Bistra Dilkina

Taoan Huang, Aaron Ferber, Yuandong Tian et al.

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 new one with a contrastive loss. We use graph attention networks and a richer set of features to further improve its performance.

Arman Zharmagambetov, Brandon Amos, Aaron Ferber et al.

Recent works in learning-integrated optimization have shown promise in settings where the optimization problem is only partially observed or where general-purpose optimizers perform poorly without expert tuning. By learning an optimizer $\mathbf{g}$ to tackle these challenging problems with $f$ as the objective, the optimization process can be substantially accelerated by leveraging past experience. The optimizer can be trained with supervision from known optimal solutions or implicitly by optimizing the compound function $f\circ \mathbf{g}$. The implicit approach may not require optimal solutions as labels and is capable of handling problem uncertainty; however, it is slow to train and deploy due to frequent calls to optimizer $\mathbf{g}$ during both training and testing. The training is further challenged by sparse gradients of $\mathbf{g}$, especially for combinatorial solvers. To address these challenges, we propose using a smooth and learnable Landscape Surrogate $M$ as a replacement for $f\circ \mathbf{g}$. This surrogate, learnable by neural networks, can be computed faster than the solver $\mathbf{g}$, provides dense and smooth gradients during training, can generalize to unseen optimization problems, and is efficiently learned via alternating optimization. We test our approach on both synthetic problems, including shortest path and multidimensional knapsack, and real-world problems such as portfolio optimization, achieving comparable or superior objective values compared to state-of-the-art baselines while reducing the number of calls to $\mathbf{g}$. Notably, our approach outperforms existing methods for computationally expensive high-dimensional problems.

Aaron Ferber, Taoan Huang, Daochen Zha et al.

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 $\textbf{SurCo}$ 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.

Junyang Cai, Weimin Huang, Brendan Long et al.

Autonomous systems must solve motion planning problems subject to increasingly complex, time-sensitive, and uncertain missions. These problems often involve high-level task specifications, such as temporal logic or chance constraints, which require solving large-scale Mixed-Integer Linear Programs (MILPs). However, existing MILP-based planning methods suffer from high computational cost and limited scalability, hindering their real-time applicability. We propose to use a neuro-symbolic approach to accelerate MILP-based motion planning by leveraging machine learning techniques to guide the solver's symbolic search. Focusing on three representative classes of diverse planning problems - Signal Temporal Logic (STL) specifications, chance constraints formulated via Conformal Predictive Programming (CPP), and Capability Temporal Logic (CaTL) specifications - we demonstrate how graph neural network-based learning methods can guide traditional symbolic MILP solvers in solving challenging planning problems, including branching variable selection and solver parameter configuration. Through extensive experiments, we show that neuro-symbolic search techniques yield scalability gains. Our approach yields substantial improvements across all three classes of planning problems, achieving an average performance gain of about 20% over state-of-the-art solver across key metrics, including runtime and solution quality.

Taoan Huang, Aaron Ferber, Yuandong Tian et al.

Large Neighborhood Search (LNS) is a popular heuristic algorithm for solving combinatorial optimization problems (COP). It starts with an initial solution to the problem and iteratively improves it by searching a large neighborhood around the current best solution. LNS relies on heuristics to select neighborhoods to search in. In this paper, we focus on designing effective and efficient heuristics in LNS for integer linear programs (ILP) since a wide range of COPs can be represented as ILPs. Local Branching (LB) is a heuristic that selects the neighborhood that leads to the largest improvement over the current solution in each iteration of LNS. LB is often slow since it needs to solve an ILP of the same size as input. Our proposed heuristics, LB-RELAX and its variants, use the linear programming relaxation of LB to select neighborhoods. Empirically, LB-RELAX and its variants compute as effective neighborhoods as LB but run faster. They achieve state-of-the-art anytime performance on several ILP benchmarks.

John Dickerson, Bistra Dilkina, Yu Ding et al.

This workshop Report Out focuses on the foundational elements of trustworthy AI and OR technology, and how to ensure all AI and OR systems implement these elements in their system designs. Four sessions on various topics within Trustworthy AI were held, these being Fairness, Explainable AI/Causality, Robustness/Privacy, and Human Alignment and Human-Computer Interaction. Following discussions of each of these topics, workshop participants also brainstormed challenge problems which require the collaboration of AI and OR researchers and will result in the integration of basic techniques from both fields to eventually benefit societal needs.

Burak Bartan, Haoming Li, Harris Teague et al.

The deployment and training of neural networks on edge computing devices pose many challenges. The low memory nature of edge devices is often one of the biggest limiting factors encountered in the deployment of large neural network models. Tensor rematerialization or recompute is a way to address high memory requirements for neural network training and inference. In this paper we consider the problem of execution time minimization of compute graphs subject to a memory budget. In particular, we develop a new constraint programming formulation called \textsc{Moccasin} with only $O(n)$ integer variables, where $n$ is the number of nodes in the compute graph. This is a significant improvement over the works in the recent literature that propose formulations with $O(n^2)$ Boolean variables. We present numerical studies that show that our approach is up to an order of magnitude faster than recent work especially for large-scale graphs.

Aaron Ferber, Arman Zharmagambetov, Taoan Huang et al.

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.

Junyang Cai, El Mehdi Er Raqabi, Pascal Van Hentenryck et al.

