Consensus Propagation

We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. We establish convergence, characterize the convergence rate for regular graphs, and demonstrate that the protocol exhibits better scaling properties than pairwise averaging, an alternative that has received much recent attention. Consensus propagation can be viewed as a special case of belief propagation, and our results contribute to the belief propagation literature. In particular, beyond singly-connected graphs, there are very few classes of relevant problems for which belief propagation is known to converge.Comment: journal versio

Contribution à une meilleure estimation des paramètres d'une crue décennale : la méthode "DELTAQIX"

L'absence ou la rareté des données hydrométriques sur les bassins ruraux nous conduit à utiliser des approches empiriques en établissant des liaisons entre les débits et les facteurs géométriques ou climatologiques des bassins versants. La méthode DELTAQIX proposée ici est une méthode intermédiaire entre deux méthodes fréquemment appliquées en France, SOCOSE et CRUPEDIX. La méthode DELTAQIX améliore l'estimation du débit instantané maximum (QIX) décennal, par la prise en compte de variables hydrologiques intermédiaires. Elle propose également une nouvelle définition d'un temps caractéristique de crue (DELTA) ainsi qu'un hydrogramme de projet en utilisant les courbes débit-durée-fréquence. (Résumé d'auteur

Optimal Dynamic Fees for Blockchain Resources

We develop a general and practical framework to address the problem of the optimal design of dynamic fee mechanisms for multiple blockchain resources. Our framework allows to compute policies that optimally trade-off between adjusting resource prices to handle persistent demand shifts versus being robust to local noise in the observed block demand. In the general case with more than one resource, our optimal policies correctly handle cross-effects (complementarity and substitutability) in resource demands. We also show how these cross-effects can be used to inform resource design, i.e. combining resources into bundles that have low demand-side cross-effects can yield simpler and more efficient price-update rules. Our framework is also practical, we demonstrate how it can be used to refine or inform the design of heuristic fee update rules such as EIP-1559 or EIP-4844 with two case studies. We then estimate a uni-dimensional version of our model using real market data from the Ethereum blockchain and empirically compare the performance of our optimal policies to EIP-1559

Approximate Dynamic Programming via a Smoothed Linear Program

We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural “projection” of a well-studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our program—the “smoothed approximate linear program”—is distinct from such approaches and relaxes the restriction to lower bounding approximations in an appropriate fashion while remaining computationally tractable. Doing so appears to have several advantages: First, we demonstrate bounds on the quality of approximation to the optimal cost-to-go function afforded by our approach. These bounds are, in general, no worse than those available for extant LP approaches and for specific problem instances can be shown to be arbitrarily stronger. Second, experiments with our approach on a pair of challenging problems (the game of Tetris and a queueing network control problem) show that the approach outperforms the existing LP approach (which has previously been shown to be competitive with several ADP algorithms) by a substantial margin