arXiv subjects

Ferdinando Fioretto

Publications and source records attributed to Ferdinando Fioretto.

At least 91 records · Page 5Linked to original sources

arXiv2021

Fast Approximations for Job Shop Scheduling: A Lagrangian Dual Deep Learning Method

The Jobs shop Scheduling Problem (JSP) is a canonical combinatorial optimization problem that is routinely solved for a variety of industrial purposes. It models the optimal scheduling of multiple sequences of tasks, each under a fixed order of operations, in which individual tasks require exclusive access to a predetermined resource for a specified processing time. The problem is NP-hard and computationally challenging even for medium-sized instances. Motivated by the increased stochasticity in production chains, this paper explores a deep learning approach to deliver efficient and accurate approximations to the JSP. In particular, this paper proposes the design of a deep neural network architecture to exploit the problem structure, its integration with Lagrangian duality to capture the problem constraints, and a post-processing optimization to guarantee solution feasibility.The resulting method, called JSP-DNN, is evaluated on hard JSP instances from the JSPLIB benchmark library. Computational results show that JSP-DNN can produce JSP approximations of high quality at negligible computational costs.

cs.LG↗

arXiv2021

A Fairness Analysis on Private Aggregation of Teacher Ensembles

The Private Aggregation of Teacher Ensembles (PATE) is an important private machine learning framework. It combines multiple learning models used as teachers for a student model that learns to predict an output chosen by noisy voting among the teachers. The resulting model satisfies differential privacy and has been shown effective in learning high-quality private models in semisupervised settings or when one wishes to protect the data labels. This paper asks whether this privacy-preserving framework introduces or exacerbates bias and unfairness and shows that PATE can introduce accuracy disparity among individuals and groups of individuals. The paper analyzes which algorithmic and data properties are responsible for the disproportionate impacts, why these aspects are affecting different groups disproportionately, and proposes guidelines to mitigate these effects. The proposed approach is evaluated on several datasets and settings.

cs.LG↗

arXiv2021

Learning Hard Optimization Problems: A Data Generation Perspective

Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for large-scale instances. Machine learning frameworks that learn to approximate solutions to such hard optimization problems are a potentially promising avenue to address these difficulties, particularly when many closely related problem instances must be solved repeatedly. Supervised learning frameworks can train a model using the outputs of pre-solved instances. However, when the outputs are themselves approximations, when the optimization problem has symmetric solutions, and/or when the solver uses randomization, solutions to closely related instances may exhibit large differences and the learning task can become inherently more difficult. This paper demonstrates this critical challenge, connects the volatility of the training data to the ability of a model to approximate it, and proposes a method for producing (exact or approximate) solutions to optimization problems that are more amenable to supervised learning tasks. The effectiveness of the method is tested on hard non-linear nonconvex and discrete combinatorial problems.

math.OC↗

arXiv2021

A Privacy-Preserving and Trustable Multi-agent Learning Framework

Distributed multi-agent learning enables agents to cooperatively train a model without requiring to share their datasets. While this setting ensures some level of privacy, it has been shown that, even when data is not directly shared, the training process is vulnerable to privacy attacks including data reconstruction and model inversion attacks. Additionally, malicious agents that train on inverted labels or random data, may arbitrarily weaken the accuracy of the global model. This paper addresses these challenges and presents Privacy-preserving and trustable Distributed Learning (PT-DL), a fully decentralized framework that relies on Differential Privacy to guarantee strong privacy protections of the agents' data, and Ethereum smart contracts to ensure trustability. The paper shows that PT-DL is resilient up to a 50% collusion attack, with high probability, in a malicious trust model and the experimental evaluation illustrates the benefits of the proposed model as a privacy-preserving and trustable distributed multi-agent learning system on several classification tasks.

cs.LG↗

arXiv2021

Differential Privacy of Hierarchical Census Data: An Optimization Approach

This paper is motivated by applications of a Census Bureau interested in releasing aggregate socio-economic data about a large population without revealing sensitive information about any individual. The released information can be the number of individuals living alone, the number of cars they own, or their salary brackets. Recent events have identified some of the privacy challenges faced by these organizations. To address them, this paper presents a novel differential-privacy mechanism for releasing hierarchical counts of individuals. The counts are reported at multiple granularities (e.g., the national, state, and county levels) and must be consistent across all levels. The core of the mechanism is an optimization model that redistributes the noise introduced to achieve differential privacy in order to meet the consistency constraints between the hierarchical levels. The key technical contribution of the paper shows that this optimization problem can be solved in polynomial time by exploiting the structure of its cost functions. Experimental results on very large, real datasets show that the proposed mechanism provides improvements of up to two orders of magnitude in terms of computational efficiency and accuracy with respect to other state-of-the-art techniques.

cs.DB↗

arXiv2021

End-to-End Constrained Optimization Learning: A Survey

This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning architectures. These approaches hold the promise to develop new hybrid machine learning and optimization methods to predict fast, approximate, solutions to combinatorial problems and to enable structural logical inference. This paper presents a conceptual review of the recent advancements in this emerging area.