Mixed-Integer Linear Programs (MIPs) are powerful and flexible tools for modeling a wide range of real-world combinatorial optimization problems. Predict-and-Search methods operate by using a predictive model to estimate promising variable assignments and then guiding a search procedure toward high-quality solutions. Recent research has demonstrated that incorporating machine learning (ML) into the Predict-and-Search framework significantly enhances its performance. Still, it is restricted to binary problems and overlooks the presence of fixed variables that commonly arise in practical settings. This work extends the Predict-and-Search (PaS) framework to parametric MIPs and introduces ID-PaS, an identity-aware learning framework that enables the ML model to handle heterogeneous variables more effectively. Experiments on several real-world large-scale problems demonstrate that ID-PaS consistently achieves superior performance compared to the state-of-the-art solver Gurobi and PaS.

Junyang Cai, Serdar Kadioglu, Bistra Dilkina

Mixed-integer programming (MIP) is a powerful paradigm for modeling and solving various important combinatorial optimization problems. Recently, learning-based approaches have shown a potential to speed up MIP solving via offline training that then guides important design decisions during the search. However, a significant drawback of these methods is their heavy reliance on offline training, which requires collecting training datasets and computationally costly training epochs yet offering only limited generalization to unseen (larger) instances. In this paper, we propose Balans, an adaptive meta-solver for MIPs with online learning capability that does not require any supervision or apriori training. At its core, Balans is based on adaptive large-neighborhood search, operating on top of an MIP solver by successive applications of destroy and repair neighborhood operators. During the search, the selection among different neighborhood definitions is guided on the fly for the instance at hand via multi-armed bandit algorithms. Our extensive experiments on hard optimization instances show that Balans offers significant performance gains over the default MIP solver, is better than committing to any single best neighborhood, and improves over the state-of-the-art large-neighborhood search for MIPs. Finally, we release Balans as a highly configurable, MIP solver agnostic, open-source software.

Bryan Wilder, Eric Ewing, Bistra Dilkina et al.

Real-world applications often combine learning and optimization problems on graphs. For instance, our objective may be to cluster the graph in order to detect meaningful communities (or solve other common graph optimization problems such as facility location, maxcut, and so on). However, graphs or related attributes are often only partially observed, introducing learning problems such as link prediction which must be solved prior to optimization. Standard approaches treat learning and optimization entirely separately, while recent machine learning work aims to predict the optimal solution directly from the inputs. Here, we propose an alternative decision-focused learning approach that integrates a differentiable proxy for common graph optimization problems as a layer in learned systems. The main idea is to learn a representation that maps the original optimization problem onto a simpler proxy problem that can be efficiently differentiated through. Experimental results show that our ClusterNet system outperforms both pure end-to-end approaches (that directly predict the optimal solution) and standard approaches that entirely separate learning and optimization. Code for our system is available at https://github.com/bwilder0/clusternet.

Weizhe Chen, Sven Koenig, Bistra Dilkina

With the explosive influence caused by the success of large language models (LLM) like ChatGPT and GPT-4, there has been an extensive amount of recent work showing that foundation models can be used to solve a large variety of tasks. However, there is very limited work that shares insights on multi-agent planning. Multi-agent planning is different from other domains by combining the difficulty of multi-agent coordination and planning, and making it hard to leverage external tools to facilitate the reasoning needed. In this paper, we focus on the problem of multi-agent path finding (MAPF), which is also known as multi-robot route planning, and study the performance of solving MAPF with LLMs. We first show the motivating success on an empty room map without obstacles, then the failure to plan on the harder room map and maze map of the standard MAPF benchmark. We present our position on why directly solving MAPF with LLMs has not been successful yet, and we use various experiments to support our hypothesis. Based on our results, we discussed how researchers with different backgrounds could help with this problem from different perspectives.

David Rolnick, Alan Aspuru-Guzik, Sara Beery et al. · mit

As applications of machine learning proliferate, innovative algorithms inspired by specific real-world challenges have become increasingly important. Such work offers the potential for significant impact not merely in domains of application but also in machine learning itself. In this paper, we describe the paradigm of application-driven research in machine learning, contrasting it with the more standard paradigm of methods-driven research. We illustrate the benefits of application-driven machine learning and how this approach can productively synergize with methods-driven work. Despite these benefits, we find that reviewing, hiring, and teaching practices in machine learning often hold back application-driven innovation. We outline how these processes may be improved.

Thomy Phan, Taoan Huang, Bistra Dilkina et al.

Anytime multi-agent path finding (MAPF) is a promising approach to scalable path optimization in large-scale multi-agent systems. State-of-the-art anytime MAPF is based on Large Neighborhood Search (LNS), where a fast initial solution is iteratively optimized by destroying and repairing a fixed number of parts, i.e., the neighborhood, of the solution, using randomized destroy heuristics and prioritized planning. Despite their recent success in various MAPF instances, current LNS-based approaches lack exploration and flexibility due to greedy optimization with a fixed neighborhood size which can lead to low quality solutions in general. So far, these limitations have been addressed with extensive prior effort in tuning or offline machine learning beyond actual planning. In this paper, we focus on online learning in LNS and propose Bandit-based Adaptive LArge Neighborhood search Combined with Exploration (BALANCE). BALANCE uses a bi-level multi-armed bandit scheme to adapt the selection of destroy heuristics and neighborhood sizes on the fly during search. We evaluate BALANCE on multiple maps from the MAPF benchmark set and empirically demonstrate cost improvements of at least 50% compared to state-of-the-art anytime MAPF in large-scale scenarios. We find that Thompson Sampling performs particularly well compared to alternative multi-armed bandit algorithms.

