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Sergio Grammatico

Publications and source records attributed to Sergio Grammatico.

At least 37 records · Page 2Linked to original sources
arXiv2025

A Frank-Wolfe Algorithm for Strongly Monotone Variational Inequalities

We propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve projecting onto the desired set at each iteration, a distinctive feature of our proposed method is the use of a linear minimization oracle in each iteration. This difference potentially reduces the projection cost, a factor that can become significant for certain sets or in high-dimensional problems. We validate the performance of the proposed algorithm on the traffic assignment problem, motivated by the fact that the projection complexity per iteration increases exponentially with respect to the number of links.

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arXiv2025

On data-driven Wasserstein distributionally robust Nash equilibrium problems with heterogeneous uncertainty

We study stochastic Nash equilibrium problems subject to heterogeneous uncertainty on the expected valued cost functions of the individual agents, where we assume no prior knowledge of the underlying probability distributions of the uncertain variables. To account for this lack of knowledge, we consider an ambiguity set around the empirical probability distribution under the Wasserstein metric. We then show that, under mild assumptions, finite-sample guarantees on the probability that any resulting distributionally robust Nash equilibrium is also robust with respect to the true probability distributions with high confidence can be obtained. Furthermore, by recasting the game as a distributionally robust variational inequality, we establish asymptotic consistency of the set of data-driven distributionally robust equilibria to the solution set of the original game. Finally, we recast the distributionally robust Nash game as a finite-dimensional Nash equilibrium problem. We illustrate the proposed distributionally robust reformulation via numerical experiments of stochastic peer-to-peer electricity markets and Nash-Cournot games.

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arXiv2025

Linear-Quadratic Dynamic Games as Receding-Horizon Variational Inequalities

We consider dynamic games with linear dynamics and quadratic objective functions. We observe that the unconstrained open-loop Nash equilibrium coincides with a linear quadratic regulator in an augmented space, thus deriving an explicit expression of the cost-to-go. With such cost-to-go as a terminal cost, we show asymptotic stability for the receding-horizon solution of the finite-horizon, constrained game. Furthermore, we show that the problem is equivalent to a non-symmetric variational inequality, which does not correspond to any Nash equilibrium problem. For unconstrained closed-loop Nash equilibria, we derive a receding-horizon controller that is equivalent to the infinite-horizon one and ensures asymptotic stability.

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arXiv2025

Sequential feedback optimization with application to wind farm control

This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order information of the steady-state input-output mapping, which is computationally prohibitive for high-dimensional nonlinear systems and often leads to poor performance when approximated around a fixed operating point. To address this limitation, we propose a sequential algorithm that adaptively updates the linearization point during optimization, maintaining local accuracy throughout the trajectory. We prove convergence to a neighborhood of the optimal steady state with explicit error bounds. To reduce the computational burden of repeated linearization operations, we further develop a multi-timescale variant where linearization updates occur at a slower timescale than optimization iterations, achieving significant computational savings while preserving convergence guarantees. The effectiveness of the proposed framework is demonstrated via numerical simulations of a realistic wind farm control problem. The results validate both the theoretical convergence predictions and the expected computational advantages of our multi-timescale formulation.

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arXiv2025

Nash equilibrium seeking for a class of quadratic-bilinear Wasserstein distributionally robust games

We consider a class of Wasserstein distributionally robust Nash equilibrium problems, where agents construct heterogeneous data-driven Wasserstein ambiguity sets using private samples and radii, in line with their individual risk-averse behaviour. By leveraging relevant properties of this class of games, we show that equilibria of the original seemingly infinite-dimensional problem can be obtained as a solution to a finite-dimensional Nash equilibrium problem. We then reformulate the problem as a finite-dimensional variational inequality and establish the connection between the corresponding solution sets. Our reformulation has scalable behaviour with respect to the data size and maintains a fixed number of constraints, independently of the number of samples. To compute a solution, we leverage two algorithms, based on the golden ratio algorithm. The efficiency of both algorithmic schemes is corroborated through extensive simulation studies on an illustrative example and a stochastic portfolio allocation game, where behavioural coupling among investors is modeled.

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arXiv2025

Non-Euclidean Enriched Contraction Theory for Monotone Operators and Monotone Dynamical Systems

We adopt an operator-theoretic perspective to analyze a class of nonlinear fixed-point iterations and discrete-time dynamical systems. Specifically, we study the Krasnoselskij iteration - at the heart of countless algorithmic schemes and underpinning the stability analysis of numerous dynamical models - by focusing on a non-Euclidean vector space equipped with the diagonally weighted supremum norm. By extending the state of the art, we introduce the notion of enriched weak contractivity, which (i) is characterized by a simple, verifiable condition for Lipschitz operators, and (ii) yields explicit bounds on the admissible step size for the Krasnoselskij iteration. Our results relate the notion of weak contractivity with that of monotonicity of operators and dynamical systems and show its generality to design larger step sizes and improved convergence speed for broader classes of dynamical systems. The newly developed theory is illustrated on two applications: the design of zero-finding algorithms for monotone operators and the design of nonlinear consensus dynamics in monotone multi-agent dynamical systems.

