performance of a proposed pseudo-backdoor, using a labeled dataset collected on a set of training MIP instances. This model can then be used to identify high-quality pseudo-backdoors on new MIP instances from the same distribution. We evaluate our method on the generalized independent set problems and find that our approach can efficiently identify high-quality pseudo-backdoors. In addition, we compare our learned approach against Gurobi, a state-of-the-art MIP solver, demonstrating that our method can be used to improve solver performance.

Details