Ferdinando Fioretto

Jayanta Mandi, James Kotary, Senne Berden et al.

Decision-focused learning (DFL) is an emerging paradigm that integrates machine learning (ML) and constrained optimization to enhance decision quality by training ML models in an end-to-end system. This approach shows significant potential to revolutionize combinatorial decision-making in real-world applications that operate under uncertainty, where estimating unknown parameters within decision models is a major challenge. This paper presents a comprehensive review of DFL, providing an in-depth analysis of both gradient-based and gradient-free techniques used to combine ML and constrained optimization. It evaluates the strengths and limitations of these techniques and includes an extensive empirical evaluation of eleven methods across seven problems. The survey also offers insights into recent advancements and future research directions in DFL. Code and benchmark: https://github.com/PredOpt/predopt-benchmarks

Jinhao Liang, Sven Koenig, Ferdinando Fioretto

Decentralized multi-robot motion planning requires each robot to generate collision-free trajectories from local observations, without global sensing or reliable communication. However, most existing planners, whether classical or learning-based, generate trajectories from a static snapshot of the local observation, which limits their ability to anticipate the future behavior of neighboring robots. This limitation is critical as the number of robots increases and the environment becomes more cluttered. To overcome this challenge, this paper introduces Simulation-Informed Diffusion (SID), a decentralized framework built on constraint-aware diffusion models (CADM). SID first uses CADM to simulate the future trajectories of neighboring robots from their currently observed states, and then uses the same CADM to plan each robot's own trajectory under safety constraints informed by these simulations. Crucially, the accurate simulation of neighbors enables a minimal communication scheme that triggers coordination only when necessary in highly congested scenarios. Experiments across diverse environments show that SID consistently outperforms baseline methods in terms of planning effectiveness and constraint satisfaction, and scales to scenarios with 108 robots and 160 obstacles.

Jacob K Christopher, Brian R Bartoldson, Tal Ben-Nun et al.

Speculative decoding has emerged as a widely adopted method to accelerate large language model inference without sacrificing the quality of the model outputs. While this technique has facilitated notable speed improvements by enabling parallel sequence verification, its efficiency remains inherently limited by the reliance on incremental token generation in existing draft models. To overcome this limitation, this paper proposes an adaptation of speculative decoding which uses discrete diffusion models to generate draft sequences. This allows parallelization of both the drafting and verification steps, providing significant speedups to the inference process. Our proposed approach, $\textit{Speculative Diffusion Decoding (SpecDiff)}$, is validated on standard language generation benchmarks and empirically demonstrated to provide up to 7.2x speedups over standard generation processes and up to 1.75x speedups over existing speculative decoding approaches.

Mostafa Mohammadian, Kyri Baker, Ferdinando Fioretto

The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics must be considered to ensure that the optimal solutions provided by these models adhere to practical dynamical constraints, avoiding frequency fluctuations and grid instabilities. Unfortunately, dynamic system models based on ordinary or partial differential equations are frequently unsuitable for direct application in control or state estimates due to their high computational costs. To address these challenges, this paper introduces a machine learning method to approximate the behavior of power systems dynamics in near real time. The proposed framework is based on gradient-enhanced physics-informed neural networks (gPINNs) and encodes the underlying physical laws governing power systems. A key characteristic of the proposed gPINN is its ability to train without the need of generating expensive training data. The paper illustrates the potential of the proposed approach in both forward and inverse problems in a single-machine infinite bus system for predicting rotor angles and frequency, and uncertain parameters such as inertia and damping to showcase its potential for a range of power systems applications.

Mason Nakamura, Abhinav Kumar, Saswat Das et al.

Multi-agent systems, where LLM agents communicate through free-form language, enable sophisticated coordination for solving complex cooperative tasks. This surfaces a unique safety problem when individual agents form a coalition and \emph{collude} to pursue secondary goals and degrade the joint objective. In this paper, we present Colosseum, a framework for auditing LLM agents' collusive behavior in multi-agent settings. We ground how agents cooperate through a Distributed Constraint Optimization Problem (DCOP) and measure collusion via regret relative to the cooperative optimum. Colosseum tests each LLM for collusion under different objectives, persuasion tactics, and network topologies. Through our audit, we show that most out-of-the-box models exhibited a propensity to collude when a secret communication channel was artificially formed. Furthermore, we discover ``collusion on paper'' when agents plan to collude in text but would often pick non-collusive actions, thus providing little effect on the joint task. Colosseum provides a new way to study collusion by measuring communications and actions in rich yet verifiable environments.

Cuong Tran, Ferdinando Fioretto, Jung-Eun Kim et al.

Network pruning is a widely-used compression technique that is able to significantly scale down overparameterized models with minimal loss of accuracy. This paper shows that pruning may create or exacerbate disparate impacts. The paper sheds light on the factors to cause such disparities, suggesting differences in gradient norms and distance to decision boundary across groups to be responsible for this critical issue. It analyzes these factors in detail, providing both theoretical and empirical support, and proposes a simple, yet effective, solution that mitigates the disparate impacts caused by pruning.

Cuong Tran, Keyu Zhu, Ferdinando Fioretto et al.

A critical concern in data-driven processes is to build models whose outcomes do not discriminate against some demographic groups, including gender, ethnicity, or age. To ensure non-discrimination in learning tasks, knowledge of the group attributes is essential. However, in practice, these attributes may not be available due to legal and ethical requirements. To address this challenge, this paper studies a model that protects the privacy of the individuals' sensitive information while also allowing it to learn non-discriminatory predictors. A key characteristic of the proposed model is to enable the adoption of off-the-selves and non-private fair models to create a privacy-preserving and fair model. The paper analyzes the relation between accuracy, privacy, and fairness, and the experimental evaluation illustrates the benefits of the proposed models on several prediction tasks. In particular, this proposal is the first to allow both scalable and accurate training of private and fair models for very large neural networks.

