Noticias en español
Stochastic Halpern iteration in normed spaces and applications to reinforcement learning.
In this seminar, I will present recent results on the oracle complexity of the stochastic Halpern iteration with minibatching, a method designed to approximate fixed points of nonexpansive and contractive operators in finite-dimensional normed spaces. Under the assumption of uniformly bounded variance from the stochastic oracle, we show that the method achieves an oracle complexity of $\tilde{O}(\varepsilon^{-5})$ to obtain an $\varepsilon$-accurate expected fixed-point residual for nonexpansive operators. This improves upon previously known rates for the stochastic Krasnoselskii-Mann...
Read MoreMean-Field Opinion Dynamics in Random Graphs.
Abstract: We consider a set of agents in a network having different opinions over a binary subject. The network is encoded as a (undirected or directed) graph, and each opinion is represented as a value between 0 and 1. At each discrete stage, each agent updates her opinion as a convex combination between the average opinion of her neighbors and her intrinsic opinion, which coincides with its initial opinion. It is well known that such dynamic converges to a stable opinion, which can be computed by inverting a matrix associated with the adjacency matrix of the network. When the network...
Read MoreA distributed proximal splitting method with linesearch for problems with locally Lipschitz gradients
Abstract: We consider finitely many agents over a connected network working cooperatively to solve a consensus optimization problem. Each agent owns a private convex cost function with a decomposable structure given by the sum of two terms, one smooth and one nonsmooth. In our distributed setting, no agent has direct access to the information of the overall network, but instead they can only communicate with their immediate neighbors. We propose a distributed primal-dual splitting method of proximal-gradient type that defines appropriate stepsizes by means of backtracking linesearch...
Read MoreThe inverse elasticity problem, its extension to porous media and applications in biomedicine.
RESUMEN: The inverse elasticity problem can be simply stated as: given a deformed configuration and the forces that act on it, find an initial stress-free configuration such that when the given forces are applied to it, one recovers the given deformed configuration. Surprisingly, this problem can be framed as a (direct) elasticity one, whose mathematical properties are inherited from the original direct problem if the underlying material is sufficiently regular. In this seminar, I will review this problem and its main mathematical properties. After this brief introduction, I will show some...
Read MoreSpeciation induced by dormancy in a model with changing environment.
Resumen: We consider a population model in which the season alternates between winter and summer. Individuals can acquire mutations that are advantageous in the summer but disadvantageous in the winter, or vice versa. Furthermore, it is assumed that individuals within the population can either be active or dormant, and that individuals can transition between these two states. Dormant individuals do not reproduce and are not subject to selective pressures. Our findings indicate that, under some conditions, two waves of adaptation emerge over time. Some individuals repeatedly acquire...
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