Weimin Huang, Natalie M. Isenberg, Ján Drgoňa et al.

Mixed Binary Quadratic Programs (MBQPs) are an important and complex set of problems in combinatorial optimization. As solving large-scale combinatorial optimization problems is challenging, primal heuristics have been developed to quickly identify high-quality solutions within a short amount of time. Recently, a growing body of research has also used machine learning to accelerate solution methods for challenging combinatorial optimization problems. Despite the increasing popularity of these ML-guided methods, a large body of work has focused on Mixed-Integer Linear Programs (MILPs). MBQPs are challenging to solve due to the combinatorial complexity coupled with nonlinearities. This work proposes ML-guided primal heuristics for Mixed Binary Quadratic Programs (MBQPs) by adapting and extending existing work on ML-guided MILP solution prediction to MBQPs. We introduce a new neural network architecture for MBQP solution prediction and a new training data collection procedure. Moreover, we extend existing loss functions in solution prediction and propose to combine contrastive and weighted cross-entropy losses. We evaluate the methods on standard and real-world MBQP benchmarks and show that the developed ML-guided methods significantly outperform existing primal heuristics and state-of-the-art solvers. Furthermore, models trained with our proposed extension with combined losses outperform other ML-based methods adapted from MILPs and improve generalization in cross-regional inference on a real-world wind farm layout optimization problem.

Junyang Cai, Taoan Huang, Bistra Dilkina

Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant potential in improving MILP-solving efficiency. However, these methods typically rely on separate offline data collection and training processes, which limits their scalability and adaptability. This paper introduces the first multi-task learning framework for ML-guided MILP solving. The proposed framework provides MILP embeddings helpful in guiding MILP solving across solvers (e.g., Gurobi and SCIP) and across tasks (e.g., Branching and Solver configuration). Through extensive experiments on three widely used MILP benchmarks, we demonstrate that our multi-task learning model performs similarly to specialized models within the same distribution. Moreover, it significantly outperforms them in generalization across problem sizes and tasks.

Weizhe Chen, Sven Koenig, Bistra Dilkina

Recent reasoning models, such as OpenAI's O1 series, have demonstrated exceptional performance on complex reasoning tasks and revealed new test-time scaling laws. Inspired by this, many people have been studying how to train models to achieve effective self-evaluation and self-correction to further enable the scaling paradigm. However, less studied is how to efficiently scale test-time compute from a fixed model, and this remains a challenge. In this paper, we address this challenge by focusing on enhancing the quality of self-reflection data generation for complex problem-solving at test time, which can also subsequently improve the training of next-generation large language models (LLMs). Specifically, we explore how systematically triggering a model's self-correction mechanisms can improve performance on challenging reasoning tasks. To this end, we propose a novel iterative deepening sampling algorithm framework designed to enhance self-correction and generate higher-quality samples. Through extensive experiments on Math500 and AIME benchmarks, we demonstrate that our method achieves a higher success rate on difficult tasks and provide detailed ablation studies to analyze its effectiveness across diverse settings.

Augustin Parjadis, Quentin Cappart, Bistra Dilkina et al.

Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient propagators in constraint programming (such as the weighted circuit constraint). However, the conventional process of deriving Lagrangian multipliers (e.g., using subgradient methods) is often computationally intensive, limiting its practicality for large-scale or time-sensitive problems. To address this challenge, we propose an innovative unsupervised learning approach that harnesses the capabilities of graph neural networks to exploit the problem structure, aiming to generate accurate Lagrangian multipliers efficiently. We apply this technique to the well-known Held-Karp Lagrangian relaxation for the travelling salesman problem. The core idea is to predict accurate Lagrangian multipliers and to employ them as a warm start for generating Held-Karp relaxation bounds. These bounds are subsequently utilized to enhance the filtering process carried out by branch-and-bound algorithms. In contrast to much of the existing literature, which primarily focuses on finding feasible solutions, our approach operates on the dual side, demonstrating that learning can also accelerate the proof of optimality. We conduct experiments across various distributions of the metric travelling salesman problem, considering instances with up to 200 cities. The results illustrate that our approach can improve the filtering level of the weighted circuit global constraint, reduce the optimality gap by a factor two for unsolved instances up to a timeout, and reduce the execution time for solved instances by 10%.

Alican Yilmaz, Junyang Cai, Serdar Kadioglu et al.

Solving Mixed-Integer Programming (MIP) problems often requires substantial computational resources due to their combinatorial nature. Parallelization has emerged as a critical strategy to accelerate solution times and enhance scalability to tackle large, complex instances. This paper investigates the parallelization capabilities of Balans, a recently proposed multi-armed bandits-based adaptive large neighborhood search for MIPs. While Balans's modular architecture inherently supports parallel exploration of diverse parameter configurations, this potential has not been thoroughly examined. To address this gap, we introduce ParBalans, an extension that leverages both solver-level and algorithmic-level parallelism to improve performance on challenging MIP instances. Our experimental results demonstrate that ParBalans exhibits competitive performance compared to the state-of-the-art commercial solver Gurobi, particularly on hard optimization benchmarks.

Weimin Huang, Ryan Piansky, Bistra Dilkina et al.