Cuong Tran, Keyu Zhu, Ferdinando Fioretto et al.

The remarkable performance of deep learning models and their applications in consequential domains (e.g., facial recognition) introduces important challenges at the intersection of equity and security. Fairness and robustness are two desired notions often required in learning models. Fairness ensures that models do not disproportionately harm (or benefit) some groups over others, while robustness measures the models' resilience against small input perturbations. This paper shows the existence of a dichotomy between fairness and robustness, and analyzes when achieving fairness decreases the model robustness to adversarial samples. The reported analysis sheds light on the factors causing such contrasting behavior, suggesting that distance to the decision boundary across groups as a key explainer for this behavior. Extensive experiments on non-linear models and different architectures validate the theoretical findings in multiple vision domains. Finally, the paper proposes a simple, yet effective, solution to construct models achieving good tradeoffs between fairness and robustness.

James Kotary, Vincenzo Di Vito, Jacob Cristopher et al.

The Predict-Then-Optimize framework uses machine learning models to predict unknown parameters of an optimization problem from exogenous features before solving. This setting is common to many real-world decision processes, and recently it has been shown that decision quality can be substantially improved by solving and differentiating the optimization problem within an end-to-end training loop. However, this approach requires significant computational effort in addition to handcrafted, problem-specific rules for backpropagation through the optimization step, challenging its applicability to a broad class of optimization problems. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by joint predictive models. The approach is generic, and based on an adaptation of the Learning-to-Optimize paradigm, from which a rich variety of existing techniques can be employed. Experimental evaluations show the ability of several Learning-to-Optimize methods to provide efficient and accurate solutions to an array of challenging Predict-Then-Optimize problems.

James Kotary, My H. Dinh, Ferdinando Fioretto

The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which typically lacks a closed form. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. While flexible and general, unrolling can encounter accuracy and efficiency issues in practice. These issues can be avoided by analytical differentiation of the optimization, but current frameworks impose rigid requirements on the optimization problem's form. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation. Additionally, it proposes a unifying view of unrolling and analytical differentiation through optimization mappings. Experiments over various model-based learning tasks demonstrate the advantages of the approach both computationally and in terms of enhanced expressiveness.

James Kotary, Vincenzo Di Vito, Jacob Christopher et al.

Many real-world decision processes are modeled by optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize framework uses machine learning models to predict unknown parameters of an optimization problem from features before solving. Recent works show that decision quality can be improved in this setting by solving and differentiating the optimization problem in the training loop, enabling end-to-end training with loss functions defined directly on the resulting decisions. However, this approach can be inefficient and requires handcrafted, problem-specific rules for backpropagation through the optimization step. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by predictive models. The approach is generic, and based on an adaptation of the Learning-to-Optimize paradigm, from which a rich variety of existing techniques can be employed. Experimental evaluations show the ability of several Learning-to-Optimize methods to provide efficient, accurate, and flexible solutions to an array of challenging Predict-Then-Optimize problems.

Keyu Zhu, Ferdinando Fioretto, Pascal Van Hentenryck et al.

Disclosure avoidance (DA) systems are used to safeguard the confidentiality of data while allowing it to be analyzed and disseminated for analytic purposes. These methods, e.g., cell suppression, swapping, and k-anonymity, are commonly applied and may have significant societal and economic implications. However, a formal analysis of their privacy and bias guarantees has been lacking. This paper presents a framework that addresses this gap: it proposes differentially private versions of these mechanisms and derives their privacy bounds. In addition, the paper compares their performance with traditional differential privacy mechanisms in terms of accuracy and fairness on US Census data release and classification tasks. The results show that, contrary to popular beliefs, traditional differential privacy techniques may be superior in terms of accuracy and fairness to differential private counterparts of widely used DA mechanisms.

Jingyi Cui, Jacob K. Christopher, Ankita Biswas et al.

Point defects affect material properties by altering electronic states and modifying local bonding environments. However, high-throughput first-principles simulations of point defects are costly due to large simulation cells and complex energy landscapes. To this end, we propose a generative framework for simulating point defects, overcoming the limits of costly first-principles simulators. By leveraging a primal-dual algorithm, we introduce a constraint-aware diffusion model which outperforms existing constrained diffusion approaches in this domain. Across six defect configuration settings for Bi2Te3, the proposed approach provides state-of-the-art performance generating physically grounded structures.

James Kotary, Vincenzo Di Vito, Ferdinando Fioretto

Model selection is a strategy aimed at creating accurate and robust models. A key challenge in designing these algorithms is identifying the optimal model for classifying any particular input sample. This paper addresses this challenge and proposes a novel framework for differentiable model selection integrating machine learning and combinatorial optimization. The framework is tailored for ensemble learning, a strategy that combines the outputs of individually pre-trained models, and learns to select appropriate ensemble members for a particular input sample by transforming the ensemble learning task into a differentiable selection program trained end-to-end within the ensemble learning model. Tested on various tasks, the proposed framework demonstrates its versatility and effectiveness, outperforming conventional and advanced consensus rules across a variety of settings and learning tasks.

Joonhyuk Ko, Juba Ziani, Saswat Das et al.

