Saverio Bolognani

Jonas G. Matt, Lukas Ortmann, Saverio Bolognani et al.

When high amounts of active power are injected into power distribution grids, the overall power flow is limited because voltages reach their upper acceptable limits. Volt/var control aims to raise this power flow limit without physically reinforcing the grid but by controlling the voltage using reactive power. We use real consumption and generation data on a low-voltage CIGRÉ grid model and an experiment on a real distribution grid feeder to analyze how different volt/var methods can enhance the grid. We show that local droop control enhances the grid but underutilizes the reactive power resources. We discuss how this inefficiency can be partly reduced by fine-tuning the droop curves through data-driven techniques but illustrate that inherent trade-off persist for any local control method. We finally demonstrate that coordinated control methods can track the optimal solution and enhance the grid to its full potential if grid-wide communication is available. Our numerical study over a whole year of real data suggests that coordinated volt/var control can enable another 10.4% of maximum active power injections compared to droop control. In a small-scale real-life experiment, coordinated control enhanced the grid by the same amount.

Zhiyu He, Saverio Bolognani, Michael Muehlebach et al.

Feedback optimization enables autonomous optimality seeking of a dynamical system through its closed-loop interconnection with iterative optimization algorithms. Among various iteration structures, model-based approaches require the input-output sensitivity matrix of the system to construct gradients, whereas model-free approaches eliminate this need by estimating gradients from real-time objective evaluations. These approaches offer complementary benefits in sample efficiency and accuracy against model mismatch, i.e., sensitivity errors. To achieve balanced closed-loop performance, we propose a gray-box feedback optimization controller, featuring systematic incorporation of approximate sensitivities into model-free updates via a tunable convex combination. We provide unified performance characterizations covering different approaches. We elucidate how cumulative sensitivity errors (model-based) and variances due to stochastic exploration (model-free) shape the closed-loop behavior and induce a trade-off between iteration and dimensional dependence. The proposed controller retains sample efficiency and provable (local) optimality for nonconvex problems despite inaccurate sensitivities. We further develop and characterize a running gray-box controller that handles constrained time-varying problems with changing objectives and steady-state input-output maps.

Ezzat Elokda, Saverio Bolognani, Florian Dörfler et al.

We perform a behavioral experiment of karma, a class of mechanisms for repeated resource allocation with attractive fairness and efficiency properties, in theory. Individuals in these mechanisms bid non-tradable credits that flow from resource consumers to yielders, like karma. Human subjects recruited on Amazon MTurk are repeatedly and randomly paired to bid karma according to time-varying and stochastic individual preferences or urgency to acquire resources. Treatments varied in the dynamic urgency process (frequent moderate urgency versus sporadic high urgency) and the richness of the bidding scheme (binary versus full range). Results are benchmarked against random allocation, and karma achieves a (almost) Pareto improvement over random, despite the MTurk subjects deviating significantly from the theoretically optimal Nash bidding policy. Maximum improvement is attained by subjects that deviate from Nash by up to one karma bid unit on average, and positive improvement is attained with average deviations of up to 3-4 bid units. These findings hold across all treatments, among which no significant differences are found, with the exception of the sporadic high urgency process with binary bidding treatment being (weakly) favorable over others. These results offer behaviorally robust lower bounds for the expected performance of karma in human populations. They also provide guidance for future testing and implementation of karma mechanisms in the real world.

Alessandro Zanardi, Pier Giuseppe Sessa, Nando Käslin et al.

We consider the interaction among agents engaging in a driving task and we model it as general-sum game. This class of games exhibits a plurality of different equilibria posing the issue of equilibrium selection. While selecting the most efficient equilibrium (in term of social cost) is often impractical from a computational standpoint, in this work we study the (in)efficiency of any equilibrium players might agree to play. More specifically, we bound the equilibrium inefficiency by modeling driving games as particular type of congestion games over spatio-temporal resources. We obtain novel guarantees that refine existing bounds on the Price of Anarchy (PoA) as a function of problem-dependent game parameters. For instance, the relative trade-off between proximity costs and personal objectives such as comfort and progress. Although the obtained guarantees concern open-loop trajectories, we observe efficient equilibria even when agents employ closed-loop policies trained via decentralized multi-agent reinforcement learning.

