Michail Fasoulakis

Michail Fasoulakis, Evangelos Markakis, Yannis Pantazis et al.

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.

Yannis Pantazis, Dipjyoti Paul, Michail Fasoulakis et al.

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.

Yannis Pantazis, Dipjyoti Paul, Michail Fasoulakis et al.

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%.