Statistical agencies rely on sampling techniques to collect socio-demographic data crucial for policy-making and resource allocation. This paper shows that surveys of important societal relevance introduce sampling errors that unevenly impact group-level estimates, thereby compromising fairness in downstream decisions. To address these issues, this paper introduces an optimization approach modeled on real-world survey design processes, ensuring sampling costs are optimized while maintaining error margins within prescribed tolerances. Additionally, privacy-preserving methods used to determine sampling rates can further impact these fairness issues. This paper explores the impact of differential privacy on the statistics informing the sampling process, revealing a surprising effect: not only is the expected negative effect from the addition of noise for differential privacy negligible, but also this privacy noise can in fact reduce unfairness as it positively biases smaller counts. These findings are validated over an extensive analysis using datasets commonly applied in census statistics.

Vladimir Dvorkin, Ferdinando Fioretto

While deep learning gradually penetrates operational planning, its inherent prediction errors may significantly affect electricity prices. This letter examines how prediction errors propagate into electricity prices, revealing notable pricing errors and their spatial disparity in congested power systems. To improve fairness, we propose to embed electricity market-clearing optimization as a deep learning layer. Differentiating through this layer allows for balancing between prediction and pricing errors, as oppose to minimizing prediction errors alone. This layer implicitly optimizes fairness and controls the spatial distribution of price errors across the system. We showcase the price-aware deep learning in the nexus of wind power forecasting and short-term electricity market clearing.

My H. Dinh, Ferdinando Fioretto

The remarkable ability of language models (LMs) has also brought challenges at the interface of AI and security. A critical challenge pertains to how much information these models retain and leak about the training data. This is particularly urgent as the typical development of LMs relies on huge, often highly sensitive data, such as emails and chat logs. To contrast this shortcoming, this paper introduces Context-Aware Differentially Private Language Model (CADP-LM) , a privacy-preserving LM framework that relies on two key insights: First, it utilizes the notion of \emph{context} to define and audit the potentially sensitive information. Second, it adopts the notion of Differential Privacy to protect sensitive information and characterize the privacy leakage. A unique characteristic of CADP-LM is its ability to target the protection of sensitive sentences and contexts only, providing a highly accurate private model. Experiments on a variety of datasets and settings demonstrate these strengths of CADP-LM.

Cuong Tran, Ferdinando Fioretto

A number of learning models used in consequential domains, such as to assist in legal, banking, hiring, and healthcare decisions, make use of potentially sensitive users' information to carry out inference. Further, the complete set of features is typically required to perform inference. This not only poses severe privacy risks for the individuals using the learning systems, but also requires companies and organizations massive human efforts to verify the correctness of the released information. This paper asks whether it is necessary to require \emph{all} input features for a model to return accurate predictions at test time and shows that, under a personalized setting, each individual may need to release only a small subset of these features without impacting the final decisions. The paper also provides an efficient sequential algorithm that chooses which attributes should be provided by each individual. Evaluation over several learning tasks shows that individuals may be able to report as little as 10\% of their information to ensure the same level of accuracy of a model that uses the complete users' information.

Saswat Das, Ferdinando Fioretto

This work addresses the computational challenge of enforcing privacy for agentic Large Language Models (LLMs), where privacy is governed by the contextual integrity framework. Indeed, existing defenses rely on LLM-mediated checking stages that add substantial latency and cost, and that can be undermined in multi-turn interactions through manipulation or benign-looking conversational scaffolding. Contrasting this background, this paper makes a key observation: internal representations associated with privacy-violating intent can be separated from benign requests using linear structure. Using this insight, the paper proposes NeuroFilter, a guardrail framework that operationalizes contextual integrity by mapping norm violations to simple directions in the model's activation space, enabling detection even when semantic filters are bypassed. The proposed filter is also extended to capture threats arising during long conversations using the concept of activation velocity, which measures cumulative drift in internal representations across turns. A comprehensive evaluation across over 150,000 interactions and covering models from 7B to 70B parameters, illustrates the strong performance of NeuroFilter in detecting privacy attacks while maintaining zero false positives on benign prompts, all while reducing the computational inference cost by several orders of magnitude when compared to LLM-based agentic privacy defenses.

Ferdinando Fioretto, Diptangshu Sen, Juba Ziani

Networks are crucial components of many sectors, including telecommunications, healthcare, finance, energy, and transportation.The information carried in such networks often contains sensitive user data, like location data for commuters and packet data for online users. Therefore, when considering data release for networks, one must ensure that data release mechanisms do not leak information about individuals, quantified in a precise mathematical sense. Differential Privacy (DP) is the widely accepted, formal, state-of-the-art technique, which has found use in a variety of real-life settings including the 2020 U.S. Census, Apple users' device data, or Google's location data. Yet, the use of DP comes with new challenges, as the noise added for privacy introduces inaccuracies or biases and further, DP techniques can also distribute these biases disproportionately across different populations, inducing fairness issues. The goal of this paper is to characterize the impact of DP on bias and unfairness in the context of releasing information about networks, taking a departure from previous work which has studied these effects in the context of private population counts release (such as in the U.S. Census). To this end, we consider a network release problem where the network structure is known to all, but the weights on edges must be released privately. We consider the impact of this private release on a simple downstream decision-making task run by a third-party, which is to find the shortest path between any two pairs of nodes and recommend the best route to users. This setting is of highly practical relevance, mirroring scenarios in transportation networks, where preserving privacy while providing accurate routing information is crucial. Our work provides theoretical foundations and empirical evidence into the bias and unfairness arising due to privacy in these networked decision problems.

Chenrui Ma, Xi Xiao, Lin Zhao et al.