To mitigate acute wildfire ignition risks, utilities de-energize power lines in high-risk areas. The Optimal Power Shutoff (OPS) problem optimizes line energization statuses to manage wildfire ignition risks through de-energizations while reducing load shedding. OPS problems are computationally challenging Mixed-Integer Linear Programs (MILPs) that must be solved rapidly and frequently in operational settings. For a particular power system, OPS instances share a common structure with varying parameters related to wildfire risks, loads, and renewable generation. This motivates the use of Machine Learning (ML) for solving OPS problems by exploiting shared patterns across instances. In this paper, we develop an ML-guided framework that quickly produces high-quality de-energization decisions by extending existing ML-guided MILP solution methods while integrating domain knowledge on the number of energized and de-energized lines. Results on a large-scale realistic California-based synthetic test system show that the proposed ML-guided method produces high-quality solutions faster than traditional optimization methods.

Weizhe Chen, Sven Koenig, Bistra Dilkina

Since the release of Deepseek-R1, reinforcement learning with verifiable rewards (RLVR) has become a central approach for training large language models (LLMs) on reasoning tasks. Recent work has largely focused on modifying loss functions to make RLVR more efficient and effective. In this paper, motivated by studies of overthinking in LLMs, we propose Length-aware Sampling for Policy Optimization (LSPO), a novel meta-RLVR algorithm that dynamically selects training data at each step based on the average response length. We evaluate LSPO across multiple base models and datasets, demonstrating that it consistently improves learning effectiveness. In addition, we conduct a detailed ablation study to examine alternative ways of incorporating length signals into dynamic sampling, offering further insights and highlighting promising directions for future research.

Junyang Cai, Serdar Kadioglu, Bistra Dilkina

Natural language descriptions of optimization or satisfaction problems are challenging to translate into correct MiniZinc models, as this process demands both logical reasoning and constraint programming expertise. We introduce Gala, a framework that addresses this challenge with a global agentic approach: multiple specialized large language model (LLM) agents decompose the modeling task by global constraint type. Each agent is dedicated to detecting and generating code for a specific class of global constraint, while a final assembler agent integrates these constraint snippets into a complete MiniZinc model. By dividing the problem into smaller, well-defined sub-tasks, each LLM handles a simpler reasoning challenge, potentially reducing overall complexity. We conduct initial experiments with several LLMs and show better performance against baselines such as one-shot prompting and chain-of-thought prompting. Finally, we outline a comprehensive roadmap for future work, highlighting potential enhancements and directions for improvement.

Weizhe Chen, Sven Koenig, Bistra Dilkina

In the past year, large language models (LLMs) have had remarkable success in domains outside the traditional natural language processing, and their capacity is further expanded into the so-called LLM agents when connected with external tools. In all domains, the prompt to the LLMs has been shown to make a big difference in what the LLM would generate and thus affect the performance of the LLM agents. Therefore, automatic prompt engineering (APE) has become an important question for many researchers and users of LLMs. However, previous works in APE rely on a final checker to evaluate the performance of the given prompt -- a requirement that is hard to meet in the case of LLM agents, where intermediate feedback is easier to obtain, and the final evaluation could be expensive, inaccurate, or even missing. In this paper, we propose a novel method, \textsc{RePrompt}, which does a ``gradient descent"-like approach to optimize the step-by-step instructions in the prompts given to LLM agents, based on the chat history obtained from interactions and reflections with LLM agents. By leveraging intermediate feedback, \textsc{RePrompt} can optimize the prompt without the need for a final solution checker. We evaluate our approach on PDDL generation, TravelPlanner, and Meeting Planning to show that our method could generally improve performance for different reasoning tasks.

Weimin Huang, Taoan Huang, Aaron M Ferber et al.

Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of this approach, there is a lack of a common repository that provides distributions of similar MILP instances across different domains, at different hardness levels, with standardized test sets. In this paper, we introduce Distributional MIPLIB, a multi-domain library of problem distributions for advancing ML-guided MILP methods. We curate MILP distributions from existing work in this area as well as real-world problems that have not been used, and classify them into different hardness levels. It will facilitate research in this area by enabling comprehensive evaluation on diverse and realistic domains. We empirically illustrate the benefits of using Distributional MIPLIB as a research vehicle in two ways. We evaluate the performance of ML-guided variable branching on previously unused distributions to identify potential areas for improvement. Moreover, we propose to learn branching policies from a mix of distributions, demonstrating that mixed distributions achieve better performance compared to homogeneous distributions when there is limited data and generalize well to larger instances. The dataset is publicly available at https://sites.google.com/usc.edu/distributional-miplib/home.

Weizhe Chen, Sven Koenig, Bistra Dilkina

Cooperative multi-agent reinforcement learning (MARL) has been an increasingly important research topic in the last half-decade because of its great potential for real-world applications. Because of the curse of dimensionality, the popular "centralized training decentralized execution" framework requires a long time in training, yet still cannot converge efficiently. In this paper, we propose a general training framework, MARL-LNS, to algorithmically address these issues by training on alternating subsets of agents using existing deep MARL algorithms as low-level trainers, while not involving any additional parameters to be trained. Based on this framework, we provide three algorithm variants based on the framework: random large neighborhood search (RLNS), batch large neighborhood search (BLNS), and adaptive large neighborhood search (ALNS), which alternate the subsets of agents differently. We test our algorithms on both the StarCraft Multi-Agent Challenge and Google Research Football, showing that our algorithms can automatically reduce at least 10% of training time while reaching the same final skill level as the original algorithm.

