arXiv subjects

Michail Fasoulakis

Publications and source records attributed to Michail Fasoulakis.

14 recordsLinked to original sources

arXiv2026

Improved Last-iterate Convergence Properties for the FLBR-MWU Dynamics

We revisit a variant of Multiplicative Weights Update (MWU), defined recently by Fasoulakis et al. [AISTATS; 2022], and denoted as Forward Looking Best Response MWU (FLBR-MWU). These dynamics are based on the approach of extra-gradient methods, with the tweak of using different learning rates in the intermediate step and the actual update step. So far, it has been proved that this algorithm attains asymptotic last-iterate convergence but no explicit rate has been known. We answer the open question from Fasoulakis et al. by establishing a concrete convergence rate for the duality gap. In particular, we show a geometric convergence rate, of the form $O(c^t)$, where $c<1$ is independent of time but dependent on game parameters, such as the maximum eigenvalue of the Jacobian matrix. We also complement our theoretical analysis with an experimental comparison to OGDA (Optimistic Gradient Descent-Ascent), which ranks among the best last-iterate methods for solving zero-sum games. We demonstrate that the performance of the FLBR-MWU method matches or, in some cases, outperforms OGDA.

cs.GT↗

arXiv2026

Delegated Fair Division

Motivated by recently introduced problems on delegated resource allocation, we study a model of fair division, where a set of indivisible goods is to be allocated to some agents, each of which belonging to some bigger central entity. Our model captures the general framework of allocating resources to organizational units, which subsequently distribute them to their affiliated members. A particularly relevant application of this framework, with immense social impact, arises in the allocation of food donations through charitable organizations. In essence, every center acts as the representative of the agents belonging to it, aligning their generally different preferences. Our goal is to distribute the goods in a way that is simultaneously fair both with respect to the centers and the agents. We distinguish two different information structures depending on whether the agents compare their bundles against every agent or only those belonging to the same center. For each one of them we provide efficient algorithms that produce allocations that satisfy envy-based fairness guarantees at both levels.

cs.GT↗

arXiv2025

On Altruism and Spite in Bimatrix Games

One common assumption in game theory is that any player optimizes a utility function that takes into account only its own payoff. However, it has long been observed that in real life players may adopt an altruistic or even spiteful behaviour. As such, there are numerous attempts in the economics literature that strive to explain the fact that players are not entirely selfish, but most of these works do not focus on the algorithmic implications of altruism or spite in games. In this paper, we relax the aforementioned ``self-interest'' assumption, and initiate the study of algorithmic aspects of bimatrix games -- such as the complexity and the quality of their (approximate) Nash equilibria -- under altruism or spite. We provide both a theoretical and an experimental treatment of these topics. Moreover, we demonstrate the potential for learning the degree of an opponent's altruistic/spiteful behaviour, and employing this for opponent selection and transfer of knowledge in bimatrix games.

cs.GT↗

arXiv2025

A Descent-based method on the Duality Gap for solving zero-sum games

We focus on the design of algorithms for finding equilibria in 2-player zero-sum games. Although it is well known that such problems can be solved by a single linear program, there has been a surge of interest in recent years for simpler algorithms, motivated in part by applications in machine learning. Our work proposes such a method, inspired by the observation that the duality gap (a standard metric for evaluating convergence in min-max optimization problems) is a convex function for bilinear zero-sum games. To this end, we analyze a descent-based approach, variants of which have also been used as a subroutine in a series of algorithms for approximating Nash equilibria in general non-zero-sum games. In particular, we study a steepest descent approach, by finding the direction that minimises the directional derivative of the duality gap function. Our main theoretical result is that the derived algorithms achieve a geometric decrease in the duality gap and improved complexity bounds until we reach an approximate equilibrium. Finally, we complement this with an experimental evaluation, which provides promising findings. Our algorithm is comparable with (and in some cases outperforms) some of the standard approaches for solving 0-sum games, such as OGDA (Optimistic Gradient Descent/Ascent), even with thousands of available strategies per player.

cs.GT↗

arXiv2024

Revisit the Arimoto-Blahut algorithm: New Analysis with Approximation

By the seminal paper of Claude Shannon \cite{Shannon48}, the computation of the capacity of a discrete memoryless channel has been considered as one of the most important and fundamental problems in Information Theory. Nearly 50 years ago, Arimoto and Blahut independently proposed identical algorithms to solve this problem in their seminal papers \cite{Arimoto1972AnAF, Blahut1972ComputationOC}. The Arimoto-Blahut algorithm was proven to converge to the capacity of the channel as $t \to \infty$, with a convergence rate upper bounded by $O\left(\log(m)/t\right)$, where $m$ is the size of the input distribution. Under the assumption that a unique optimal solution is in the interior of the input probability simplex, the convergence becomes inverse exponential after an iteration $t^0$ \cite{Arimoto1972AnAF}. More recently, it was demonstrated in \cite{Nakagawa2020AnalysisOT} that in certain specific cases, the convergence rate is at worst case inverse linear. In this paper, we revisit this fundamental algorithm analyzing its rate of convergence focusing on the approximation of the capacity. Our main result shows that the convergence rate to an $\varepsilon$-optimal solution, for any sufficiently small constant $\varepsilon > 0$, is inverse exponential $O\left(\log(m)/c^t\right)$, for some constant $c > 1$. Given this, we derive new and complementary results for the computation of capacity, particularly in cases where an exact solution is sought.

