arXiv subjects

Emilio Frazzoli

Publications and source records attributed to Emilio Frazzoli.

At least 19 recordsLinked to original sources

arXiv2025

Invariant Price of Anarchy: a Metric for Welfarist Traffic Control

The Price of Anarchy (PoA) is a standard metric for quantifying inefficiency in socio-technical systems, widely used to guide policies like traffic tolling. Conventional PoA analysis relies on exact numerical costs. However, in many settings, costs represent agents' preferences and may be defined only up to possibly arbitrary scaling and shifting, representing informational and modeling ambiguities. We observe that while such transformations preserve equilibrium and optimal outcomes, they change the PoA value. To resolve this issue, we rely on results from Social Choice Theory and define the Invariant PoA. By connecting admissible transformations to degrees of comparability of agents' costs, we derive the specific social welfare functions which ensure that efficiency evaluations do not depend on arbitrary rescalings or translations of individual costs. Case studies on a toy example and the Zurich network demonstrate that identical tolling strategies can lead to substantially different efficiency estimates depending on the assumed comparability. Our framework thus demonstrates that explicit axiomatic foundations are necessary in order to define efficiency metrics and to appropriately guide policy in large-scale infrastructure design robustly and effectively.

cs.GT↗

arXiv2025

Hierarchical Strategic Decision-Making in Layered Mobility Systems

Mobility systems are complex socio-technical environments influenced by multiple stakeholders with hierarchically interdependent decisions, rendering effective control and policy design inherently challenging. We bridge hierarchical game-theoretic modeling with online feedback optimization by casting urban mobility as a tri-level Stackelberg game (travelers, operators, municipality) closed in a feedback loop. The municipality iteratively updates taxes, subsidies, and operational constraints using a projected two-point (gradient-free) scheme, while lower levels respond through equilibrium computations (Frank-Wolfe for traveler equilibrium; operator best responses). This model-free pipeline enforces constraints, accommodates heterogeneous users and modes, and scales to higher-dimensional policy vectors without differentiating through equilibrium maps. On a real multimodal network for Zurich, Switzerland, our method attains substantially better municipal objectives than Bayesian optimization and Genetic algorithms, and identifies integration incentives that increase multimodal usage while improving both operator objectives. The results show that feedback-based regulation can steer competition toward cooperative outcomes and deliver tangible welfare gains in complex, data-rich mobility ecosystems.

eess.SY↗

arXiv2025

Co-Investment with Payoff-Sharing Mechanism for Cooperative Decision-Making in Network Design Games

Network-based systems are inherently interconnected, with the design and performance of subnetworks being interdependent. However, the decisions of self-interested operators may lead to suboptimal outcomes for users and the overall system. This paper explores cooperative mechanisms that can simultaneously benefit both operators and users. We address this challenge using a game-theoretical framework that integrates both non-cooperative and cooperative game theory. In the non-cooperative stage, we propose a network design game in which subnetwork decision-makers strategically design local infrastructures. In the cooperative stage, co-investment with payoff-sharing mechanism is developed to enlarge collective benefits and fairly distribute them. To demonstrate the effectiveness of our framework, we conduct case studies on the Sioux Falls network and real-world public transport networks in Zurich and Winterthur, Switzerland. Our evaluation considers impacts on environmental sustainability, social welfare, and economic efficiency. The proposed framework provides a foundation for improving interdependent networked systems by enabling strategic cooperation among self-interested operators.

eess.SY↗

arXiv2025

A Vision for Trustworthy, Fair, and Efficient Socio-Technical Control using Karma Economies

Control systems will play a pivotal role in addressing societal-scale challenges as they drive the development of sustainable future smart cities. At the heart of these challenges is the trustworthy, fair, and efficient allocation of scarce public resources, including renewable energy, transportation, data, computation, etc.. Historical evidence suggests that monetary control -- the prototypical mechanism for managing resource scarcity -- is not always well-accepted in socio-technical resource contexts. In this vision article, we advocate for karma economies as an emerging non-monetary mechanism for socio-technical control. Karma leverages the repetitive nature of many socio-technical resources to jointly attain trustworthy, fair, and efficient allocations; by budgeting resource consumption over time and letting resource users ``play against their future selves.'' To motivate karma, we review related concepts in economics through a control systems lens, and make a case for a) shifting the viewpoint of resource allocations from single-shot and static to repeated and dynamic games; and b) adopting long-run Nash welfare as the formalization of ``fairness and efficiency'' in socio-technical contexts. We show that in many dynamic resource settings, karma Nash equilibria maximize long-run Nash welfare. Moreover, we discuss implications for a future smart city built on multi-karma economies: by choosing whether to combine different socio-technical resources, e.g., electricity and transportation, in a single karma economy, or separate into resource-specific economies, karma provides new flexibility to design the scope of fairness and efficiency.