Iterative generative models such as Flow Matching and Diffusion models have demonstrated strong test-time scaling behavior, where additional inference computation can improve generation quality. In contrast, Drift Models offer efficient one-step generation, but their direct generation paradigm limits such flexibility. In this work, we propose Drift Flow Matching (DFM), a framework that connects drifting generative modeling with flow-based iterative generation. DFM preserves the efficiency of direct transport maps while enabling generation to be refined through multiple inference steps when desired. This bridges the gap between one-step Drift Models and multi-step Flow Matching methods, and provides a novel generative paradigm that can adapt sampling computation to different quality--efficiency requirements. Extensive experiments across different tasks and datasets demonstrate the effectiveness and generality of the proposed framework.

Jameson Sandler, Jacob K. Christopher, Thomas Hartvigsen et al.

Speculative decoding has become the standard approach for accelerating Large Language Model (LLM) inference. It exploits a lossless draft-then-verify procedure to circumvent the latency of autoregressive decoding, achieving impressive speed-ups. Yet, current speculative decoding approaches remain limited by two fundamental bottlenecks: (1) the autoregressive dependency during drafting which limits parallelism, and (2) frequent rejections of draft tokens caused by misalignment between the draft and verify models. This paper proposes SpecDiff-2, a novel framework to jointly address these two bottlenecks. It leverages discrete diffusion as a non-autoregressive drafter to address bottleneck (1) and develops novel techniques to calibrate discrete diffusion drafters with autoregressive verifiers, addressing bottleneck (2). Experimental results across a comprehensive benchmark suite show that SpecDiff-2 achieves a new state-of-the-art across reasoning, coding, and mathematical benchmarks, improving tokens-per-second by up to an average of +55% over previous baselines and obtaining up to 5.5x average speed-up over standard decoding, without any loss of accuracy.

Stefano Zampini, Jacob K. Christopher, Luca Oneto et al.

Stable diffusion models represent the state-of-the-art in data synthesis across diverse domains and hold transformative potential for applications in science and engineering, e.g., by facilitating the discovery of novel solutions and simulating systems that are computationally intractable to model explicitly. While there is increasing effort to incorporate physics-based constraints into generative models, existing techniques are either limited in their applicability to latent diffusion frameworks or lack the capability to strictly enforce domain-specific constraints. To address this limitation this paper proposes a novel integration of stable diffusion models with constrained optimization frameworks, enabling the generation of outputs satisfying stringent physical and functional requirements. The effectiveness of this approach is demonstrated through material design experiments requiring adherence to precise morphometric properties, challenging inverse design tasks involving the generation of materials inducing specific stress-strain responses, and copyright-constrained content generation tasks. All code has been released at https://github.com/RAISELab-atUVA/Constrained-Stable-Diffusion.

Lize Shao, Michael Cardei, Zichen Xie et al.

Discrete diffusion models are a powerful, emerging paradigm for code generation. They construct programs through iterative refinement of partially corrupted token sequences and enable parallel token refinement. Importantly, this paradigm exposes a global program state at each denoising step, which provides a natural intervention point for enforcing program-level functionality and security constraints, guiding the generation before the final code is committed. Building on this observation, the paper introduces Constrained Diffusion for Code (CDC), a training-free neurosymbolic inference framework that integrates constraint satisfaction directly into the reverse denoising process. CDC augments the base discrete diffusion sampler with constraint-aware denoising operators that combine mathematical optimization with program analysis to identify constraint-relevant regions of the intermediate program state and locally adjust the denoising trajectory, steering generation toward feasible programs while remaining close to the base model. Across code generation benchmarks, CDC consistently improves constraint satisfaction in functional correctness, security, and even syntax, outperforming discrete diffusion and autoregressive baselines with less corrective computation and more localized edits.

Jacob K. Christopher, James E. Warner, Ferdinando Fioretto

Deep generative models provide state-of-the-art performance across a wide array of applications, with recent studies showing increasing applicability for science and engineering. Despite a growing corpus of literature focused on the integration of physics-based constraints into the generation process, existing approaches fail to enforce strict constraint satisfaction while maintaining sample quality. In particular, training-free constrained sampling methods, while providing per-sample feasibility guarantees, introduce a fundamental mismatch between the training objective and the constrained sampling procedure, often leading to performance degradation. Identifying this training-sampling misalignment as a central limitation of current constrained generative modeling approaches, this paper proposes Constraint-Aware Flow Matching, a novel end-to-end framework that explicitly incorporates constraint projections into the training objective. By aligning the model's learned dynamics with the constrained sampling process, the proposed method mitigates distributional shift induced by projection-based corrections, enabling high-quality constrained generation. The proposed approach is evaluated on three challenging real-world benchmarks, illustrating the generality and efficacy of the method.

Jacob K Christopher, Stephen Baek, Ferdinando Fioretto

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative diffusion models as a constrained optimization problem, steering the generated data distribution to remain within a specified region to ensure adherence to the given constraints. These capabilities are validated on applications featuring both convex and challenging, non-convex, constraints as well as ordinary differential equations, in domains spanning from synthesizing new materials with precise morphometric properties, generating physics-informed motion, optimizing paths in planning scenarios, and human motion synthesis.

Jinhao Liang, Jacob K Christopher, Sven Koenig et al.

Recent advances in diffusion models hold significant potential in robotics, enabling the generation of diverse and smooth trajectories directly from raw representations of the environment. Despite this promise, applying diffusion models to motion planning remains challenging due to their difficulty in enforcing critical constraints, such as collision avoidance and kinematic feasibility. These limitations become even more pronounced in Multi-Robot Motion Planning (MRMP), where multiple robots must coordinate in shared spaces. To address these challenges, this work proposes Simultaneous MRMP Diffusion (SMD), a novel approach integrating constrained optimization into the diffusion sampling process to produce collision-free, kinematically feasible trajectories. Additionally, the paper introduces a comprehensive MRMP benchmark to evaluate trajectory planning algorithms across scenarios with varying robot densities, obstacle complexities, and motion constraints. Experimental results show SMD consistently outperforms classical and other learning-based motion planners, achieving higher success rates and efficiency in complex multi-robot environments.