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arXiv2025

Data-driven stabilization of switched and constrained linear systems

We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov-Metzler inequalities, we derive data-dependent bilinear programs whose solution directly returns a provably stabilizing controller and ensures $\mathcal{H}_2$ or $\mathcal{H}_{\infty}$ performance. We further present relaxations that considerably reduce the computational cost, still without requiring stabilizability of any of the switching modes. Finally, we showcase the flexibility of our approach on the constrained stabilization problem for a perturbed linear system. We validate our theoretical findings numerically, demonstrating the favourable trade-off between conservatism and tractability achieved by the proposed relaxations.

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arXiv2025

User-centric Vehicle-to-Grid Optimization with an Input Convex Neural Network-based Battery Degradation Model

We propose a data-driven, user-centric vehicle-to-grid (V2G) methodology based on multi-objective optimization to balance battery degradation and V2G revenue according to EV user preference. Given the lack of accurate and generalizable battery degradation models, we leverage input convex neural networks (ICNNs) to develop a data-driven degradation model trained on extensive experimental datasets. This approach enables our model to capture nonconvex dependencies on battery temperature and time while maintaining convexity with respect to the charging rate. Such a partial convexity property ensures that the second stage of our methodology remains computationally efficient. In the second stage, we integrate our data-driven degradation model into a multi-objective optimization framework to generate an optimal smart charging profile for each EV. This profile effectively balances the trade-off between financial benefits from V2G participation and battery degradation, controlled by a hyperparameter reflecting the user prioritization of battery health. Numerical simulations show the high accuracy of the ICNN model in predicting battery degradation for unseen data. Finally, we present a trade-off curve illustrating financial benefits from V2G versus losses from battery health degradation based on user preferences and showcase smart charging strategies under realistic scenarios.

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arXiv2025

Automated Lane Merging via Game Theory and Branch Model Predictive Control

We propose an integrated behavior and motion planning framework for the lane-merging problem. The behavior planner combines search-based planning with game theory to model vehicle interactions and plan multi-vehicle trajectories. Inspired by human drivers, we model the lane-merging problem as a gap selection process and determine the appropriate gap by solving a matrix game. Moreover, we introduce a branch model predictive control (BMPC) framework to account for the uncertain equilibrium strategies adopted by the surrounding vehicles, including Nash and Stackelberg strategies. A tailored numerical solver is developed to enhance computational efficiency by exploiting the tree structure inherent in BMPC. Finally, we validate our proposed integrated planner using real traffic data and demonstrate its effectiveness in handling interactions in dense traffic scenarios. The code is publicly available at: https://github.com/SailorBrandon/GT-BMPC.

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arXiv2024

Probabilistic Game-Theoretic Traffic Routing

We examine the routing problem for self-interested vehicles using stochastic decision strategies. By approximating the road latency functions and a non-linear variable transformation, we frame the problem as an aggregative game. We characterize the approximation error and we derive a new monotonicity condition for a broad category of games that encompasses the problem under consideration. Next, we propose a semi-decentralized algorithm to calculate the routing as a variational generalized Nash equilibrium and demonstrate the solution's benefits with numerical simulations. In the particular case of potential games, which emerges for linear latency functions, we explore a receding-horizon formulation of the routing problem, showing asymptotic convergence to destinations and analysing closed-loop performance dependence on horizon length through numerical simulations.

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arXiv2024

Estimation Network Design framework for efficient distributed optimization

Distributed decision problems features a group of agents that can only communicate over a peer-to-peer network, without a central memory. In applications such as network control and data ranking, each agent is only affected by a small portion of the decision vector: this sparsity is typically ignored in distributed algorithms, while it could be leveraged to improve efficiency and scalability. To address this issue, our recent paper introduces Estimation Network Design (END), a graph theoretical language for the analysis and design of distributed iterations. END algorithms can be tuned to exploit the sparsity of specific problem instances, reducing communication overhead and minimizing redundancy, yet without requiring case-by-case convergence analysis. In this paper, we showcase the flexility of END in the context of distributed optimization. In particular, we study the sparsity-aware version of many established methods, including ADMM, AugDGM and Push-Sum DGD. Simulations on an estimation problem in sensor networks demonstrate that END algorithms can boost convergence speed and greatly reduce the communication and memory cost.