cs.GT↗

arXiv2025

Reproducibility in the Control of Autonomous Mobility-on-Demand Systems

Autonomous Mobility-on-Demand (AMoD) systems, powered by advances in robotics, control, and Machine Learning (ML), offer a promising paradigm for future urban transportation. AMoD offers fast and personalized travel services by leveraging centralized control of autonomous vehicle fleets to optimize operations and enhance service performance. However, the rapid growth of this field has outpaced the development of standardized practices for evaluating and reporting results, leading to significant challenges in reproducibility. As AMoD control algorithms become increasingly complex and data-driven, a lack of transparency in modeling assumptions, experimental setups, and algorithmic implementation hinders scientific progress and undermines confidence in the results. This paper presents a systematic study of reproducibility in AMoD research. We identify key components across the research pipeline, spanning system modeling, control problems, simulation design, algorithm specification, and evaluation, and analyze common sources of irreproducibility. We survey prevalent practices in the literature, highlight gaps, and propose a structured framework to assess and improve reproducibility. Specifically, concrete guidelines are offered, along with a "reproducibility checklist", to support future work in achieving replicable, comparable, and extensible results. While focused on AMoD, the principles and practices we advocate generalize to a broader class of cyber-physical systems that rely on networked autonomy and data-driven control. This work aims to lay the foundation for a more transparent and reproducible research culture in the design and deployment of intelligent mobility systems.

cs.RO↗

arXiv2025

Test Automation for Interactive Scenarios via Promptable Traffic Simulation

Autonomous vehicle (AV) planners must undergo rigorous evaluation before widespread deployment on public roads, particularly to assess their robustness against the uncertainty of human behaviors. While recent advancements in data-driven scenario generation enable the simulation of realistic human behaviors in interactive settings, leveraging these models to construct comprehensive tests for AV planners remains an open challenge. In this work, we introduce an automated method to efficiently generate realistic and safety-critical human behaviors for AV planner evaluation in interactive scenarios. We parameterize complex human behaviors using low-dimensional goal positions, which are then fed into a promptable traffic simulator, ProSim, to guide the behaviors of simulated agents. To automate test generation, we introduce a prompt generation module that explores the goal domain and efficiently identifies safety-critical behaviors using Bayesian optimization. We apply our method to the evaluation of an optimization-based planner and demonstrate its effectiveness and efficiency in automatically generating diverse and realistic driving behaviors across scenarios with varying initial conditions.

cs.AI↗

arXiv2025

CODEI: Resource-Efficient Task-Driven Co-Design of Perception and Decision Making for Mobile Robots Applied to Autonomous Vehicles

This paper discusses the integration challenges and strategies for designing mobile robots, by focusing on the task-driven, optimal selection of hardware and software to balance safety, efficiency, and minimal usage of resources such as costs, energy, computational requirements, and weight. We emphasize the interplay between perception and motion planning in decision-making by introducing the concept of occupancy queries to quantify the perception requirements for sampling-based motion planners. Sensor and algorithm performance are evaluated using False Negative Rates (FPR) and False Positive Rates (FPR) across various factors such as geometric relationships, object properties, sensor resolution, and environmental conditions. By integrating perception requirements with perception performance, an Integer Linear Programming (ILP) approach is proposed for efficient sensor and algorithm selection and placement. This forms the basis for a co-design optimization that includes the robot body, motion planner, perception pipeline, and computing unit. We refer to this framework for solving the co-design problem of mobile robots as CODEI, short for Co-design of Embodied Intelligence. A case study on developing an Autonomous Vehicle (AV) for urban scenarios provides actionable information for designers, and shows that complex tasks escalate resource demands, with task performance affecting choices of the autonomy stack. The study demonstrates that resource prioritization influences sensor choice: cameras are preferred for cost-effective and lightweight designs, while lidar sensors are chosen for better energy and computational efficiency.