cs.IT↗

arXiv2022

A Polynomial-Time Algorithm for 1/2-Well-Supported Nash Equilibria in Bimatrix Games

Since the seminal PPAD-completeness result for computing a Nash equilibrium even in two-player games, an important line of research has focused on relaxations achievable in polynomial time. In this paper, we consider the notion of $\varepsilon$-well-supported Nash equilibrium, where $\varepsilon \in [0,1]$ corresponds to the approximation guarantee. Put simply, in an $\varepsilon$-well-supported equilibrium, every player chooses with positive probability actions that are within $\varepsilon$ of the maximum achievable payoff, against the other player's strategy. Ever since the initial approximation guarantee of 2/3 for well-supported equilibria, which was established more than a decade ago, the progress on this problem has been extremely slow and incremental. Notably, the small improvements to 0.6608, and finally to 0.6528, were achieved by algorithms of growing complexity. Our main result is a simple and intuitive algorithm, that improves the approximation guarantee to 1/2. Our algorithm is based on linear programming and in particular on exploiting suitably defined zero-sum games that arise from the payoff matrices of the two players. As a byproduct, we show how to achieve the same approximation guarantee in a query-efficient way.

cs.GT↗

arXiv2022

A Polynomial-Time Algorithm for 1/3-Approximate Nash Equilibria in Bimatrix Games

Since the celebrated PPAD-completeness result for Nash equilibria in bimatrix games, a long line of research has focused on polynomial-time algorithms that compute $\varepsilon$-approximate Nash equilibria. Finding the best possible approximation guarantee that we can have in polynomial time has been a fundamental and non-trivial pursuit on settling the complexity of approximate equilibria. Despite a significant amount of effort, the algorithm of Tsaknakis and Spirakis, with an approximation guarantee of $(0.3393+δ)$, remains the state of the art over the last 15 years. In this paper, we propose a new refinement of the Tsaknakis-Spirakis algorithm, resulting in a polynomial-time algorithm that computes a $(\frac{1}{3}+δ)$-Nash equilibrium, for any constant $δ>0$. The main idea of our approach is to go beyond the use of convex combinations of primal and dual strategies, as defined in the optimization framework of Tsaknakis and Spirakis, and enrich the pool of strategies from which we build the strategy profiles that we output in certain bottleneck cases of the algorithm.

cs.GT↗

arXiv2022

Forward Looking Best-Response Multiplicative Weights Update Methods for Bilinear Zero-sum Games

Our work focuses on extra gradient learning algorithms for finding Nash equilibria in bilinear zero-sum games. The proposed method, which can be formally considered as a variant of Optimistic Mirror Descent \cite{DBLP:conf/iclr/MertikopoulosLZ19}, uses a large learning rate for the intermediate gradient step which essentially leads to computing (approximate) best response strategies against the profile of the previous iteration. Although counter-intuitive at first sight due to the irrationally large, for an iterative algorithm, intermediate learning step, we prove that the method guarantees last-iterate convergence to an equilibrium. Particularly, we show that the algorithm reaches first an $η^{1/ρ}$-approximate Nash equilibrium, with $ρ> 1$, by decreasing the Kullback-Leibler divergence of each iterate by at least $Ω(η^{1+\frac{1}ρ})$, for sufficiently small learning rate, $η$, until the method becomes a contracting map, and converges to the exact equilibrium. Furthermore, we perform experimental comparisons with the optimistic variant of the multiplicative weights update method, by \cite{Daskalakis2019LastIterateCZ} and show that our algorithm has significant practical potential since it offers substantial gains in terms of accelerated convergence.

cs.GT↗

arXiv2021

Cumulant GAN

In this paper, we propose a novel loss function for training Generative Adversarial Networks (GANs) aiming towards deeper theoretical understanding as well as improved stability and performance for the underlying optimization problem. The new loss function is based on cumulant generating functions giving rise to \emph{Cumulant GAN}. Relying on a recently-derived variational formula, we show that the corresponding optimization problem is equivalent to R{é}nyi divergence minimization, thus offering a (partially) unified perspective of GAN losses: the R{é}nyi family encompasses Kullback-Leibler divergence (KLD), reverse KLD, Hellinger distance and $χ^2$-divergence. Wasserstein GAN is also a member of cumulant GAN. In terms of stability, we rigorously prove the linear convergence of cumulant GAN to the Nash equilibrium for a linear discriminator, Gaussian distributions and the standard gradient descent ascent algorithm. Finally, we experimentally demonstrate that image generation is more robust relative to Wasserstein GAN and it is substantially improved in terms of both inception score and Fréchet inception distance when both weaker and stronger discriminators are considered.