James Kotary, Ferdinando Fioretto

Learning to Optimize (LtO) is a problem setting in which a machine learning (ML) model is trained to emulate a constrained optimization solver. Learning to produce optimal and feasible solutions subject to complex constraints is a difficult task, but is often made possible by restricting the input space to a limited distribution of related problems. Most LtO methods focus on directly learning solutions to the primal problem, and applying correction schemes or loss function penalties to encourage feasibility. This paper proposes an alternative approach, in which the ML model is trained instead to predict dual solution estimates directly, from which primal estimates are constructed to form dual-feasible solution pairs. This enables an end-to-end training scheme is which the dual objective is maximized as a loss function, and solution estimates iterate toward primal feasibility, emulating a Dual Ascent method. First it is shown that the poor convergence properties of classical Dual Ascent are reflected in poor convergence of the proposed training scheme. Then, by incorporating techniques from practical Augmented Lagrangian methods, we show how the training scheme can be improved to learn highly accurate constrained optimization solvers, for both convex and nonconvex problems.

Michael Cardei, Huu Binh Ta, Ferdinando Fioretto

Masked diffusion models (MDMs) generate discrete sequences by iterative denoising under an absorbing masking process. In standard masked diffusion, if a token remains masked after a reverse update, the model discards its clean-state prediction for that position. Thus, still-masked positions must be repeatedly inferred from the mask token alone. This design choice limits cross-step refinement. To address this limitation, this paper proposes a simple, yet effective, post-training adaptation for MDMs that conditions each denoising step on the model's own previous clean-state predictions. The resulting method, called Self-Conditioned Masked Diffusion Models (SCMDM), requires minimal architectural change, does not introduce a recurrent latent-state pathway, does not rely on an auxiliary reference model, and adds no extra denoiser evaluations during sampling. This is an important departure from partial self-conditioning approaches which requires expensive model training from scratch. In particular, the paper shows that partial self-conditioning, including the commonly used 50% dropout strategy for training self-conditioned models from scratch, is suboptimal in the post-training regime. Instead, once the model's self-generated clean-state estimates become informative, the specialization to refinement is preferable to mixing conditional and unconditional objectives. SCMDM is evaluated across multiple domains, demonstrating consistent improvement over vanilla MDM baselines, achieving nearly a 50% reduction in generative perplexity on OWT-trained models (42.89 to 23.72), alongside strong improvements in discretized image synthesis quality, small molecular generation, and enhanced fidelity in genomic distribution modeling.

Ethan King, James Kotary, Ferdinando Fioretto et al.

Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial intelligence and optimal control has led to a variety of approaches, based on distinct strategies. This work proposes a novel approach to learning optimization, in which the underlying metric space of a proximal operator splitting algorithm is learned so as to maximize its convergence rate. While prior works in optimization theory have derived optimal metrics for limited classes of problems, the results do not extend to many practical problem forms including general Quadratic Programming (QP). This paper shows how differentiable optimization can enable the end-to-end learning of proximal metrics, enhancing the convergence of proximal algorithms for QP problems beyond what is possible based on known theory. Additionally, the results illustrate a strong connection between the learned proximal metrics and active constraints at the optima, leading to an interpretation in which the learning of proximal metrics can be viewed as a form of active set learning.

Jacob K. Christopher, Michael Cardei, Jinhao Liang et al.

Despite the remarkable generative capabilities of diffusion models, their integration into safety-critical or scientifically rigorous applications remains hindered by the need to ensure compliance with stringent physical, structural, and operational constraints. To address this challenge, this paper introduces Neuro-Symbolic Diffusion (NSD), a novel framework that interleaves diffusion steps with symbolic optimization, enabling the generation of certifiably consistent samples under user-defined functional and logic constraints. This key feature is provided for both standard and discrete diffusion models, enabling, for the first time, the generation of both continuous (e.g., images and trajectories) and discrete (e.g., molecular structures and natural language) outputs that comply with constraints. This ability is demonstrated on tasks spanning three key challenges: (1) Safety, in the context of non-toxic molecular generation and collision-free trajectory optimization; (2) Data scarcity, in domains such as drug discovery and materials engineering; and (3) Out-of-domain generalization, where enforcing symbolic constraints allows adaptation beyond the training distribution.

Sree Harsha Nelaturu, Nishaanth Kanna Ravichandran, Cuong Tran et al.

In the machine learning ecosystem, hardware selection is often regarded as a mere utility, overshadowed by the spotlight on algorithms and data. This oversight is particularly problematic in contexts like ML-as-a-service platforms, where users often lack control over the hardware used for model deployment. How does the choice of hardware impact generalization properties? This paper investigates the influence of hardware on the delicate balance between model performance and fairness. We demonstrate that hardware choices can exacerbate existing disparities, attributing these discrepancies to variations in gradient flows and loss surfaces across different demographic groups. Through both theoretical and empirical analysis, the paper not only identifies the underlying factors but also proposes an effective strategy for mitigating hardware-induced performance imbalances.

Prince Zizhuang Wang, Jinhao Liang, Shuyi Chen et al.

