Andrea Censi’s research while affiliated with ETH Zurich and other places

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Publications (78)


Iterative VCG-based Mechanism Fosters Cooperation in Multi-Regional Network Design
  • Preprint
  • File available

March 2025

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7 Reads

Mingjia He

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Andrea Censi

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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.

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

March 2025

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14 Reads

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.


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

January 2025

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3 Reads

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2 Citations

IEEE Transactions on Robotics

This paper discusses the integration challenges and strategies for designing mobile robots, by focusing on the taskdriven, 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 decisionmaking 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 Rate (FNR) and False Positive Rate (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.


Fig. 1. Example of coupled public resources. fraction of the total population, of which s pr [r] ∈ [0, s[r]) is dedicated for congestion-free, priority access (e.g., a highway express lane; or a reserved parking lot), and the remaining s gp [r] = s[r] − s pr [r] is left for potentially congested, general purpose access. In particular, in case more than s gp [r] users are granted general purpose access, a time delay proportional to the excess demand is incurred by those users. Priority access to each resource is regulated by means of a karma economy. Each user is endowed with a nontradable, resource-specific karma credit k[r] ∈ K[r] = {0, . . . , k max [r]} 1 , and K = [k[1], . . . , k[n r ]] ∈ r K[r] denotes the vector of karma credits. The user may use its karma to place a bid b ∈ N for priority access. The highest s pr [r] bidders gain priority access and pay their bids, while all other bidders get general purpose access and do not make a payment. The total payment is redistributed to the users according to a redistribution rule to be described hereafter.
To Travel Quickly or to Park Conveniently: Coupled Resource Allocations with Multi-Karma Economies

December 2024

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36 Reads

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.


Fig. 1. The interactive network design framework, featuring a noncooperative, as well as a cooperative phase.
Fig. 3. Sioux Falls network, subdivided between Region 1 and 2.
Fig. 4. Equilibrium solutions of interactive network design.
Fig. 6. The impact of interactive network design for heterogeneous regions.
Co-investment with Payoff Sharing Benefit Operators and Users in Network Design

September 2024

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53 Reads

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.


CARMA: Fair and Efficient Bottleneck Congestion Management via Nontradable Karma Credits

September 2024

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43 Reads

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13 Citations

Transportation Science

This paper proposes a nonmonetary 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 nontradable 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, that is, its ability to tailor to the private preferences of commuters without centrally collecting the information. History: This paper has been accepted for the Transportation Science Special Issue on TSL Conference 2023. Funding: This work was supported by NCCR Automation, a National Centre of Competence in Research, funded by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung [Grant 180545]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2023.0323 .



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

January 2024

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15 Reads

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3 Citations

IEEE Control Systems Letters

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 .




Citations (45)


... We recognize that parallel yet disconnected efforts exist to address these challenges. For instance, efficient category theory-based algorithms have recently been developed for the co-design of self-driving vehicles, considering diverse design values such as cost, compute requirements, vehicle mass, and power [40][41][42]. In Machine Learning (ML), there is a strong emphasis on generative models for design generation [43], with recent applications in soft robot co-design [32,44], enabling optimization in a reduced-order space while recovering the full design description. ...

Reference:

Soft yet Effective Robots via Holistic Co-Design
CODEI: Resource-Efficient Task-Driven Co-Design of Perception and Decision Making for Mobile Robots Applied to Autonomous Vehicles
  • Citing Article
  • January 2025

IEEE Transactions on Robotics

... Finally, in addition to if different karma economies should be coupled there is a question of how to implement such coupling. Inspired by monetary economies, one could envision introducing exchange rates between different economies, e.g., one unit of transportation karma exchanges for two units of electricity karma; however, it has been shown that exchange rates are inconsequential in equilibrium as they are counter-acted by the scale of bids (Elokda et al., 2024d). Moreover, if the goal is to maximize the combined long-run Nash welfare, then Theorem 5 dictates the straightforward coupling in which there is simply one karma account to use for all resources. ...

To Travel Quickly or to Park Conveniently: Coupled Resource Allocations with Multi-Karma Economies
  • Citing Article
  • January 2024

IFAC-PapersOnLine

... On the other hand, the importance of fairness is widely acknowledged, yet this intuitive notion is difficult to define formally and incorporate in control objectives. An emerging body of literature has thus aimed at incorporating fairness in control (Jalota et al., 2021;Villa et al., 2025;Bang et al., 2024;Annaswamy and Venkataramanan, 2024;Elokda et al., 2024c;Shilov et al., 2025;Hall et al., 2025). ...