cs.LG↗

arXiv2018

Training Generative Adversarial Networks with Weights

The impressive success of Generative Adversarial Networks (GANs) is often overshadowed by the difficulties in their training. Despite the continuous efforts and improvements, there are still open issues regarding their convergence properties. In this paper, we propose a simple training variation where suitable weights are defined and assist the training of the Generator. We provide theoretical arguments why the proposed algorithm is better than the baseline training in the sense of speeding up the training process and of creating a stronger Generator. Performance results showed that the new algorithm is more accurate in both synthetic and image datasets resulting in improvements ranging between 5% and 50%.

cs.LG↗

arXiv2018

Jamming in multiple independent Gaussian channels as a game

We study the problem of \emph{jamming} in multiple independent \emph{Gaussian channels} as a zero-sum game. We show that in the unique Nash equilibrium of the game the best-response strategy of the transmitter is the \emph{waterfilling} to the sum of the jamming and the noise power in each channel and the best-response strategy of the jammer is the \emph{waterfilling} only to the noise power.

cs.GT↗

arXiv2018

A New Theoretical Evaluation Framework for Satisfaction Equilibria in Wireless Networks

In this paper, a theoretical evaluation framework regarding the \textit{Satisfaction Equilibrium (SE)} in wireless communication networks is introduced and examined. To study these equilibria operation points, we coin some new concepts, namely the \textit{Valued Satisfaction Equilibrium}, the \textit{Price of Efficiency} and the \textit{Max Price of Satisfaction}, which can be used for measuring the efficiency of the obtained equilibria solutions. The aforementioned framework is analyzed and evaluated in a wireless communication environment under the presence of the Gaussian Interference channel (GIC). Within this setting, a non-cooperative game among the users is studied, where users aim in a selfish manner to meet their Quality of Service (QoS) prerequisite. However instead of maximizing the QoS which is generally energy costly, we evangelize that better energy-efficiency is achieved by targeting satisfactory QoS levels only. The sufficient and necessary conditions that lead to the \textit{Satisfaction Equilibrium} are provided for the two-user case and the \textit{Efficient Satisfaction Equilibrium (ESE)} is determined, where the users satisfy their QoS constraints with the lowest possible cost. Moreover, specific measures for evaluating the efficiency of various satisfaction equilibria, in a formal and quantitative manner, expressing the tradeoff with respect to the achieved utility or a given objective function and corresponding cost, are defined and analyzed.

cs.GT↗

arXiv2015

Distributed Methods for Computing Approximate Equilibria

We present a new, distributed method to compute approximate Nash equilibria in bimatrix games. In contrast to previous approaches that analyze the two payoff matrices at the same time (for example, by solving a single LP that combines the two players payoffs), our algorithm first solves two independent LPs, each of which is derived from one of the two payoff matrices, and then compute approximate Nash equilibria using only limited communication between the players. Our method has several applications for improved bounds for efficient computations of approximate Nash equilibria in bimatrix games. First, it yields a best polynomial-time algorithm for computing \emph{approximate well-supported Nash equilibria (WSNE)}, which guarantees to find a 0.6528-WSNE in polynomial time. Furthermore, since our algorithm solves the two LPs separately, it can be used to improve upon the best known algorithms in the limited communication setting: the algorithm can be implemented to obtain a randomized expected-polynomial-time algorithm that uses poly-logarithmic communication and finds a 0.6528-WSNE. The algorithm can also be carried out to beat the best known bound in the query complexity setting, requiring $O(n \log n)$ payoff queries to compute a 0.6528-WSNE. Finally, our approach can also be adapted to provide the best known communication efficient algorithm for computing \emph{approximate Nash equilibria}: it uses poly-logarithmic communication to find a 0.382-approximate Nash equilibrium.

cs.GT↗

arXiv2014

Approximate well-supported Nash equilibria in symmetric bimatrix games

The $\varepsilon$-well-supported Nash equilibrium is a strong notion of approximation of a Nash equilibrium, where no player has an incentive greater than $\varepsilon$ to deviate from any of the pure strategies that she uses in her mixed strategy. The smallest constant $\varepsilon$ currently known for which there is a polynomial-time algorithm that computes an $\varepsilon$-well-supported Nash equilibrium in bimatrix games is slightly below $2/3$. In this paper we study this problem for symmetric bimatrix games and we provide a polynomial-time algorithm that gives a $(1/2+δ)$-well-supported Nash equilibrium, for an arbitrarily small positive constant $δ$.

cs.GT↗