Decision-focused learning (DFL) integrates predictive models with downstream optimization, directly training machine learning models to minimize decision errors. While DFL has been shown to provide substantial advantages when compared to a counterpart that treats the predictive and prescriptive models separately, it has also been shown to struggle in high-dimensional and risk-sensitive settings, limiting its applicability in real-world settings. To address this limitation, this paper introduces decision-focused generative learning (Gen-DFL), a novel framework that leverages generative models to adaptively model uncertainty and improve decision quality. Instead of relying on fixed uncertainty sets, Gen-DFL learns a structured representation of the optimization parameters and samples from the tail regions of the learned distribution to enhance robustness against worst-case scenarios. This approach mitigates over-conservatism while capturing complex dependencies in the parameter space. The paper shows, theoretically, that Gen-DFL achieves improved worst-case performance bounds compared to traditional DFL. Empirically, it evaluates Gen-DFL on various scheduling and logistics problems, demonstrating its strong performance against existing DFL methods.

Jinhao Liang, Jacob K. Christopher, Sven Koenig et al.

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics, requiring the computation of collision-free paths for multiple agents moving from their respective start to goal positions. Coordinating multiple agents in a shared environment poses significant challenges, especially in continuous spaces where traditional optimization algorithms struggle with scalability. Moreover, these algorithms often depend on discretized representations of the environment, which can be impractical in image-based or high-dimensional settings. Recently, diffusion models have shown promise in single-agent path planning, capturing complex trajectory distributions and generating smooth paths that navigate continuous, high-dimensional spaces. However, directly extending diffusion models to MAPF introduces new challenges since these models struggle to ensure constraint feasibility, such as inter-agent collision avoidance. To overcome this limitation, this work proposes a novel approach that integrates constrained optimization with diffusion models for MAPF in continuous spaces. This unique combination directly produces feasible multi-agent trajectories that respect collision avoidance and kinematic constraints. The effectiveness of our approach is demonstrated across various challenging simulated scenarios of varying dimensionality.

Saswat Das, Marco Romanelli, Ferdinando Fioretto

Ensuring privacy-preserving inference on cryptographically secure data is a well-known computational challenge. To alleviate the bottleneck of costly cryptographic computations in non-linear activations, recent methods have suggested linearizing a targeted portion of these activations in neural networks. This technique results in significantly reduced runtimes with often negligible impacts on accuracy. In this paper, we demonstrate that such computational benefits may lead to increased fairness costs. Specifically, we find that reducing the number of ReLU activations disproportionately decreases the accuracy for minority groups compared to majority groups. To explain these observations, we provide a mathematical interpretation under restricted assumptions about the nature of the decision boundary, while also showing the prevalence of this problem across widely used datasets and architectures. Finally, we show how a simple procedure altering the fine-tuning step for linearized models can serve as an effective mitigation strategy.

Jinhao Liang, Sven Koenig, Ferdinando Fioretto

Multi-Robot Motion Planning (MRMP) involves generating collision-free trajectories for multiple robots operating in a shared continuous workspace. While discrete multi-agent path finding (MAPF) methods are broadly adopted due to their scalability, their coarse discretization severely limits trajectory quality. In contrast, continuous optimization-based planners offer higher-quality paths but suffer from the curse of dimensionality, resulting in poor scalability with respect to the number of robots. This paper tackles the limitations of these two approaches by introducing a novel framework that integrates discrete MAPF solvers with constrained generative diffusion models. The resulting framework, called Discrete-Guided Diffusion (DGD), has three key characteristics: (1) it decomposes the original nonconvex MRMP problem into tractable subproblems with convex configuration spaces, (2) it combines discrete MAPF solutions with constrained optimization techniques to guide diffusion models capture complex spatiotemporal dependencies among robots, and (3) it incorporates a lightweight constraint repair mechanism to ensure trajectory feasibility. The proposed method sets a new state-of-the-art performance in large-scale, complex environments, scaling to 100 robots while achieving planning efficiency and high success rates.

Saswat Das, Jameson Sandler, Ferdinando Fioretto

LLM agents have begun to appear as personal assistants, customer service bots, and clinical aides. While these applications deliver substantial operational benefits, they also require continuous access to sensitive data, which increases the likelihood of unauthorized disclosures. Moreover, these disclosures go beyond mere explicit disclosure, leaving open avenues for gradual manipulation or sidechannel information leakage. This study proposes an auditing framework for conversational privacy that quantifies an agent's susceptibility to these risks. The proposed Conversational Manipulation for Privacy Leakage (CMPL) framework is designed to stress-test agents that enforce strict privacy directives against an iterative probing strategy. Rather than focusing solely on a single disclosure event or purely explicit leakage, CMPL simulates realistic multi-turn interactions to systematically uncover latent vulnerabilities. Our evaluation on diverse domains, data modalities, and safety configurations demonstrates the auditing framework's ability to reveal privacy risks that are not deterred by existing single-turn defenses, along with an in-depth longitudinal study of the temporal dynamics of leakage, strategies adopted by adaptive adversaries, and the evolution of adversarial beliefs about sensitive targets. In addition to introducing CMPL as a diagnostic tool, the paper delivers (1) an auditing procedure grounded in quantifiable risk metrics and (2) an open benchmark for evaluation of conversational privacy across agent implementations.

Shuyi Chen, Ferdinando Fioretto, Feng Qiu et al.