cs.RO↗

arXiv2025

Iterative VCG-based Mechanism Fosters Cooperation in Multi-Regional Network Design

Transportation network design often involves multiple stakeholders with diverse priorities. We consider a system with a hierarchical multi-agent structure, featuring self-optimized subnetwork operators at the lower level and a central organization at the upper level. Independent regional planning can lead to inefficiencies due to the lack of coordination, hindering interregional travel and cross-border infrastructure development, while centralized methods may struggle to align local interests and can be impractical to implement. To support decision making for such a system, we introduce an iterative VCG-based mechanism for multi-regional network design that fosters cooperation among subnetwork operators. By leveraging the Vickery-Clarke-Groves (VCG) mechanism, the framework determines collective investment decisions and the necessary payments from both operators and the central organization to achieve efficient outcomes. A case study on the European Railway System validates the effectiveness of the proposed method, demonstrating significant improvements in overall network performance through enhanced cross-region cooperation.

eess.SY↗

arXiv2024

To Travel Quickly or to Park Conveniently: Coupled Resource Allocations with Multi-Karma Economies

The large-scale allocation of public resources (e.g., transportation, energy) is among the core challenges of future Cyber-Physical-Human Systems (CPHS). In order to guarantee that these systems are efficient and fair, recent works have investigated non-monetary resource allocation schemes, including schemes that employ karma. Karma is a non-tradable token that flows from users gaining resources to users yielding resources. Thus far karma-based solutions considered the allocation of a single public resource, however, modern CPHS are complex as they involve the allocation of multiple coupled resources. For example, a user might want to trade-off fast travel on highways for convenient parking in the city center, and different users could have heterogeneous preferences for such coupled resources. In this paper, we explore how to optimally combine multiple karma economies for coupled resource allocations, using two mechanism-design instruments: (non-uniform) karma redistribution; and (non-unit) exchange rates. We first extend the existing Dynamic Population Game (DPG) model that predicts the Stationary Nash Equilibrium (SNE) of the multi-karma economies. Then, in a numerical case study, we demonstrate that the design of redistribution significantly affects the coupled resource allocations, while non-unit exchange rates play a minor role. To assess the allocation outcomes under user heterogeneity, we adopt Nash welfare as our social welfare function, since it makes no interpersonal comparisons and it is axiomatically rooted in social choice theory. Our findings suggest that the simplest mechanism design, that is, uniform redistribution with unit exchange rates, also attains maximum social welfare.

cs.GT↗

arXiv2024

Co-investment with Payoff Sharing Benefit Operators and Users in Network Design

Network-based complex systems are inherently interconnected, with the design and performance of subnetworks being interdependent. However, the decisions of self-interested operators may lead to suboptimal outcomes for users. In this paper, we consider the question of what cooperative mechanisms can benefit both operators and users simultaneously. We address this question in a game theoretical setting, integrating both non-cooperative and cooperative game theory. During the non-cooperative stage, subnetwork decision-makers strategically design their local networks. In the cooperative stage, the co-investment mechanism and the payoff-sharing mechanism are developed to enlarge collective benefits and fairly distribute them. A case study of the Sioux Falls network is conducted to demonstrate the efficiency of the proposed framework. The impact of this interactive network design on environmental sustainability, social welfare and economic efficiency is evaluated, along with an examination of scenarios involving regions with heterogeneous characteristics.

eess.SY↗

arXiv2024

Optimization of Rulebooks via Asymptotically Representing Lexicographic Hierarchies for Autonomous Vehicles

A key challenge in autonomous driving is that Autonomous Vehicles (AVs) must contend with multiple, often conflicting, planning requirements. These requirements naturally form in a hierarchy -- e.g., avoiding a collision is more important than maintaining lane. While the exact structure of this hierarchy remains unknown, to progress towards ensuring that AVs satisfy pre-determined behavior specifications, it is crucial to develop approaches that systematically account for it. Motivated by lexicographic behavior specification in AVs, this work addresses a lexicographic multi-objective motion planning problem, where each objective is incomparably more important than the next -- consider that avoiding a collision is incomparably more important than a lane change violation. This work ties together two elements. Firstly, a multi-objective candidate function that asymptotically represents lexicographic orders is introduced. Unlike existing multi-objective cost function formulations, this approach assures that returned solutions asymptotically align with the lexicographic behavior specification. Secondly, inspired by continuation methods, we propose two algorithms that asymptotically approach minimum rank decisions -- i.e., decisions that satisfy the highest number of important rules possible. Through a couple practical examples, we showcase that the proposed candidate function asymptotically represents the lexicographic hierarchy, and that both proposed algorithms return minimum rank decisions, even when other approaches do not.

