arXiv subjects

Tatiana Tatarenko

Publications and source records attributed to Tatiana Tatarenko.

At least 19 recordsLinked to original sources

arXiv2026

Learning Parametric Monotone Games

We study the problem of learning from data a parametric Nash equilibrium (NE) problem that is monotone (or strongly monotone) for all parameter values. In the presence of local and shared convex constraints, monotonicity enables efficient computation of generalized Nash equilibria of the learned game. We consider two learning scenarios: (i) direct learning of the NE problem from samples of the agents' costs, and (ii) inverse learning of surrogate agents' costs from samples of their best responses. We propose two methods to solve these tasks. The first is a penalty-based approach that promotes monotonicity of the learned game during training. The second, based on a representation theorem we introduce for a broad class of monotone games, parameterizes the agents' costs so that monotonicity of the NE problem is guaranteed by construction, for all parameter values, regardless of the training data used. We illustrate the applicability of the proposed methods on several numerical examples. A Python library and the examples reported in the paper are available at https://github.com/bemporad/learn_monotone_games.

math.OC↗

arXiv2026

Solving Monotone Linear-Quadratic Generalized Nash Equilibrium Problems via Quadratic Programming

We consider generalized Nash equilibrium problems among $N$ players with convex quadratic costs and shared affine constraints, assuming only that the game's pseudogradient is merely monotone. We show that computing a variational generalized Nash equilibrium (v-GNE) is equivalent to solving a single convex quadratic program (QP) derived from the players' joint Karush--Kuhn--Tucker conditions. Building on this, we show that the regularization of such a QP yields an $\varepsilon$-approximated v-GNE with suboptimality vanishing linearly in the regularization parameter. Next, we propose an accelerated proximal-point scheme and an accelerated projected-gradient method, both attaining an $\mathcal O(1/k^2)$-approximated v-GNE at the $k$-th iteration. We also demonstrate that an invertible Jacobian of the game allows for reduction to a lower-dimensional QP. Theoretical analysis and numerical experiments show the proposed methods substantially outperform the existing approaches to solve monotone linear-quadratic v-GNE problems.

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arXiv2026

Inverse Learning in $2\times2$ Games: From Synthetic Interactions to Traffic Simulation

Understanding how agents coordinate or compete from limited behavioral data is central to modeling strategic interactions in traffic, robotics, and other multi-agent systems. In this work, we investigate the following complementary formulations of inverse game-theoretic learning: (i) a Closed-form Correlated Equilibrium Maximum-Likelihood estimator (CE-ML) specialized for $2\times2$ games; and (ii) a Logit Best Response Maximum-Likelihood estimator (LBR-ML) that captures long-run adaptation dynamics via stochastic response processes. Together, these approaches span the spectrum between static equilibrium consistency and dynamic behavioral realism. We evaluate them on synthetic "chicken-dare" games and traffic-interaction scenarios simulated in SUMO, comparing parameter recovery and distributional fit. Results reveal clear trade-offs between interpretability, computational tractability, and behavioral expressiveness across models.

cs.GT↗

arXiv2025

Learning Generalized Nash Equilibria in Non-Monotone Games with Quadratic Costs

We study generalized Nash equilibrium (GNE) problems in games with quadratic costs and individual linear equality constraints. Departing from approaches that require strong monotonicity and/or shared constraints, we reformulate the KKT conditions of the (generally non-monotone) games into a tractable convex program whose objective satisfies the Polyak-Lojasiewicz (PL) condition. This PL geometry enables a distributed gradient method over a fixed communication graph with global geometric (linear) convergence to a GNE. When gradient information is unavailable or costly, we further develop a zero-order fully distributed scheme in which each player uses only local cost evaluations and their own constraint residuals. With an appropriate step size policy, the proposed zero-order method converges to a GNE, provided one exists, at rate O(1/t).

