Mario Bravo

Universidad Adolfo Ibáñez

We analyze the oracle complexity of the stochastic Halpern iteration with variance reduction, where we aim to approximate fixed-points of nonexpansive and contractive operators in a normed finite-dimensional space. We show that if the underlying stochastic oracle is with uniformly bounded variance, our method exhibits an overall oracle complexity o...

We study the convergence of a stochastic version of the well-known Krasnoselski-Mann iteration, for computing fixed points of nonexpansive maps in finite dimensional spaces. Under suitable conditions on the stochastic noise and stepsizes, we establish the almost sure convergence of the iterates towards a random fixed point. We also provide non-asym...

We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for general Krasnosel'skii-Mann fixed point iterations for non-expansive maps. We also describe some of their ver...

While payoff‐based learning models are almost exclusively devised for finite action games, where players can test every action, it is harder to design such learning processes for continuous games. We construct a stochastic learning rule, designed for games with continuous action sets, which requires no sophistication from the players and is simple...

This paper examines the long-run behavior of learning with bandit feedback in non-cooperative concave games. The bandit framework accounts for extremely low-information environments where the agents may not even know they are playing a game; as such, the agents' most sensible choice in this setting would be to employ a no-regret learning algorithm....

We introduce a stochastic learning process called the dampened gradient approximation process. While learning models have almost exclusively focused on finite games, in this paper we design a learning process for games with continuous action sets. It is payoff-based and thus requires from players no sophistication and no knowledge of the game. We s...

We introduce a stochastic learning process called the dampened gradient approximation process. While learning models have almost exclusively focused on finite games, in this paper we design a learning process for games with continuous action sets. It is payoff-based and thus requires from players no sophistication and no knowledge of the game. We s...

We establish sharp estimates for the convergence rate of the Kranosel’skiĭ–Mann fixed point iteration in general normed spaces, and we use them to show that the optimal constant of asymptotic regularity is exactly \(1\sqrt \pi \). To this end we consider a nested family of optimal transport problems that provide a recursive bound for the distance b...

We study the convergence of an inexact version of the classical Krasnosel'skii-Mann iteration for computing fixed points of nonexpansive maps in Banach spaces. Our main result establishes a new metric bound for the fixed-point residuals, from which we derive their rate of convergence as well as the convergence of the iterates towards a fixed point....

We establish sharp estimates for the convergence rate of the Kranosel'ski\v{\i}-Mann fixed point iteration in general normed spaces, and we use them to show that the asymptotic regularity bound recently proved in [11] (Israel Journal of Mathematics 199(2), 757-772, 2014) with constant $1/\sqrt{\pi}$ is sharp and cannot be improved. To this end we c...

We study a general class of game-theoretic learning dynamics in the presence of random payoff disturbances and observation noise, and we provide a unified framework that extends several rationality properties of the (stochastic) replicator dynamics and other game dynamics. In the unilateral case, we show that the stochastic dynamics under study lea...

Consider a 2-player normal-form game repeated over time. We introduce an adaptive learning procedure, where the players only observe their own realized payoff at each stage. We assume that agents do not know their own payoff function, and have no information on the other player. Furthermore, we assume that they have restrictions on their own action...

We study a simple adaptive model in the framework of an $N$-player normal form game. The model consists of a repeated game where the players only know their own strategy space and their own payoff scored at each stage. The information about the other agents (actions and payoffs) is unknown. In particular, we consider a variation of the procedure st...

The agents’ decisions, from their residential location to their members’ trip choices through the network, are jointly analyzed as an integrated long term equilibrium in which the location, travel decisions, and route choices are represented by logit or entropy models. In this approach, consumers optimize their combined residence and transport opti...

The agents' decisions, from their residential location to their members' trip choices through the network, are jointly analyzed as an integrated long term equilibrium in which the location, travel decisions, and route choices are represented by logit or entropy models. In this approach, consumers optimize their combined residence and transport opti...

En el presente trabajo se construye un modelo en el cual las decisiones de los usuarios, incluyendo la localización y el transporte, se analizan en el contexto de equilibrios de tipo entropía y modelos logit. El enfoque propuesto supone que los consumidores optimizan sus opciones de residencia y transporte al momento de localizarse. En ese contexto...