Extreme hazard events such as wildfires and hurricanes increasingly threaten power systems, causing widespread outages and disrupting critical services. Recently, predict-then-optimize approaches have gained traction in grid operations, where system functionality forecasts are first generated and then used as inputs for downstream decision-making. However, this two-stage method often results in a misalignment between prediction and optimization objectives, leading to suboptimal resource allocation. To address this, we propose predict-all-then-optimize-globally (PATOG), a framework that integrates outage prediction with globally optimized interventions. At its core, our global-decision-focused (GDF) neural ODE model captures outage dynamics while optimizing resilience strategies in a decision-aware manner. Unlike conventional methods, our approach ensures spatially and temporally coherent decision-making, improving both predictive accuracy and operational efficiency. Experiments on synthetic and real-world datasets demonstrate significant improvements in outage prediction consistency and grid resilience.

Michael Cardei, Jacob K Christopher, Thomas Hartvigsen et al.

Discrete diffusion models are a class of generative models that construct sequences by progressively denoising samples from a categorical noise distribution. Beyond their rapidly growing ability to generate coherent natural language, these models present a new and important opportunity to enforce sequence-level constraints, a capability that current autoregressive models cannot natively provide. This paper capitalizes on this opportunity by introducing Constrained Discrete Diffusion (CDD), a novel integration of differentiable constraint optimization within the diffusion process to ensure adherence to constraints, logic rules, or safety requirements for generated sequences. Unlike conventional text generators that often rely on post-hoc filtering or model retraining for controllable generation, CDD directly imposes constraints into the discrete diffusion sampling process, resulting in a training-free and effective approach. Experiments in toxicity-controlled text generation, property-constrained molecule design, and instruction-constrained text completion demonstrate that CDD achieves zero constraint violations in a diverse array of tasks while preserving fluency, novelty, and coherence while outperforming autoregressive and existing discrete diffusion approaches.

Ferdinando Fioretto, Pascal Van Hentenryck, Juba Ziani

This chapter is meant to be part of the book "Differential Privacy in Artificial Intelligence: From Theory to Practice" and provides an introduction to Differential Privacy. It starts by illustrating various attempts to protect data privacy, emphasizing where and why they failed, and providing the key desiderata of a robust privacy definition. It then defines the key actors, tasks, and scopes that make up the domain of privacy-preserving data analysis. Following that, it formalizes the definition of Differential Privacy and its inherent properties, including composition, post-processing immunity, and group privacy. The chapter also reviews the basic techniques and mechanisms commonly used to implement Differential Privacy in its pure and approximate forms.

My H Dinh, James Kotary, Ferdinando Fioretto

Many decision processes in artificial intelligence and operations research are modeled by parametric optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize (PtO) paradigm in machine learning aims to maximize downstream decision quality by training the parametric inference model end-to-end with the subsequent constrained optimization. This requires backpropagation through the optimization problem using approximation techniques specific to the problem's form, especially for nondifferentiable linear and mixed-integer programs. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives, known for their ability to ensure properties of fairness and robustness in decision models. Through a collection of training techniques and proposed application settings, it shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.

My H. Dinh, James Kotary, Ferdinando Fioretto

Learning to Rank (LTR) is one of the most widely used machine learning applications. It is a key component in platforms with profound societal impacts, including job search, healthcare information retrieval, and social media content feeds. Conventional LTR models have been shown to produce biases results, stimulating a discourse on how to address the disparities introduced by ranking systems that solely prioritize user relevance. However, while several models of fair learning to rank have been proposed, they suffer from deficiencies either in accuracy or efficiency, thus limiting their applicability to real-world ranking platforms. This paper shows how efficiently-solvable fair ranking models, based on the optimization of Ordered Weighted Average (OWA) functions, can be integrated into the training loop of an LTR model to achieve favorable balances between fairness, user utility, and runtime efficiency. In particular, this paper is the first to show how to backpropagate through constrained optimizations of OWA objectives, enabling their use in integrated prediction and decision models.

Huu Binh Ta, Michael Cardei, Alvaro Velasquez et al.

Discrete diffusion models generate sequences by iteratively denoising samples corrupted by categorical noise, offering an appealing alternative to autoregressive decoding for structured and symbolic generation. However, standard training targets a likelihood-based objective that primarily matches the data distribution and provides no native mechanism for enforcing hard constraints or optimizing non-differentiable properties at inference time. This work addresses this limitation and introduces Search-Augmented Masked Diffusion (SearchDiff), a training-free neurosymbolic inference framework that integrates informed search directly into the reverse denoising process. At each denoising step, the model predictions define a proposal set that is optimized under a user-specified property satisfaction, yielding a modified reverse transition that steers sampling toward probable and feasible solutions. Experiments in biological design and symbolic reasoning illustrate that SearchDiff substantially improves constraint satisfaction and property adherence, while consistently outperforming discrete diffusion and autoregressive baselines.

Jameson Sandler, Ahmet Üstün, Marco Romanelli et al.

The practice of speculative decoding, whereby inference is probabilistically supported by a smaller, cheaper, ``drafter'' model, has become a standard technique for systematically reducing the decoding time of large language models. This paper conducts an analysis of speculative decoding through the lens of its potential disparate speed-up rates across tasks. Crucially, the paper shows that speed-up gained from speculative decoding is not uniformly distributed across tasks, consistently diminishing for under-fit, and often underrepresented tasks. To better understand this phenomenon, we derive an analysis to quantify this observed ``unfairness'' and draw attention to the factors that motivate such disparate speed-ups to emerge. Further, guided by these insights, the paper proposes a mitigation strategy designed to reduce speed-up disparities and validates the approach across several model pairs, revealing on average a 12% improvement in our fairness metric.

Jacob K. Christopher, Austin Seamann, Jingyi Cui et al.