CARMA: Fair and Efficient Bottleneck Congestion Management via Nontradable Karma Credits
  • Citing Article
  • September 2024

Transportation Science

... For this purpose, a complementary Dynamic Population Game (DPG) model was developed that gives fine grained insights on the karma economy (Elokda et al., 2024b,c). DPGs are a tractable subclass of mean-field games that enable computing complex and high-dimensional Stationary Nash Equilibria (SNE) (Elokda et al., 2024a). The SNE is a finer-grained solution concept than the KE that fully accounts for the karma budget in every time-step, considers discounted future rewards, and provides detailed bidding policies mapping both urgency and karma to (potentially probabilistic) bids. ...

Dynamic Population Games: A Tractable Intersection of Mean-Field Games and Population Games
  • Citing Article
  • January 2024

IEEE Control Systems Letters

... For example, the SNE allows to quantify the fraction of times users are expected to spend below a certain karma level, as well as whether 'karma wealth inequalities' can arise (Elokda et al., 2024b). The DPG model was applied in multiple extensions, including endogenous redistribution shares that depend on the users' actions, e.g., at what time they depart during the morning rush hour (Elokda et al., 2024c), elastic population of users (Elokda et al., 2023), and pairwise or otherwise limited resource contests such as in autonomous driving (Elokda et al., 2024b;Chavoshi et al., 2024). However, the DPG model is computational in nature and less amenable to analysis, for which the high-level KE is advantageous. ...

A Dynamic Population Game Model of Non-Monetary Bottleneck Congestion Management Under Elastic Demand Using Karma
  • Citing Conference Paper
  • December 2023

... These limitations motivate the need for online, scalable, and parallelizable planning tools to support real-time robot coordination at scale. Factorization for scalable multi-agent planning -Factorization has emerged as a powerful tool across domains such as game theory [17] and motion planning [18] to mitigate the curse of dimensionality by exploiting the problem structure. ...

Factorization of Multi-Agent Sampling-Based Motion Planning
  • Citing Conference Paper
  • December 2023

... In the context of traffic demand management, pilot studies on Karma have investigated its potential use for high occupancy and priority toll lanes 28,36 , auction-controlled intersection management with fully connected vehicles 27,29 , and transportation modality pricing 37,38 . ...

Karma Priority lanes for fair and efficient bottleneck congestion management
  • Citing Conference Paper
  • June 2023

... The system's dynamics are formulated in state-space notation asẋ(t) = f (x(t), u(t)), with the state vector x(t) ∈ R 8 and the input vector u(t) ∈ R 2 . These equations are expressed in a local reference frame defined by the curvilinear coordinate s that represents the vehicle's position along the road centerline, and the lateral deviation from the centerline y, as in (9). The orientation error ξ is defined as the difference between the vehicle's heading angle and the tangent angle of the road centerline in the global coordinate system, given by ...

A Learning-Based Nonlinear Model Predictive Controller for a Real Go-Kart Based on Black-Box Dynamics Modeling Through Gaussian Processes

IEEE Transactions on Control Systems Technology

... Moreover, in addition to optimal bidding policies, the SNE predicts the stationary distribution of karma in the population, which holds more information than the stationary bids b ⋆ . For example, the SNE allows to quantify the fraction of times users are expected to spend below a certain karma level, as well as whether 'karma wealth inequalities' can arise (Elokda et al., 2024b). The DPG model was applied in multiple extensions, including endogenous redistribution shares that depend on the users' actions, e.g., at what time they depart during the morning rush hour (Elokda et al., 2024c), elastic population of users (Elokda et al., 2023), and pairwise or otherwise limited resource contests such as in autonomous driving (Elokda et al., 2024b;Chavoshi et al., 2024). ...

A Self-Contained Karma Economy for the Dynamic Allocation of Common Resources

Dynamic Games and Applications

... Other attempts in assessing AVs' riskiness often involve either first principle statistics [1], or reachability-based analysis [16], [17], [18]. The latter, in particular, includes different approaches that engineer specific surrogate safety measures to gauge the criticality of a scenario. ...

Formal Estimation of Collision Risks for Autonomous Vehicles: A Compositional Data-Driven Approach
  • Citing Article
  • March 2023

IEEE Transactions on Control of Network Systems