The Impact of Recommendation Systems on Opinion Dynamics: Microscopic versus Macroscopic Effects

Recommendation systems are widely used in web services, such as social networks and e-commerce platforms, to serve personalized content to the users and, thus, enhance their experience. While personalization assists users in navigating through the available options, there have been growing concerns regarding its repercussions on the users and their opinions. Examples of negative impacts include the emergence of filter bubbles and the amplification of users' confirmation bias, which can cause opinion polarization and radicalization. In this paper, we study the impact of recommendation systems on users, both from a microscopic (i.e., at the level of individual users) and a macroscopic (i.e., at the level of a homogenous population) perspective. Specifically, we build on recent work on the interactions between opinion dynamics and recommendation systems to propose a model for this closed loop, which we then study both analytically and numerically. Among others, our analysis reveals that shifts in the opinions of individual users do not always align with shifts in the opinion distribution of the population. In particular, even in settings where the opinion distribution appears unaltered (e.g., measured via surveys across the population), the opinion of individual users might be significantly distorted by the recommendation system.Comment: Accepted for presentation at, and publication in the proceedings of, the 62nd IEEE Conference on Decision and Contro

Capture, Propagate, and Control Distributional Uncertainty

We study stochastic dynamical systems in settings where only partial statistical information about the noise is available, e.g., in the form of a limited number of noise realizations. Such systems are particularly challenging to analyze and control, primarily due to an absence of a distributional uncertainty model which: (1) is expressive enough to capture practically relevant scenarios; (2) can be easily propagated through system maps; (3) is invariant under propagation; and (4) allows for computationally tractable control actions. In this paper, we propose to model distributional uncertainty via Optimal Transport ambiguity sets and show that such modeling choice satisfies all of the above requirements. We then specialize our results to stochastic LTI systems, and start by showing that the distributional uncertainty can be efficiently captured, with high probability, within an Optimal Transport ambiguity set on the space of noise trajectories. Then, we show that such ambiguity sets propagate exactly through the system dynamics, giving rise to stochastic tubes that contain, with high probability, all trajectories of the stochastic system. Finally, we show that the control task is very interpretable, unveiling an interesting decomposition between the roles of the feedforward and the feedback control terms. Our results are actionable and successfully applied in stochastic reachability analysis and in trajectory planning under distributional uncertainty.Comment: arXiv admin note: text overlap with arXiv:2205.0034

Stochastic Wasserstein Gradient Flows using Streaming Data with an Application in Predictive Maintenance

We study estimation problems in safety-critical applications with streaming data. Since estimation problems can be posed as optimization problems in the probability space, we devise a stochastic projected Wasserstein gradient flow that keeps track of the belief of the estimated quantity and can consume samples from online data. We show the convergence properties of our algorithm. Our analysis combines recent advances in the Wasserstein space and its differential structure with more classical stochastic gradient descent. We apply our methodology for predictive maintenance of safety-critical processes: Our approach is shown to lead to superior performance when compared to classical least squares, enabling, among others, improved robustness for decision-making.Comment: Accepted for presentation at, and publication in the proceedings of, the 2023 IFAC World Congres

On the Co-Design of AV-Enabled Mobility Systems

The design of autonomous vehicles (AVs) and the design of AV-enabled mobility systems are closely coupled. Indeed, knowledge about the intended service of AVs would impact their design and deployment process, whilst insights about their technological development could significantly affect transportation management decisions. This calls for tools to study such a coupling and co-design AVs and AV-enabled mobility systems in terms of different objectives. In this paper, we instantiate a framework to address such co-design problems. In particular, we leverage the recently developed theory of co-design to frame and solve the problem of designing and deploying an intermodal Autonomous Mobility-on-Demand system, whereby AVs service travel demands jointly with public transit, in terms of fleet sizing, vehicle autonomy, and public transit service frequency. Our framework is modular and compositional, allowing one to describe the design problem as the interconnection of its individual components and to tackle it from a system-level perspective. To showcase our methodology, we present a real-world case study for Washington D.C., USA. Our work suggests that it is possible to create user-friendly optimization tools to systematically assess costs and benefits of interventions, and that such analytical techniques might gain a momentous role in policy-making in the future.Comment: 8 pages, 4 figures. Published in the Proceeding of the 23rd IEEE Intelligent Transportation Systems Conference, ITSC 2020. arXiv admin note: substantial text overlap with arXiv:1910.07714, arXiv:2008.0897

Modeling of Political Systems using Wasserstein Gradient Flows

The study of complex political phenomena such as parties' polarization calls for mathematical models of political systems. In this paper, we aim at modeling the time evolution of a political system whereby various parties selfishly interact to maximize their political success (e.g., number of votes). More specifically, we identify the ideology of a party as a probability distribution over a one-dimensional real-valued ideology space, and we formulate a gradient flow in the probability space (also called a Wasserstein gradient flow) to study its temporal evolution. We characterize the equilibria of the arising dynamic system, and establish local convergence under mild assumptions. We calibrate and validate our model with real-world time-series data of the time evolution of the ideologies of the Republican and Democratic parties in the US Congress. Our framework allows to rigorously reason about various political effects such as parties' polarization and homogeneity. Among others, our mechanistic model can explain why political parties become more polarized and less inclusive with time (their distributions get "tighter"), until all candidates in a party converge asymptotically to the same ideological position

Modeling of Political Systems using Wasserstein Gradient Flows

The study of complex political phenomena such as parties' polarization calls for mathematical models of political systems. In this paper, we aim at modeling the time evolution of a political system whereby various parties selfishly interact to maximize their political success (e.g., number of votes). More specifically, we identify the ideology of a party as a probability distribution over a one-dimensional real-valued ideology space, and we formulate a gradient flow in the probability space (also called a Wasserstein gradient flow) to study its temporal evolution. We characterize the equilibria of the arising dynamic system, and establish local convergence under mild assumptions. We calibrate and validate our model with real-world time-series data of the time evolution of the ideologies of the Republican and Democratic parties in the US Congress. Our framework allows to rigorously reason about various political effects such as parties' polarization and homogeneity. Among others, our mechanistic model can explain why political parties become more polarized and less inclusive with time (their distributions get "tighter"), until all candidates in a party converge asymptotically to the same ideological position

Dynamic Programming in Probability Spaces via Optimal Transport

We study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the solution of dynamic programming in probability spaces results from two ingredients: (i) the solution of dynamic programming in the “ground space” (i.e., the space on which the probability measures live) and (ii) the solution of an optimal transport problem. From a multi-agent control perspective, a separation principle holds: “low-level control of the agents of the fleet” (how does one reach the destination?) and “fleet-level control” (who goes where?) are decoupled.ISSN:0363-0129ISSN:1095-713