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arXiv2024

An Efficient Risk-aware Branch MPC for Automated Driving that is Robust to Uncertain Vehicle Behaviors

One of the critical challenges in automated driving is ensuring safety of automated vehicles despite the unknown behavior of the other vehicles. Although motion prediction modules are able to generate a probability distribution associated with various behavior modes, their probabilistic estimates are often inaccurate, thus leading to a possibly unsafe trajectory. To overcome this challenge, we propose a risk-aware motion planning framework that appropriately accounts for the ambiguity in the estimated probability distribution. We formulate the risk-aware motion planning problem as a min-max optimization problem and develop an efficient iterative method by incorporating a regularization term in the probability update step. Via extensive numerical studies, we validate the convergence of our method and demonstrate its advantages compared to the state-of-the-art approaches.

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arXiv2023

Probably approximately correct stability of allocations in uncertain coalitional games with private sampling

We study coalitional games with exogenous uncertainty in the coalition value, in which each agent is allowed to have private samples of the uncertainty. As a consequence, the agents may have a different perception of stability of the grand coalition. In this context, we propose a novel methodology to study the out-of-sample coalitional rationality of allocations in the set of stable allocations (i.e., the core). Our analysis builds on the framework of probably approximately correct learning. Initially, we state a priori and a posteriori guarantees for the entire core. Furthermore, we provide a distributed algorithm to compute a compression set that determines the generalization properties of the a posteriori statements. We then refine our probabilistic robustness bounds by specialising the analysis to a single payoff allocation, taking, also in this case, both a priori and a posteriori approaches. Finally, we consider a relaxed $ζ$-core to include nearby allocations and also address the case of empty core. For this case, probabilistic statements are given on the eventual stability of allocations in the $ζ$-core.

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arXiv2023

The END: Estimation Network Design for games under partial-decision information

Multi-agent decision problems are typically solved via distributed iterative algorithms, where the agents only communicate between themselves on a peer-to-peer network. Each agent usually maintains a copy of each decision variable, while agreement among the local copies is enforced via consensus protocols. Yet, each agent is often directly influenced by a small portion of the decision variables only: neglecting this sparsity results in redundancy, poor scalability with the network size, communication and memory overhead. To address these challenges, we develop Estimation Network Design (END), a framework for the design and analysis of distributed algorithms, generalizing several recent approaches. END algorithms can be tuned to exploit problem-specific sparsity structures, by optimally allocating copies of each variable only to a subset of agents, to improve efficiency and minimize redundancy. We illustrate the END's potential by designing new algorithms for generalised Nash equilibrium (GNE) seeking under partial-decision information, that can leverage the sparsity in cost functions, constraints and aggregation values. Finally, we test numerically our methods on a unicast rate allocation problem, revealing greatly reduced communication and memory costs.

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arXiv2023

Distributionally robust stability of payoff allocations in stochastic coalitional games

We consider multi-agent coalitional games with uncertainty in the coalitional values. We provide a novel methodology to study the stability of the grand coalition in the case where each coalition constructs ambiguity sets for the (possibly) unknown probability distribution of the uncertainty. As a less conservative solution concept compared to worst-case approaches for coalitional stability, we consider a stochastic version of the so-called core set, i.e., the expected value core. Unfortunately, without exact knowledge of the probability distribution, the evaluation of the expected value core is an extremely challenging task. Hence, we propose the concept of distributionaly robust (DR) core. Leveraging tools from data-driven DR optimization under the Wasserstein distance, we provide finite-sample guarantees that any allocation which lies in the DR core is also stable with respect to the true probability distribution. Furthermore, we show that as the number of samples grows unbounded, the DR core converges almost surely to the true expected value core. We dedicate the last section to the computational tractability of finding an allocation in the DR core.

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arXiv2023

A Semi-Decentralized Tikhonov-based Algorithm for Optimal Generalized Nash Equilibrium Selection

To optimally select a generalized Nash equilibrium, in this paper, we propose a semi-decentralized algorithm based on a double-layer Tikhonov regularization method. Technically, we extend the Tikhonov method for equilibrium selection in non-generalized games to the generalized case by coupling it with the preconditioned forward-backward splitting, which guarantees linear convergence to the solutions of the inner layer problem and allows for a semi-decentralized implementation. We then establish a conceptual connection and draw a comparison between the proposed algorithm and the hybrid steepest descent method, the other known distributed framework for solving the selection problem.

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arXiv2023

Linear convergence in time-varying generalized Nash equilibrium problems

We study generalized games with full row rank equality constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.

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