cs.LG↗

arXiv2021

Bilevel Optimization for Differentially Private Optimization in Energy Systems

This paper studies how to apply differential privacy to constrained optimization problems whose inputs are sensitive. This task raises significant challenges since random perturbations of the input data often render the constrained optimization problem infeasible or change significantly the nature of its optimal solutions. To address this difficulty, this paper proposes a bilevel optimization model that can be used as a post-processing step: It redistributes the noise introduced by a differentially private mechanism optimally while restoring feasibility and near-optimality. The paper shows that, under a natural assumption, this bilevel model can be solved efficiently for real-life large-scale nonlinear nonconvex optimization problems with sensitive customer data. The experimental results demonstrate the accuracy of the privacy-preserving mechanism and showcases significant benefits compared to standard approaches.

math.OC↗

arXiv2020

Bias and Variance of Post-processing in Differential Privacy

Post-processing immunity is a fundamental property of differential privacy: it enables the application of arbitrary data-independent transformations to the results of differentially private outputs without affecting their privacy guarantees. When query outputs must satisfy domain constraints, post-processing can be used to project the privacy-preserving outputs onto the feasible region. Moreover, when the feasible region is convex, a widely adopted class of post-processing steps is also guaranteed to improve accuracy. Post-processing has been applied successfully in many applications including census data-release, energy systems, and mobility. However, its effects on the noise distribution is poorly understood: It is often argued that post-processing may introduce bias and increase variance. This paper takes a first step towards understanding the properties of post-processing. It considers the release of census data and examines, both theoretically and empirically, the behavior of a widely adopted class of post-processing functions.

cs.LG↗

arXiv2020

Differentially Private and Fair Deep Learning: A Lagrangian Dual Approach

A critical concern in data-driven decision making 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 sensitive attributes is essential, while, 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. The method relies on the notion of differential privacy and the use of Lagrangian duality to design neural networks that can accommodate fairness constraints while guaranteeing the privacy of sensitive attributes. The paper analyses the tension between accuracy, privacy, and fairness and the experimental evaluation illustrates the benefits of the proposed model on several prediction tasks.

cs.LG↗

arXiv2020

Differentially Private Optimal Power Flow for Distribution Grids

Although distribution grid customers are obliged to share their consumption data with distribution system operators (DSOs), a possible leakage of this data is often disregarded in operational routines of DSOs. This paper introduces a privacy-preserving optimal power flow (OPF) mechanism for distribution grids that secures customer privacy from unauthorised access to OPF solutions, e.g., current and voltage measurements. The mechanism is based on the framework of differential privacy that allows to control the participation risks of individuals in a dataset by applying a carefully calibrated noise to the output of a computation. Unlike existing private mechanisms, this mechanism does not apply the noise to the optimization parameters or its result. Instead, it optimizes OPF variables as affine functions of the random noise, which weakens the correlation between the grid loads and OPF variables. To ensure feasibility of the randomized OPF solution, the mechanism makes use of chance constraints enforced on the grid limits. The mechanism is further extended to control the optimality loss induced by the random noise, as well as the variance of OPF variables. The paper shows that the differentially private OPF solution does not leak customer loads up to specified parameters.

math.OC↗

arXiv2020

High-Fidelity Machine Learning Approximations of Large-Scale Optimal Power Flow

The AC Optimal Power Flow (AC-OPF) is a key building block in many power system applications. It determines generator setpoints at minimal cost that meet the power demands while satisfying the underlying physical and operational constraints. It is non-convex and NP-hard, and computationally challenging for large-scale power systems. Motivated by the increased stochasticity in generation schedules and increasing penetration of renewable sources, this paper explores a deep learning approach to deliver highly efficient and accurate approximations to the AC-OPF. In particular, the paper proposes an integration of deep neural networks and Lagrangian duality to capture the physical and operational constraints. The resulting model, called OPF-DNN, is evaluated on real case studies from the French transmission system, with up to 3,400 buses and 4,500 lines. Computational results show that OPF-DNN produces highly accurate AC-OPF approximations whose costs are within 0.01% of optimality. OPF-DNN generates, in milliseconds, solutions that capture the problem constraints with high fidelity.

eess.SP↗

arXiv2020

Differentially Private Convex Optimization with Feasibility Guarantees

This paper develops a novel differentially private framework to solve convex optimization problems with sensitive optimization data and complex physical or operational constraints. Unlike standard noise-additive algorithms, that act primarily on the problem data, objective or solution, and disregard the problem constraints, this framework requires the optimization variables to be a function of the noise and exploits a chance-constrained problem reformulation with formal feasibility guarantees. The noise is calibrated to provide differential privacy for identity and linear queries on the optimization solution. For many applications, including resource allocation problems, the proposed framework provides a trade-off between the expected optimality loss and the variance of optimization results.