Junyang Cai, Taoan Huang, Bistra Dilkina

Many real-world problems can be efficiently modeled as Mixed Integer Linear Programs (MILPs) and solved with the Branch-and-Bound method. Prior work has shown the existence of MILP backdoors, small sets of variables such that prioritizing branching on them when possible leads to faster running times. However, finding high-quality backdoors that improve running times remains an open question. Previous work learns to estimate the relative solver speed of randomly sampled backdoors through ranking and then decide whether to use the highest-ranked backdoor candidate. In this paper, we utilize the Monte-Carlo tree search method to collect backdoors for training, rather than relying on random sampling, and adapt a contrastive learning framework to train a Graph Attention Network model to predict backdoors. Our method, evaluated on several common MILP problem domains, demonstrates performance improvements over both Gurobi and previous models.

Elias B. Khalil, Pashootan Vaezipoor, Bistra Dilkina

In Mixed Integer Linear Programming (MIP), a (strong) backdoor is a "small" subset of an instance's integer variables with the following property: in a branch-and-bound procedure, the instance can be solved to global optimality by branching only on the variables in the backdoor. Constructing datasets of pre-computed backdoors for widely used MIP benchmark sets or particular problem families can enable new questions around novel structural properties of a MIP, or explain why a problem that is hard in theory can be solved efficiently in practice. Existing algorithms for finding backdoors rely on sampling candidate variable subsets in various ways, an approach which has demonstrated the existence of backdoors for some instances from MIPLIB2003 and MIPLIB2010. However, these algorithms fall short of consistently succeeding at the task due to an imbalance between exploration and exploitation. We propose BaMCTS, a Monte Carlo Tree Search framework for finding backdoors to MIPs. Extensive algorithmic engineering, hybridization with traditional MIP concepts, and close integration with the CPLEX solver have enabled our method to outperform baselines on MIPLIB2017 instances, finding backdoors more frequently and more efficiently.

Kai Wang, Bryan Wilder, Sze-chuan Suen et al.

There is significant interest in learning and optimizing a complex system composed of multiple sub-components, where these components may be agents or autonomous sensors. Among the rich literature on this topic, agent-based and domain-specific simulations can capture complex dynamics and subgroup interaction, but optimizing over such simulations can be computationally and algorithmically challenging. Bayesian approaches, such as Gaussian processes (GPs), can be used to learn a computationally tractable approximation to the underlying dynamics but typically neglect the detailed information about subgroups in the complicated system. We attempt to find the best of both worlds by proposing the idea of decomposed feedback, which captures group-based heterogeneity and dynamics. We introduce a novel decomposed GP regression to incorporate the subgroup decomposed feedback. Our modified regression has provably lower variance -- and thus a more accurate posterior -- compared to previous approaches; it also allows us to introduce a decomposed GP-UCB optimization algorithm that leverages subgroup feedback. The Bayesian nature of our method makes the optimization algorithm trackable with a theoretical guarantee on convergence and no-regret property. To demonstrate the wide applicability of this work, we execute our algorithm on two disparate social problems: infectious disease control in a heterogeneous population and allocation of distributed weather sensors. Experimental results show that our new method provides significant improvement compared to the state-of-the-art.

Aaron Ferber, Jialin Song, Bistra Dilkina et al.

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.

Umang Gupta, Aaron M Ferber, Bistra Dilkina et al.

Controlling bias in training datasets is vital for ensuring equal treatment, or parity, between different groups in downstream applications. A naive solution is to transform the data so that it is statistically independent of group membership, but this may throw away too much information when a reasonable compromise between fairness and accuracy is desired. Another common approach is to limit the ability of a particular adversary who seeks to maximize parity. Unfortunately, representations produced by adversarial approaches may still retain biases as their efficacy is tied to the complexity of the adversary used during training. To this end, we theoretically establish that by limiting the mutual information between representations and protected attributes, we can assuredly control the parity of any downstream classifier. We demonstrate an effective method for controlling parity through mutual information based on contrastive information estimators and show that they outperform approaches that rely on variational bounds based on complex generative models. We test our approach on UCI Adult and Heritage Health datasets and demonstrate that our approach provides more informative representations across a range of desired parity thresholds while providing strong theoretical guarantees on the parity of any downstream algorithm.

Taoan Huang, Bistra Dilkina, Sven Koenig

Conflict-Based Search (CBS) is a state-of-the-art algorithm for multi-agent path finding. At the high level, CBS repeatedly detects conflicts and resolves one of them by splitting the current problem into two subproblems. Previous work chooses the conflict to resolve by categorizing the conflict into three classes and always picking a conflict from the highest-priority class. In this work, we propose an oracle for conflict selection that results in smaller search tree sizes than the one used in previous work. However, the computation of the oracle is slow. Thus, we propose a machine-learning framework for conflict selection that observes the decisions made by the oracle and learns a conflict-selection strategy represented by a linear ranking function that imitates the oracle's decisions accurately and quickly. Experiments on benchmark maps indicate that our method significantly improves the success rates, the search tree sizes and runtimes over the current state-of-the-art CBS solver.

Hejia Zhang, Matthew C. Fontaine, Amy K. Hoover et al.

Recent advancements in procedural content generation via machine learning enable the generation of video-game levels that are aesthetically similar to human-authored examples. However, the generated levels are often unplayable without additional editing. We propose a generate-then-repair framework for automatic generation of playable levels adhering to specific styles. The framework constructs levels using a generative adversarial network (GAN) trained with human-authored examples and repairs them using a mixed-integer linear program (MIP) with playability constraints. A key component of the framework is computing minimum cost edits between the GAN generated level and the solution of the MIP solver, which we cast as a minimum cost network flow problem. Results show that the proposed framework generates a diverse range of playable levels, that capture the spatial relationships between objects exhibited in the human-authored levels.