Matteo Cederle, Saverio Bolognani, Gian Antonio Susto

Mobility-on-demand systems like ride-hailing have transformed urban transportation, but they have also exacerbated socio-economic inequalities in access to these services, also due to surge pricing strategies. Although several fairness-aware frameworks have been proposed in smart mobility, they often overlook the temporal and situational variability of user urgency that shapes real-world transportation demands. This paper introduces a non-monetary, Karma-based mechanism that models endogenous urgency, allowing user time-sensitivity to evolve in response to system conditions as well as external factors. We develop a theoretical framework maintaining the efficiency and fairness guarantees of classical Karma economies, while accommodating this realistic user behavior modeling. Applied to a simplified simulated mobility-on-demand scenario, we provide a proof-of-concept illustration of the proposed framework, showing that it exhibits promising behavior in terms of system efficiency and equitable resource allocation, while acknowledging that a full treatment of realistic MoD complexity remains an important direction for future work.

Matteo Cederle, Saverio Bolognani, Gian Antonio Susto

Dynamic Population Games (DPGs) provide a tractable framework for modeling strategic interactions in large populations of self-interested agents, and have been successfully applied to the design of Karma economies, a class of fair non-monetary resource allocation mechanisms. Despite their appealing theoretical properties, existing computational tools for DPGs assume full knowledge of the game model and operate in a centralized fashion, limiting their applicability in realistic settings where agents have access only to their own private experience. This paper takes a step towards addressing this gap by studying model-free equilibrium learning in Karma DPGs. First, we analyze the setting in which a novel agent joins a Karma DPG already at its Stationary Nash Equilibrium (SNE) and learns a policy via Deep Q-Networks (DQN) without knowledge of the game model. Leveraging recent convergence results for DQN, we establish a suboptimality bound consisting of a DQN approximation error of order $O(1/\sqrt{N_s})$ and a mean field perturbation error of order $O(1/N)$, where $N_s$ is the replay buffer size and $N$ is the population size. Second, we consider the challenging problem of learning the SNE from scratch. We show empirically that combining deep RL with fictitious play and smoothed policy iteration allows agents to converge, in a model-free fashion, to a configuration close to the centrally computed SNE. Together, these contributions support the vision of Karma economies as practical tools for fair resource allocation.

Andreas Feik, Nicolas Lanzetti, Saverio Bolognani et al.

In many multiagent settings, such as electric vehicle charging and traffic routing, agents must make decisions in the face of uncertain behavior exhibited by others. Often, this uncertainty arises from multiple sources, such as incomplete information, limited computation, or bounded rationality, ultimately impacting the aggregate behavior. To tackle this challenge, we follow recent work on strategically robust game theory and postulate that agents seek protection directly against deviations around the emergent behavior, as opposed to explicitly modeling all sources of uncertainty. Specifically, we propose that each agent protects itself against the worst-case aggregate behavior within an optimal-transport-based ambiguity set centered at the emergent aggregate population behavior. This leads to a novel equilibrium concept, called strategically robust Wardrop equilibrium, that enables one to interpolate between standard Wardrop equilibria (no robustness) and security strategies (maximum robustness). In the setting of convex aggregative games, we establish the existence of a pure strategically robust Wardrop equilibrium and provide tractable computational tools for computing it. Through an application in electric vehicle charging, we demonstrate that strategically robust Wardrop equilibria lead to better decisions, protecting agents against the uncertain aggregate behavior of the population. Remarkably, we also observe that strategic robustness can lead to lower equilibrium costs for all agents, uncovering a "coordination-via-robustification" effect.

Ilia Shilov, Heinrich H. Nax, Saverio Bolognani

The Price of Anarchy (PoA) is a popular measure of the costs of decentralization in terms of efficiency losses. Almost all PoA analyses operate within a framework assuming both Cardinal Full-Comparability (CFC) and smoothness, in which case any derived bounds conveniently extend beyond pure Nash to coarse correlated equilibria and no-regret learning outcomes. However, interpersonal utility comparability is an additional assumption that generally has to be justified. Without it, cardinal utilities (e.g. defined under classical von Neumann--Morgenstern framework) are unique only up to agent-specific affine transformations, rendering both the utilitarian PoA and the classical smoothness conditions representation-dependent. In this paper, we operate under a more general Cardinal Non-Comparability (CNC) framework, under which the weighted Nash welfare is a canonical admissible aggregator. We introduce multiplicative smoothness, a product-form condition matched to the multiplicative structure of Nash welfare, and obtain PoA bounds that are CNC-invariant and extend to coarse correlated equilibria. We demonstrate applicability of our framework on single-choice welfare games, deriving the bounds through simple proof relying on multiplicative retention envelope and geometric closure. The interpretation of this bound in terms of the true cost of decentralization depends crucially on interpersonal comparability of utilities.