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arXiv2025

Distributed Nash Equilibrium Seeking in Non-Monotone Games over the Simplex

In this work, we present a novel characterization of approximate Nash equilibria in a class of convex games over the simplex. To achieve this, we regularize the utility functions using the Shannon entropy term, connect the solutions to the regularized game with the set of Nash equilibria, and formulate a multi-objective optimization problem to solve the regularized game. Based on the obtained properties of the stationary points in this optimization problem, we formulate two distributed heuristic algorithms to compute an approximate Nash equilibrium of the original game.

math.OC↗

arXiv2025

Convergence Rate of Generalized Nash Equilibrium Learning in Strongly Monotone Games with Linear Constraints

We consider payoff-based learning of a generalized Nash equilibrium (GNE) in multi-agent systems. Our focus is on games with jointly convex constraints of a linear structure and strongly monotone pseudo-gradients. We present a convergent procedure based on a partial regularization technique and establish the convergence rate of its iterates under one- and two-point payoff-based feedback. To the best of our knowledge, this work is the first one characterizing the convergence speed of iterates to a variational GNE in the class of games under consideration.

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arXiv2025

Fast Distributed Nash Equilibrium Seeking in Monotone Games

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with merely monotone and restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [5] to solve variational inequalities, we develop the algorithm converging to Nash equilibria in games, where players have no access to the full information but are able to communicate with neighbors over some communication graph. The convergence rate is demonstrated to be geometric and improves the rates obtained by the previously presented procedures seeking Nash equilibria in the class of games under consideration.

math.OC↗

arXiv2024

Convergence Rate of Payoff-based Generalized Nash Equilibrium Learning

We consider generalized Nash equilibrium (GNE) problems in games with strongly monotone pseudo-gradients and jointly linear coupling constraints. We establish the convergence rate of a payoff-based approach intended to learn a variational GNE (v-GNE) in such games. While convergent algorithms have recently been proposed in this setting given full or partial information of the gradients, rate of convergence in the payoff-based information setting has been an open problem. Leveraging properties of a game extended from the original one by a dual player, we establish a convergence rate of $O(\frac{1}{t^{4/7}})$ to a v-GNE of the game.

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arXiv2024

Convergence Rate of Learning a Strongly Variationally Stable Equilibrium

We derive the rate of convergence to the strongly variationally stable Nash equilibrium in a convex game, for a zeroth-order learning algorithm. Though we do not assume strong monotonicity of the game, our rates for the one-point feedback and for the two-point feedback match the best known rates for strongly monotone games under zeroth-order information.

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arXiv2023

Huber Loss-Based Penalty Approach to Problems with Linear Constraints

We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss function with two penalty parameters. We study the infeasibility properties of the solutions of penalized problems for nonconvex and convex objective functions, as the penalty parameters vary with time. Then, we propose a random incremental penalty method for solving the original problem, and investigate its convergence properties for convex and strongly convex objective functions. We show that the iterates of the method converge to a solution of the original problem almost surely and in expectation for suitable choices of the penalty parameters and the stepsize. Also, we establish convergence rate of the method in terms of the expected function values by utilizing appropriately defined weighted averages of the iterates. We show $O(\ln^{1/2+ε} k/{\sqrt k})$-convergence rate when the objective function is convex and $O(\ln^ε k/k)$-convergence rate when the objective function is strongly convex, with $ε>0$ being an arbitrarily small scalar. } To the best of our knowledge, these are the first results on the convergence rate for the penalty-based incremental subgradient method with time-varying penalty parameters.

math.OC↗

arXiv2023

Accelerating Distributed Nash Equilibrium Seeking

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to solve variational inequalities, we develop the algorithm converging to Nash equilibria in games, where players have no access to the full information but are able to communicate with neighbors over some communication graph. The convergence rate is demonstrated to be geometric and improves the rates obtained by the previously presented procedures seeking Nash equilibria in the class of games under consideration.

math.OC↗

arXiv2023

Bandit Learning in Convex Non-Strictly Monotone Games

We address learning Nash equilibria in convex games under the payoff information setting. We consider the case in which the game pseudo-gradient is monotone but not necessarily strictly monotone. This relaxation of strict monotonicity enables application of learning algorithms to a larger class of games, such as, for example, a zero-sum game with a merely convex-concave cost function. We derive an algorithm whose iterates provably converge to the least-norm Nash equilibrium in this setting. {From the perspective of a single player using the proposed algorithm, we view the game as an instance of online optimization}. Through this lens, we quantify the regret rate of the algorithm and provide an approach to choose the algorithm's parameters to minimize the regret rate.

