The COVID-19 pandemic has demonstrated the importance and value of multi-period asset allocation strategies responding to rapid changes in market behavior. In this article, we formulate and solve a multi-stage stochastic optimization problem, choosing the ...
It is shown that, in the framework of Scale Relativity Theory, correlations of type informational entropy/cross entropy - probability density, in the description of the dynamics of any complex system, can be perceived as interactions. Explaining these inte ...
Surprise-based learning allows agents to rapidly adapt to nonstationary stochastic environments characterized by sudden changes. We show that exact Bayesian inference in a hierarchical model gives rise to a surprise-modulated trade-off between forgetting o ...
We consider a general discrete state-space system with both unidirectional and bidirectional links. In contrast to bidirectional links, there is no reverse transition along the unidirectional links Herein, we first compute the statistical length and the th ...
The aim of this work is to provide bounds connecting two probability measures of the same event using Rényi α-Divergences and Sibson’s α-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence and Shannon’s Mutual ...
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show ...
This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm’s convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges with prob ...