Sophie Hall, Kai Zhang, Ilia Shilov et al.

At the core of most socio-technical systems lies a scarce resource that is allocated among agents: highway lanes, public transit, road space, water rights, energy access, grid capacity, user attention, pollution rights, etc. With further automation of the underlying allocation processes, control engineers are increasingly tasked to make decisive assumptions regarding what society wants. In practice to date, design choices are largely driven by industry norms and conventions rather than a result of conscientiously responsible and ethical design. In this paper, we look at tools available to control engineers to design systems in a more principled manner in order to match the societal mandate. We consider three control design paradigms: online feedback optimization, control of Markov decision processes, and model predictive control. Beginning with aggregating individual agents' preferences into control design objectives, subsequently ensuring and certifying the fulfillment of those specifications, we argue that the feedback nature of control systems enables appropriate allocation of the shared resources in ways hitherto unparalleled.

Florian Dörfler, Zhiyu He, Giuseppe Belgioioso et al.

Traditionally, numerical algorithms are seen as isolated pieces of code confined to an {\em in silico} existence. However, this perspective is not appropriate for many modern computational approaches in control, learning, or optimization, wherein {\em in vivo} algorithms interact with their environment. Examples of such {\em open algorithms} include various real-time optimization-based control strategies, reinforcement learning, decision-making architectures, online optimization, and many more. Further, even {\em closed} algorithms in learning or optimization are increasingly abstracted in block diagrams with interacting dynamic modules and pipelines. In this opinion paper, we state our vision on a to-be-cultivated {\em systems theory of algorithms} and argue in favor of viewing algorithms as open dynamical systems interacting with other algorithms, physical systems, humans, or databases. Remarkably, the manifold tools developed under the umbrella of systems theory are well suited for addressing a range of challenges in the algorithmic domain. We survey various instances where the principles of algorithmic systems theory are being developed and outline pertinent modeling, analysis, and design challenges.

Nicolò Pagan, Joachim Baumann, Ezzat Elokda et al.

Prediction-based decision-making systems are becoming increasingly prevalent in various domains. Previous studies have demonstrated that such systems are vulnerable to runaway feedback loops, e.g., when police are repeatedly sent back to the same neighborhoods regardless of the actual rate of criminal activity, which exacerbate existing biases. In practice, the automated decisions have dynamic feedback effects on the system itself that can perpetuate over time, making it difficult for short-sighted design choices to control the system's evolution. While researchers started proposing longer-term solutions to prevent adverse outcomes (such as bias towards certain groups), these interventions largely depend on ad hoc modeling assumptions and a rigorous theoretical understanding of the feedback dynamics in ML-based decision-making systems is currently missing. In this paper, we use the language of dynamical systems theory, a branch of applied mathematics that deals with the analysis of the interconnection of systems with dynamic behaviors, to rigorously classify the different types of feedback loops in the ML-based decision-making pipeline. By reviewing existing scholarly work, we show that this classification covers many examples discussed in the algorithmic fairness community, thereby providing a unifying and principled framework to study feedback loops. By qualitative analysis, and through a simulation example of recommender systems, we show which specific types of ML biases are affected by each type of feedback loop. We find that the existence of feedback loops in the ML-based decision-making pipeline can perpetuate, reinforce, or even reduce ML biases.

Andrea Censi, Saverio Bolognani, Julian G. Zilly et al.

We present a new type of coordination mechanism among multiple agents for the allocation of a finite resource, such as the allocation of time slots for passing an intersection. We consider the setting where we associate one counter to each agent, which we call karma value, and where there is an established mechanism to decide resource allocation based on agents exchanging karma. The idea is that agents might be inclined to pass on using resources today, in exchange for karma, which will make it easier for them to claim the resource use in the future. To understand whether such a system might work robustly, we only design the protocol and not the agents' policies. We take a game-theoretic perspective and compute policies corresponding to Nash equilibria for the game. We find, surprisingly, that the Nash equilibria for a society of self-interested agents are very close in social welfare to a centralized cooperative solution. These results suggest that many resource allocation problems can have a simple, elegant, and robust solution, assuming the availability of a karma accounting mechanism.