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arXiv2022

Projected gradient-tracking in multi-cluster games and its application to power management

We are concerned with a distributed approach to solve multi-cluster games arising in multi-agent systems. In such games, agents are separated into distinct clusters. The agents belonging to the same cluster cooperate with each other to achieve a common cluster goal while a non-cooperative game is played between the clusters. To be able to deal with the sparsity of information, as each agent only knows a specific part of the problem, we combine gradient-tracking and consensus methods for information distribution into an algorithm that can solve both the cooperative and non-cooperative problem in a single run. The constraints of the problem are taken into account by the corresponding projection operators and linear convergence is proven given an appropriate constant step size. The algorithm is applied to a day-ahead power management problem, posed as a multi-cluster game, and its efficiency is demonstrated by simulations.

eess.SY↗

arXiv2022

On the Rate of Convergence of Payoff-based Algorithms to Nash Equilibrium in Strongly Monotone Games

We derive the rate of convergence to Nash equilibria for the payoff-based algorithm proposed in \cite{tat_kam_TAC}. These rates are achieved under the standard assumption of convexity of the game, strong monotonicity and differentiability of the pseudo-gradient. In particular, we show the algorithm achieves $O(\frac{1}{T})$ in the two-point function evaluating setting and $O(\frac{1}{\sqrt{T}})$ in the one-point function evaluation under additional requirement of Lipschitz continuity of the pseudo-gradient. These rates are to our knowledge the best known rates for the corresponding problem classes.

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arXiv2021

Gradient Play in $n$-Cluster Games with Zero-Order Information

We study a distributed approach for seeking a Nash equilibrium in $n$-cluster games with strictly monotone mappings. Each player within each cluster has access to the current value of her own smooth local cost function estimated by a zero-order oracle at some query point. We assume the agents to be able to communicate with their neighbors in the same cluster over some undirected graph. The goal of the agents in the cluster is to minimize their collective cost. This cost depends, however, on actions of agents from other clusters. Thus, a game between the clusters is to be solved. We present a distributed gradient play algorithm for determining a Nash equilibrium in this game. The algorithm takes into account the communication settings and zero-order information under consideration. We prove almost sure convergence of this algorithm to a Nash equilibrium given appropriate estimations of the local cost functions' gradients.

cs.GT↗

arXiv2021

Gradient-Tracking over Directed Graphs for solving Leaderless Multi-Cluster Games

We are concerned with finding Nash Equilibria in agent-based multi-cluster games, where agents are separated into distinct clusters. While the agents inside each cluster collaborate to achieve a common goal, the clusters are considered to be virtual players that compete against each other in a non-cooperative game with respect to a coupled cost function. In such scenarios, the inner-cluster problem and the game between the clusters need to be solved simultaneously. Therefore, the resulting inter-cluster Nash Equilibrium should also be a minimizer of the social welfare problem inside the clusters. In this work, this setup is cast as a distributed optimization problem with sparse state information. Hence, critical information, such as the agent's cost functions, remain private. We present a distributed algorithm that converges with a linear rate to the optimal solution. Furthermore, we apply our algorithm to an extended cournot game to verify our theoretical results.

eess.SY↗

arXiv2020

Revisiting Consensus-Based Energy-Management in Smart Grid with Transmission Losses and Directed Communication

We discovered a deficiency in Algorithm 1 and Theorem 3 of [1]. The algorithm called CEMA aims to solve an energy management problem distributively. However, by means of a counter example, we show that Theorem 2 and 3 of [1] contradict each other in the case of a valid scenario, proving that the suggested algorithm does not always find the optimum. Furthermore, we provide theoretic results, showing that Theorem 3 of [1] does not hold generally. At last, we provide a rectification by adjusting the algorithm and the corresponding proof of Theorem 3.

eess.SY↗

arXiv2020

Projected Push-Sum Gradient Descent-Ascent for Convex Optimizationwith Application to Economic Dispatch Problems

We propose a novel algorithm for solving convex, constrained and distributed optimization problems defined on multi-agent-networks, where each agent has exclusive access to a part of the global objective function. The agents are able to exchange information over a directed, weighted communication graph, which can be represented as a column-stochastic matrix. The algorithm combines an adjusted push-sum consensus protocol for information diffusion and a gradient descent-ascent on the local cost functions, providing convergence to the optimum of their sum. We provide results on a reformulation of the push-sum into single matrix-updates and prove convergence of the proposed algorithm to an optimal solution, given standard assumptions in distributed optimization. The algorithm is applied to a distributed economic dispatch problem, in which the constraints can be expressed in local and global subsets.

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