cs.RO↗

arXiv2024

Dynamic Population Games: A Tractable Intersection of Mean-Field Games and Population Games

In many real-world large-scale decision problems, self-interested agents have individual dynamics and optimize their own long-term payoffs. Important examples include the competitive access to shared resources (e.g., roads, energy, or bandwidth) but also non-engineering domains like epidemic propagation and control. These problems are natural to model as mean-field games. Existing mathematical formulations of mean field games have had limited applicability in practice, since they require solving non-standard initial-terminal-value problems that are tractable only in limited special cases. In this letter, we propose a novel formulation, along with computational tools, for a practically relevant class of Dynamic Population Games (DPGs), which correspond to discrete-time, finite-state-and-action, stationary mean-field games. Our main contribution is a mathematical reduction of Stationary Nash Equilibria (SNE) in DPGs to standard Nash Equilibria (NE) in static population games. This reduction is leveraged to guarantee the existence of a SNE, develop an evolutionary dynamics-based SNE computation algorithm, and derive simple conditions that guarantee stability and uniqueness of the SNE. We provide two examples of applications: fair resource allocation with heterogeneous agents and control of epidemic propagation. Open source software for SNE computation: https://gitlab.ethz.ch/elokdae/dynamic-population-games

math.OC↗

arXiv2024

To Spend or to Gain: Online Learning in Repeated Karma Auctions

Recent years have seen a surge of artificial currency-based mechanisms in contexts where monetary instruments are deemed unfair or inappropriate, e.g., in allocating food donations to food banks, course seats to students, and, more recently, even for traffic congestion management. Yet the applicability of these mechanisms remains limited in repeated auction settings, as it is challenging for users to learn how to bid an artificial currency that has no value outside the auctions. Indeed, users must jointly learn the value of the currency in addition to how to spend it optimally. Moreover, in the prominent class of karma mechanisms, in which artificial karma payments are redistributed to users at each time step, users do not only spend karma to obtain public resources but also gain karma for yielding them. For this novel class of karma auctions, we propose an adaptive karma pacing strategy that learns to bid optimally, and show that this strategy a) is asymptotically optimal for a single user bidding against competing bids drawn from a stationary distribution; b) leads to convergent learning dynamics when all users adopt it; and c) constitutes an approximate Nash equilibrium as the number of users grows. Our results require a novel analysis in comparison to adaptive pacing strategies in monetary auctions, since we depart from the classical assumption that the currency has known value outside the auctions, and consider that the currency is both spent and gained through the redistribution of payments.

cs.GT↗

arXiv2023

Reliability-aware Control of Power Converters in Mobility Applications

This paper introduces an automatic control method designed to enhance the operation of electric vehicles, besides the speed tracking objectives, by including reliability and lifetime requirements. The research considers an automotive power converter which supplies electric power to a permanent magnet synchronous motor (PMSM). The primary control objective is to mitigate the thermal stress on the power electronic Insulate Gate Bipolar Transistors (IGBTs), while simultaneously ensuring effective speed tracking performance. To achieve these goals, we propose an extended H-inf design framework, which includes reliability models. The method is tested in two distinct scenarios: reliability-aware, and reliability-free cases. Furthermore, the paper conducts a lifetime analysis of the IGBTs, leveraging the Rainflow algorithm and temperature data.

eess.SY↗

arXiv2023

A Counterfactual Safety Margin Perspective on the Scoring of Autonomous Vehicles' Riskiness

Autonomous Vehicles (AVs) promise a range of societal advantages, including broader access to mobility, reduced road accidents, and enhanced transportation efficiency. However, evaluating the risks linked to AVs is complex due to limited historical data and the swift progression of technology. This paper presents a data-driven framework for assessing the risk of different AVs' behaviors in various operational design domains (ODDs), based on counterfactual simulations of "misbehaving" road users. We propose the notion of counterfactual safety margin, which represents the minimum deviation from nominal behavior that could cause a collision. This methodology not only pinpoints the most critical scenarios but also quantifies the (relative) risk's frequency and severity concerning AVs. Importantly, we show that our approach is applicable even when the AV's behavioral policy remains undisclosed, through worst- and best-case analyses, benefiting external entities like regulators and risk evaluators. Our experimental outcomes demonstrate the correlation between the safety margin, the quality of the driving policy, and the ODD, shedding light on the relative risks of different AV providers. Overall, this work contributes to the safety assessment of AVs and addresses legislative and insurance concerns surrounding this burgeoning technology.