Lucas Hu, Caleb Robinson, Bistra Dilkina

Recent work has shown that deep learning models can be used to classify land-use data from geospatial satellite imagery. We show that when these deep learning models are trained on data from specific continents/seasons, there is a high degree of variability in model performance on out-of-sample continents/seasons. This suggests that just because a model accurately predicts land-use classes in one continent or season does not mean that the model will accurately predict land-use classes in a different continent or season. We then use clustering techniques on satellite imagery from different continents to visualize the differences in landscapes that make geospatial generalization particularly difficult, and summarize our takeaways for future satellite imagery-related applications.

Jialin Song, Ravi Lanka, Yisong Yue et al.

This paper studies a strategy for data-driven algorithm design for large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic or complete approaches and their software implementations. We show that one can learn a good neighborhood selector using imitation and reinforcement learning techniques. Through an extensive empirical validation in bounded-time optimization, we demonstrate that our LNS framework can significantly outperform compared to state-of-the-art commercial solvers such as Gurobi.

Aaron Ferber, Bryan Wilder, Bistra Dilkina et al.

Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused learning explicitly integrates the downstream decision problem when training the predictive model, in order to optimize the quality of decisions induced by the predictions. It has been successfully applied to several limited combinatorial problem classes, such as those that can be expressed as linear programs (LP), and submodular optimization. However, these previous applications have uniformly focused on problems from specific classes with simple constraints. Here, we enable decision-focused learning for the broad class of problems that can be encoded as a Mixed Integer Linear Program (MIP), hence supporting arbitrary linear constraints over discrete and continuous variables. We show how to differentiate through a MIP by employing a cutting planes solution approach, which is an exact algorithm that iteratively adds constraints to a continuous relaxation of the problem until an integral solution is found. We evaluate our new end-to-end approach on several real world domains and show that it outperforms the standard two phase approaches that treat prediction and prescription separately, as well as a baseline approach of simply applying decision-focused learning to the LP relaxation of the MIP.

Caleb Robinson, Anthony Ortiz, Kolya Malkin et al.

We propose incorporating human labelers in a model fine-tuning system that provides immediate user feedback. In our framework, human labelers can interactively query model predictions on unlabeled data, choose which data to label, and see the resulting effect on the model's predictions. This bi-directional feedback loop allows humans to learn how the model responds to new data. Our hypothesis is that this rich feedback allows human labelers to create mental models that enable them to better choose which biases to introduce to the model. We compare human-selected points to points selected using standard active learning methods. We further investigate how the fine-tuning methodology impacts the human labelers' performance. We implement this framework for fine-tuning high-resolution land cover segmentation models. Specifically, we fine-tune a deep neural network -- trained to segment high-resolution aerial imagery into different land cover classes in Maryland, USA -- to a new spatial area in New York, USA. The tight loop turns the algorithm and the human operator into a hybrid system that can produce land cover maps of a large area much more efficiently than the traditional workflows. Our framework has applications in geospatial machine learning settings where there is a practically limitless supply of unlabeled data, of which only a small fraction can feasibly be labeled through human efforts.

Payam Siyari, Bistra Dilkina, Constantine Dovrolis

Many complex systems, both in technology and nature, exhibit hierarchical modularity: smaller modules, each of them providing a certain function, are used within larger modules that perform more complex functions. Previously, we have proposed a modeling framework, referred to as Evo-Lexis, that provides insight to some fundamental questions about evolving hierarchical systems. The predictions of the Evo-Lexis model should be tested using real data from evolving systems in which the outputs can be well represented by sequences. In this paper, we investigate the time series of iGEM synthetic DNA dataset sequences, and whether the resulting iGEM hierarchies exhibit the qualitative properties predicted by the Evo-Lexis framework. Contrary to Evo-Lexis, in iGEM the amount of reuse decreases during the timeline of the dataset. Although this results in development of less cost-efficient and less deep Lexis-DAGs, the dataset exhibits a bias in reusing specific nodes more often than others. This results in the Lexis-DAGs to take the shape of an hourglass with relatively high H-score values and stable set of core nodes. Despite the reuse bias and stability of the core set, the dataset presents a high amount of diversity among the targets which is in line with modeling of Evo-Lexis.

Lily Xu, Shahrzad Gholami, Sara Mc Carthy et al.

Illegal wildlife poaching threatens ecosystems and drives endangered species toward extinction. However, efforts for wildlife protection are constrained by the limited resources of law enforcement agencies. To help combat poaching, the Protection Assistant for Wildlife Security (PAWS) is a machine learning pipeline that has been developed as a data-driven approach to identify areas at high risk of poaching throughout protected areas and compute optimal patrol routes. In this paper, we take an end-to-end approach to the data-to-deployment pipeline for anti-poaching. In doing so, we address challenges including extreme class imbalance (up to 1:200), bias, and uncertainty in wildlife poaching data to enhance PAWS, and we apply our methodology to three national parks with diverse characteristics. (i) We use Gaussian processes to quantify predictive uncertainty, which we exploit to improve robustness of our prescribed patrols and increase detection of snares by an average of 30%. We evaluate our approach on real-world historical poaching data from Murchison Falls and Queen Elizabeth National Parks in Uganda and, for the first time, Srepok Wildlife Sanctuary in Cambodia. (ii) We present the results of large-scale field tests conducted in Murchison Falls and Srepok Wildlife Sanctuary which confirm that the predictive power of PAWS extends promisingly to multiple parks. This paper is part of an effort to expand PAWS to 800 parks around the world through integration with SMART conservation software.