cs.CR↗

arXiv2020

Lagrangian Duality for Constrained Deep Learning

This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. Such constraints arise in many science and engineering domains, where the task amounts to learning optimization problems which must be solved repeatedly and include hard physical and operational constraints. The paper also considers applications where the learning task must enforce constraints on the predictor itself, either because they are natural properties of the function to learn or because it is desirable from a societal standpoint to impose them. This paper demonstrates experimentally that Lagrangian duality brings significant benefits for these applications. In energy domains, the combination of Lagrangian duality and deep learning can be used to obtain state-of-the-art results to predict optimal power flows, in energy systems, and optimal compressor settings, in gas networks. In transprecision computing, Lagrangian duality can complement deep learning to impose monotonicity constraints on the predictor without sacrificing accuracy. Finally, Lagrangian duality can be used to enforce fairness constraints on a predictor and obtain state-of-the-art results when minimizing disparate treatments.

cs.LG↗

arXiv2020

Differential Privacy for Stackelberg Games

This paper introduces a differentially private (DP) mechanism to protect the information exchanged during the coordination of sequential and interdependent markets. This coordination represents a classic Stackelberg game and relies on the exchange of sensitive information between the system agents. The paper is motivated by the observation that the perturbation introduced by traditional DP mechanisms fundamentally changes the underlying optimization problem and even leads to unsatisfiable instances. To remedy such limitation, the paper introduces the Privacy-Preserving Stackelberg Mechanism (PPSM), a framework that enforces the notions of feasibility and fidelity of the privacy-preserving information to the original problem objective. PPSM complies with the notion of differential privacy and ensures that the outcomes of the privacy-preserving coordination mechanism are close-to-optimality for each agent. Experimental results on several gas and electricity market benchmarks based on a real case study demonstrate the effectiveness of the approach.

math.OC↗

arXiv2019

Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods

The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It is often needed to be solved repeatedly under various conditions, either in real-time or in large-scale studies. This need is further exacerbated by the increasing stochasticity of power systems due to renewable energy sources in front and behind the meter. To address these challenges, this paper presents a deep learning approach to the OPF. The learning model exploits the information available in the prior states of the system (which is commonly available in practical applications), as well as a dual Lagrangian method to satisfy the physical and engineering constraints present in the OPF. The proposed model is evaluated on a large collection of realistic power systems. The experimental results show that its predictions are highly accurate with average errors as low as 0.2%. Additionally, the proposed approach is shown to improve the accuracy of widely adopted OPF linear DC approximation by at least two orders of magnitude.

eess.SP↗

arXiv2019

PPSM: A Privacy-Preserving Stackelberg Mechanism: Privacy Guarantees for the Coordination of Sequential Electricity and Gas Markets

This paper introduces a differentially private mechanism to protect the information exchanged during the coordination of the sequential market-clearing of electricity and natural gas systems. The coordination between these sequential and interdependent markets represents a classic Stackelberg game and relies on the exchange of sensitive information between the system agents, including the supply and demand bids in each market or the characteristics of the systems. The paper is motivated by the observation that traditional differential privacy mechanisms are unsuitable for the problem of interest: The perturbation introduced by these mechanisms fundamentally changes the underlying optimization problem and even leads to unsatisfiable instances. To remedy such limitation, the paper introduces the Privacy-Preserving Stackelberg Mechanism (PPSM), a framework that enforces the notions of consistency and fidelity of the privacy-preserving information to the original problem objective. The PPSM has strong properties: It complies with the notion of differential privacy and ensures that the outcomes of the privacy-preserving coordination mechanisms are close-to-optimality for each agent. The fidelity property is analyzed by providing theoretical guarantees on the cost of privacy of PPSM and experimental results on several gas and electricity market benchmarks based on a real case study demonstrate the effectiveness of the approach.

eess.SY↗

arXiv2019

Privacy-Preserving Obfuscation for Distributed Power Systems

This paper considers the problem of releasing privacy-preserving load data of a decentralized operated power system. The paper focuses on data used to solve Optimal Power Flow (OPF) problems and proposes a distributed algorithm that complies with the notion of Differential Privacy, a strong privacy framework used to bound the risk of re-identification. The problem is challenging since the application of traditional differential privacy mechanisms to the load data fundamentally changes the nature of the underlying optimization problem and often leads to severe feasibility issues. The proposed differentially private distributed algorithm is based on the Alternating Direction Method of Multipliers (ADMM) and guarantees that the released privacy-preserving data retains high fidelity and satisfies the AC power flow constraints. Experimental results on a variety of OPF benchmarks demonstrate the effectiveness of the approach.

math.OC↗

arXiv2019

Privacy-Preserving Obfuscation of Critical Infrastructure Networks

The paper studies how to release data about a critical infrastructure network (e.g., the power network or a transportation network) without disclosing sensitive information that can be exploited by malevolent agents, while preserving the realism of the network. It proposes a novel obfuscation mechanism that combines several privacy-preserving building blocks with a bi-level optimization model to significantly improve accuracy. The obfuscation is evaluated for both realism and privacy properties on real energy and transportation networks. Experimental results show the obfuscation mechanism substantially reduces the potential damage of an attack exploiting the released data to harm the real network.

cs.CR↗