cs.RO↗

arXiv2023

CARMA: Fair and efficient bottleneck congestion management via non-tradable karma credits

This paper proposes a non-monetary traffic demand management scheme, named CARMA, as a fair solution to the morning commute congestion. We consider heterogeneous commuters traveling through a single bottleneck that differ in both the desired arrival time and Value of Time (VOT). We consider a generalized notion of VOT by allowing it to vary dynamically on each day (e.g., according to trip purpose and urgency), rather than being a static characteristic of each individual. In our CARMA scheme, the bottleneck is divided into a fast lane that is kept in free flow and a slow lane that is subject to congestion. We introduce a non-tradable mobility credit, named karma, that is used by commuters to bid for access to the fast lane. Commuters who get outbid or do not participate in the CARMA scheme instead use the slow lane. At the end of each day, karma collected from the bidders is redistributed, and the process repeats day by day. We model the collective commuter behaviors under CARMA as a Dynamic Population Game (DPG), in which a Stationary Nash Equilibrium (SNE) is guaranteed to exist. Unlike existing monetary schemes, CARMA is demonstrated, both analytically and numerically, to achieve a) an equitable traffic assignment with respect to heterogeneous income classes and b) a strong Pareto improvement in the long-term average travel disutility with respect to no policy intervention. With extensive numerical analysis, we show that CARMA is able to retain the same congestion reduction as an optimal monetary tolling scheme under uniform karma redistribution and even outperform tolling under a well-designed redistribution scheme. We also highlight the privacy-preserving feature of CARMA, i.e., its ability to tailor to the private preferences of commuters without centrally collecting the information.

eess.SY↗

arXiv2023

Strategic Interactions in Multi-modal Mobility Systems: A Game-Theoretic Perspective

The evolution of existing transportation systems,mainly driven by urbanization and increased availability of mobility options, such as private, profit-maximizing ride-hailing companies, calls for tools to reason about their design and regulation. To study this complex socio-technical problem, one needs to account for the strategic interactions of the heterogeneous stakeholders involved in the mobility ecosystem and analyze how they influence the system. In this paper, we focus on the interactions between citizens who compete for the limited resources of a mobility system to complete their desired trip. Specifically, we present a game-theoretic framework for multi-modal mobility systems, where citizens, characterized by heterogeneous preferences, have access to various mobility options and seek individually-optimal decisions. We study the arising game and prove the existence of an equilibrium, which can be efficiently computed via a convex optimization problem. Through both an analytical and a numerical case study for the classic scenario of Sioux Falls, USA, we illustrate the capabilities of our model and perform sensitivity analyses. Importantly, we show how to embed our framework into a "larger" game among stakeholders of the mobility ecosystem (e.g., municipality, Mobility Service Providers, and citizens), effectively giving rise to tools to inform strategic interventions and policy-making in the mobility ecosystem.

cs.MA↗

arXiv2023

Categorification of Negative Information using Enrichment

In many engineering applications it is useful to reason about "negative information". For example, in planning problems, providing an optimal solution is the same as giving a feasible solution (the "positive" information) together with a proof of the fact that there cannot be feasible solutions better than the one given (the "negative" information). We model negative information by introducing the concept of "norphisms", as opposed to the positive information of morphisms. A "nategory" is a category that has "nom"-sets in addition to hom-sets, and specifies the interaction between norphisms and morphisms. In particular, we have composition rules of the form morphism + norphism $\to$ norphism. Norphisms do not compose by themselves; rather, they use morphisms as catalysts. After providing several applied examples, we connect nategories to enriched category theory. Specifically, we prove that categories enriched in de Paiva's dialectica categories GC, in the case C = Set and equipped with a modified monoidal product, define nategories which satisfy additional regularity properties. This formalizes negative information categorically in a way that makes negative and positive morphisms equal citizens.

math.CT↗