Research

Stochastic Generalized Nash Equilibrium Problems

Several problems of interest cannot be modelled without uncertainty. Among others, consider transportation systems, where one of the source of uncertainty is due to the drivers perception of travel time, or electricity markets where generators produce energy without knowing the actual demand. Such problems can be modelled with Stochastic Generalized Nash equlibrium problems where expected value cost functions and shared constraints are present.

We aim at finding distributed algorithms for stochastic generalized Nash equilibrium problems and prove their convergence towards a Nash equilibrium. Most of the research is conducted leveraging on monotone and fixed point operator theory.

Generative Adversarial Networks

Generative adversarial networks (GANs) are an example of generative models. Specifically, the model takes a training set, consisting of samples drawn from a probability distribution, and learns how to represent an estimate of that distribution. The key feature of GANs is that there are two antagonistic neural networks: the generator and the discriminator.

The problem is an instance of a two-player game and depending on the cost functions, it can also be considered as a zero-sum game. The main bottleneck for their implementation is that the neural networks are very hard to train. One way to improve their performance is to design reliable algorithms for the adversarial process.

Wisdom of Crowds

In the so-called naive learning setting, a crowd of individuals holds opinions that are statistically independent estimates of an unknown parameter; the crowd is wise when the average opinion converges to the true parameter in the limit of infinitely many individuals. Unfortunately, even starting from wise initial opinions, a crowd subject to certain influence systems may lose its wisdom. It is of great interest to characterize when an influence system preserves the crowd wisdom effect.

We study finite-time executions of the French-DeGroot influence process and establish in this novel context the notion of prominent families (as a group of individuals with outsize influence). Surprisingly, finite-time wisdom preservation of the influence system is strictly distinct from its infinite-time version.

Network Cloud Storage

The use of game theory in the design and control of large scale networked systems is becoming increasingly more important. We follow this approach to efficiently solve a network allocation problem motivated by peer-to-peer cloud storage models as alternatives to classical centralized cloud storage services. The setting is that of a network of units (e.g. computers) that collaborate and offer each other space for the back up of the data of each unit. We formulate the problem as an optimization problem, we cast it into a game theoretic setting and we then propose a decentralized allocation algorithm based on the log-linear learning rule. Our main technical result is to prove the convergence of the algorithm to the optimal allocation.