Andrew Perrault, Bryan Wilder, Eric Ewing et al.

Stackelberg security games are a critical tool for maximizing the utility of limited defense resources to protect important targets from an intelligent adversary. Motivated by green security, where the defender may only observe an adversary's response to defense on a limited set of targets, we study the problem of learning a defense that generalizes well to a new set of targets with novel feature values and combinations. Traditionally, this problem has been addressed via a two-stage approach where an adversary model is trained to maximize predictive accuracy without considering the defender's optimization problem. We develop an end-to-end game-focused approach, where the adversary model is trained to maximize a surrogate for the defender's expected utility. We show both in theory and experimental results that our game-focused approach achieves higher defender expected utility than the two-stage alternative when there is limited data.

Jackson A. Killian, Bryan Wilder, Amit Sharma et al.

Digital Adherence Technologies (DATs) are an increasingly popular method for verifying patient adherence to many medications. We analyze data from one city served by 99DOTS, a phone-call-based DAT deployed for Tuberculosis (TB) treatment in India where nearly 3 million people are afflicted with the disease each year. The data contains nearly 17,000 patients and 2.1M dose records. We lay the groundwork for learning from this real-world data, including a method for avoiding the effects of unobserved interventions in training data used for machine learning. We then construct a deep learning model, demonstrate its interpretability, and show how it can be adapted and trained in different clinical scenarios to better target and improve patient care. In the real-time risk prediction setting our model could be used to proactively intervene with 21% more patients and before 76% more missed doses than current heuristic baselines. For outcome prediction, our model performs 40% better than baseline methods, allowing cities to target more resources to clinics with a heavier burden of patients at risk of failure. Finally, we present a case study demonstrating how our model can be trained in an end-to-end decision focused learning setting to achieve 15% better solution quality in an example decision problem faced by health workers.

Elias B. Khalil, Amrita Gupta, Bistra Dilkina

Binarized Neural Networks (BNNs) have recently attracted significant interest due to their computational efficiency. Concurrently, it has been shown that neural networks may be overly sensitive to "attacks" - tiny adversarial changes in the input - which may be detrimental to their use in safety-critical domains. Designing attack algorithms that effectively fool trained models is a key step towards learning robust neural networks. The discrete, non-differentiable nature of BNNs, which distinguishes them from their full-precision counterparts, poses a challenge to gradient-based attacks. In this work, we study the problem of attacking a BNN through the lens of combinatorial and integer optimization. We propose a Mixed Integer Linear Programming (MILP) formulation of the problem. While exact and flexible, the MILP quickly becomes intractable as the network and perturbation space grow. To address this issue, we propose IProp, a decomposition-based algorithm that solves a sequence of much smaller MILP problems. Experimentally, we evaluate both proposed methods against the standard gradient-based attack (FGSM) on MNIST and Fashion-MNIST, and show that IProp performs favorably compared to FGSM, while scaling beyond the limits of the MILP.

Bryan Wilder, Bistra Dilkina, Milind Tambe

Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is first trained via a measure of predictive accuracy, and then its predictions are used as input into an optimization algorithm which produces a decision. However, the loss function used to train the model may easily be misaligned with the end goal, which is to make the best decisions possible. Hand-tuning the loss function to align with optimization is a difficult and error-prone process (which is often skipped entirely). We focus on combinatorial optimization problems and introduce a general framework for decision-focused learning, where the machine learning model is directly trained in conjunction with the optimization algorithm to produce high-quality decisions. Technically, our contribution is a means of integrating common classes of discrete optimization problems into deep learning or other predictive models, which are typically trained via gradient descent. The main idea is to use a continuous relaxation of the discrete problem to propagate gradients through the optimization procedure. We instantiate this framework for two broad classes of combinatorial problems: linear programs and submodular maximization. Experimental results across a variety of domains show that decision-focused learning often leads to improved optimization performance compared to traditional methods. We find that standard measures of accuracy are not a reliable proxy for a predictive model's utility in optimization, and our method's ability to specify the true goal as the model's training objective yields substantial dividends across a range of decision problems.

Payam Siyari, Bistra Dilkina, Constantine Dovrolis

It is well known that many complex systems, both in technology and nature, exhibit hierarchical modularity: smaller modules, each of them providing a certain function, are used within larger modules that perform more complex functions. What is not well understood however is how this hierarchical structure (which is fundamentally a network property) emerges, and how it evolves over time. We propose a modeling framework, referred to as Evo-Lexis, that provides insight to some fundamental questions about evolving hierarchical systems. Evo-Lexis models the most elementary modules of the system as symbols ("sources") and the modules at the highest level of the hierarchy as sequences of those symbols ("targets"). Evo-Lexis computes the optimized adjustment of a given hierarchy when the set of targets changes over time by additions and removals (a process referred to as "incremental design"). In this paper we use computation modeling to show that: - Low-cost and deep hierarchies emerge when the population of target sequences evolves through tinkering and mutation. - Strong selection on the cost of new candidate targets results in reuse of more complex (longer) nodes in an optimized hierarchy. - The bias towards reuse of complex nodes results in an "hourglass architecture" (i.e., few intermediate nodes that cover almost all source-target paths). - With such bias, the core nodes are conserved for relatively long time periods although still being vulnerable to major transitions and punctuated equilibria. - Finally, we analyze the differences in terms of cost and structure between incrementally designed hierarchies and the corresponding "clean-slate" hierarchies which result when the system is designed from scratch after a change.