Diffusion models offer a powerful means of capturing the manifold of realistic protein structures, enabling rapid design for protein engineering tasks. However, existing approaches observe critical failure modes when precise constraints are necessary for functional design. To this end, we present a constrained diffusion framework for structure-guided protein design, ensuring strict adherence to functional requirements while maintaining precise stereochemical and geometric feasibility. The approach integrates proximal feasibility updates with ADMM decomposition into the generative process, scaling effectively to the complex constraint sets of this domain. We evaluate on challenging protein design tasks, including motif scaffolding and vacancy-constrained pocket design, while introducing a novel curated benchmark dataset for motif scaffolding in the PDZ domain. Our approach achieves state-of-the-art, providing perfect satisfaction of bonding and geometric constraints with no degradation in structural diversity.

Jinhao Liang, Yixuan Sun, Anirban Samaddar et al.

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples onto the feasible set; however, repeated projection can distort the learned distribution and induce a mismatch with the data manifold. Thus, recent multi-stage procedures attempt to defer projection to clean samples during sampling, but they increase algorithmic complexity and accumulate errors across steps. This paper addresses these challenges by proposing a novel training-free method, Chance-constrained Flow Matching (CCFM), that integrates stochastic optimization into the sampling process, enabling effective enforcement of hard constraints while maintaining high-fidelity sample generation. Importantly, CCFM guarantees feasibility in the same manner as conventional repeated projection, yet, despite operating directly on noisy intermediate samples, it is theoretically equivalent to projecting onto the feasible set defined by clean samples. This yields a sampler that mitigates distributional distortion. Empirical experiments show that CCFM outperforms current state-of-the-art constrained generative models in modeling complex physical systems governed by partial differential equations and molecular docking problems, delivering higher feasibility and fidelity.

Yusuf Guven, Vincenzo Di Vito, Ferdinando Fioretto

Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or design parameters) are tightly coupled with the PDE state variables, and the feasible set is implicitly defined by the governing PDE constraints. This coupling makes the problems computationally demanding, as it requires handling high dimensional discretization and dynamic constraints. To address these challenges, this paper introduces a learning-based framework that integrates a dynamic predictor with an optimization surrogate. The dynamic predictor, a novel time-discrete Neural Operator (Lu et al.), efficiently approximate system trajectories governed by PDE dynamics, while the optimization surrogate leverages proxy optimizer techniques (Kotary et al.) to approximate the associated optimal decisions. This dual-network design enables real-time approximation of optimal strategies while explicitly capturing the coupling between decisions and PDE dynamics. We validate the proposed approach on benchmark PDE-constrained optimization tasks inlacing Burgers' equation, heat equation and voltage regulation, and demonstrate that it achieves solution quality comparable to classical control-based algorithms, such as the Direct Method and Model Predictive Control (MPC), while providing up to four orders of magnitude improvement in computational speed.

Robin Staab, Nikola Jovanović, Kimberly Mai et al.

Data minimization (DM) describes the principle of collecting only the data strictly necessary for a given task. It is a foundational principle across major data protection regulations like GDPR and CPRA. Violations of this principle have substantial real-world consequences, with regulatory actions resulting in fines reaching hundreds of millions of dollars. Notably, the relevance of data minimization is particularly pronounced in machine learning (ML) applications, which typically rely on large datasets, resulting in an emerging research area known as Data Minimization in Machine Learning (DMML). At the same time, existing work on other ML privacy and security topics often addresses concerns relevant to DMML without explicitly acknowledging the connection. This disconnect leads to confusion among practitioners, complicating their efforts to implement DM principles and interpret the terminology, metrics, and evaluation criteria used across different research communities. To address this gap, our work introduces a comprehensive framework for DMML, including a unified data pipeline, adversaries, and points of minimization. This framework allows us to systematically review the literature on data minimization and \emph{DM-adjacent} methodologies, for the first time presenting a structured overview designed to help practitioners and researchers effectively apply DM principles. Our work facilitates a unified DM-centric understanding and broader adoption of data minimization strategies in AI/ML.

James Kotary, Himanshu Sharma, Ethan King et al.

Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems, as a function of their defining parameters. Prior L2O methods focus almost entirely on single-level programs, in contrast to the bilevel programs, whose constraints are themselves expressed in terms of optimization subproblems. Bilevel programs have numerous important use cases but are notoriously difficult to solve, particularly under stringent time demands. This paper proposes a framework for learning to solve a broad class of challenging bilevel optimization problems, by leveraging modern techniques for differentiation through optimization problems. The framework is illustrated on an array of synthetic bilevel programs, as well as challenging control system co-design problems, showing how neural networks can be trained as efficient approximators of parametric bilevel optimization.

My H Dinh, James Kotary, Lauryn P. Gouldin et al.

Criminal courts across the United States handle millions of cases every year, and the scheduling of those cases must accommodate a diverse set of constraints, including the preferences and availability of courts, prosecutors, and defense teams. When criminal court schedules are formed, defendants' scheduling preferences often take the least priority, although defendants may face significant consequences (including arrest or detention) for missed court dates. Additionally, studies indicate that defendants' nonappearances impose costs on the courts and other system stakeholders. To address these issues, courts and commentators have begun to recognize that pretrial outcomes for defendants and for the system would be improved with greater attention to court processes, including \emph{court scheduling practices}. There is thus a need for fair criminal court pretrial scheduling systems that account for defendants' preferences and availability, but the collection of such data poses logistical challenges. Furthermore, optimizing schedules fairly across various parties' preferences is a complex optimization problem, even when such data is available. In an effort to construct such a fair scheduling system under data uncertainty, this paper proposes a joint optimization and learning framework that combines machine learning models trained end-to-end with efficient matching algorithms. This framework aims to produce court scheduling schedules that optimize a principled measure of fairness, balancing the availability and preferences of all parties.