Amrita Gupta, Mehrdad Farajtabar, Bistra Dilkina et al.

The spread of invasive species to new areas threatens the stability of ecosystems and causes major economic losses in agriculture and forestry. We propose a novel approach to minimizing the spread of an invasive species given a limited intervention budget. We first model invasive species propagation using Hawkes processes, and then derive closed-form expressions for characterizing the effect of an intervention action on the invasion process. We use this to obtain an optimal intervention plan based on an integer programming formulation, and compare the optimal plan against several ecologically-motivated heuristic strategies used in practice. We present an empirical study of two variants of the invasive control problem: minimizing the final rate of invasions, and minimizing the number of invasions at the end of a given time horizon. Our results show that the optimized intervention achieves nearly the same level of control that would be attained by completely eradicating the species, with a 20% cost saving. Additionally, we design a heuristic intervention strategy based on a combination of the density and life stage of the invasive individuals, and find that it comes surprisingly close to the optimized strategy, suggesting that this could serve as a good rule of thumb in invasive species management.

Caleb Robinson, Bistra Dilkina

Human migration is a type of human mobility, where a trip involves a person moving with the intention of changing their home location. Predicting human migration as accurately as possible is important in city planning applications, international trade, spread of infectious diseases, conservation planning, and public policy development. Traditional human mobility models, such as gravity models or the more recent radiation model, predict human mobility flows based on population and distance features only. These models have been validated on commuting flows, a different type of human mobility, and are mainly used in modeling scenarios where large amounts of prior ground truth mobility data are not available. One downside of these models is that they have a fixed form and are therefore not able to capture more complicated migration dynamics. We propose machine learning models that are able to incorporate any number of exogenous features, to predict origin/destination human migration flows. Our machine learning models outperform traditional human mobility models on a variety of evaluation metrics, both in the task of predicting migrations between US counties as well as international migrations. In general, predictive machine learning models of human migration will provide a flexible base with which to model human migration under different what-if conditions, such as potential sea level rise or population growth scenarios.

Caleb Robinson, Fred Hohman, Bistra Dilkina

Knowing where people live is a fundamental component of many decision making processes such as urban development, infectious disease containment, evacuation planning, risk management, conservation planning, and more. While bottom-up, survey driven censuses can provide a comprehensive view into the population landscape of a country, they are expensive to realize, are infrequently performed, and only provide population counts over broad areas. Population disaggregation techniques and population projection methods individually address these shortcomings, but also have shortcomings of their own. To jointly answer the questions of "where do people live" and "how many people live there," we propose a deep learning model for creating high-resolution population estimations from satellite imagery. Specifically, we train convolutional neural networks to predict population in the USA at a $0.01^{\circ} \times 0.01^{\circ}$ resolution grid from 1-year composite Landsat imagery. We validate these models in two ways: quantitatively, by comparing our model's grid cell estimates aggregated at a county-level to several US Census county-level population projections, and qualitatively, by directly interpreting the model's predictions in terms of the satellite image inputs. We find that aggregating our model's estimates gives comparable results to the Census county-level population projections and that the predictions made by our model can be directly interpreted, which give it advantages over traditional population disaggregation methods. In general, our model is an example of how machine learning techniques can be an effective tool for extracting information from inherently unstructured, remotely sensed data to provide effective solutions to social problems.

Hanjun Dai, Elias B. Khalil, Yuyu Zhang et al.

The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the algorithms instead? In many real-world applications, it is typically the case that the same optimization problem is solved again and again on a regular basis, maintaining the same problem structure but differing in the data. This provides an opportunity for learning heuristic algorithms that exploit the structure of such recurring problems. In this paper, we propose a unique combination of reinforcement learning and graph embedding to address this challenge. The learned greedy policy behaves like a meta-algorithm that incrementally constructs a solution, and the action is determined by the output of a graph embedding network capturing the current state of the solution. We show that our framework can be applied to a diverse range of optimization problems over graphs, and learns effective algorithms for the Minimum Vertex Cover, Maximum Cut and Traveling Salesman problems.

Payam Siyari, Bistra Dilkina, Constantine Dovrolis

Data represented as strings abounds in biology, linguistics, document mining, web search and many other fields. Such data often have a hierarchical structure, either because they were artificially designed and composed in a hierarchical manner or because there is an underlying evolutionary process that creates repeatedly more complex strings from simpler substrings. We propose a framework, referred to as "Lexis", that produces an optimized hierarchical representation of a given set of "target" strings. The resulting hierarchy, "Lexis-DAG", shows how to construct each target through the concatenation of intermediate substrings, minimizing the total number of such concatenations or DAG edges. The Lexis optimization problem is related to the smallest grammar problem. After we prove its NP-Hardness for two cost formulations, we propose an efficient greedy algorithm for the construction of Lexis-DAGs. We also consider the problem of identifying the set of intermediate nodes (substrings) that collectively form the "core" of a Lexis-DAG, which is important in the analysis of Lexis-DAGs. We show that the Lexis framework can be applied in diverse applications such as optimized synthesis of DNA fragments in genomic libraries, hierarchical structure discovery in protein sequences, dictionary-based text compression, and feature extraction from a set of documents.