Pooling or sampling: Collective dynamics for electrical flow estimation

The computation of electrical flows is a crucial primitive for many recently proposed optimization algorithms on weighted networks. While typically implemented as a centralized subroutine, the ability to perform this task in a fully decentralized way is implicit in a number of biological systems. Thus, a natural question is whether this task can provably be accomplished in an efficient way by a network of agents executing a simple protocol. We provide a positive answer, proposing two distributed approaches to electrical flow computation on a weighted network: a deterministic process mimicking Jacobi's iterative method for solving linear systems, and a randomized token diffusion process, based on revisiting a classical random walk process on a graph with an absorbing node. We show that both processes converge to a solution of Kirchhoff's node potential equations, derive bounds on their convergence rates in terms of the weights of the network, and analyze their time and message complexity

Robustness of large-scale stochastic matrices to localized perturbations

Upper bounds are derived on the total variation distance between the invariant distributions of two stochastic matrices differing on a subset W of rows. Such bounds depend on three parameters: the mixing time and the minimal expected hitting time on W for the Markov chain associated to one of the matrices; and the escape time from W for the Markov chain associated to the other matrix. These results, obtained through coupling techniques, prove particularly useful in scenarios where W is a small subset of the state space, even if the difference between the two matrices is not small in any norm. Several applications to large-scale network problems are discussed, including robustness of Google's PageRank algorithm, distributed averaging and consensus algorithms, and interacting particle systems.Comment: 12 pages, 4 figure

Ant colony optimization with direct communication for the traveling salesman problem

This article is posted here with permission from IEEE - Copyright @ 2010 IEEEAnts in conventional ant colony optimization (ACO) algorithms use pheromone to communicate. Usually, this indirect communication leads the algorithm to a stagnation behaviour, where the ants follow the same path from early stages. This occurs because high levels of pheromone are developed, which force the ants to follow the same corresponding trails. As a result, the population gets trapped into a local optimum solution which is difficult to escape from it. In this paper, a direct communication (DC) scheme is proposed where ants are able to exchange cities with other ants that belong to their communication range. Experiments show that the DC scheme delays convergence and improves the solution quality of conventional ACO algorithms regarding the traveling salesman problem, since it guides the population towards the global optimum solution. The ACO algorithm with the proposed DC scheme has better performance, especially on large problem instances, even though it increases the computational time in comparison with a conventional ACO algorithm

ASPiRe:Adaptive Skill Priors for Reinforcement Learning

We introduce ASPiRe (Adaptive Skill Prior for RL), a new approach that leverages prior experience to accelerate reinforcement learning. Unlike existing methods that learn a single skill prior from a large and diverse dataset, our framework learns a library of different distinction skill priors (i.e., behavior priors) from a collection of specialized datasets, and learns how to combine them to solve a new task. This formulation allows the algorithm to acquire a set of specialized skill priors that are more reusable for downstream tasks; however, it also brings up additional challenges of how to effectively combine these unstructured sets of skill priors to form a new prior for new tasks. Specifically, it requires the agent not only to identify which skill prior(s) to use but also how to combine them (either sequentially or concurrently) to form a new prior. To achieve this goal, ASPiRe includes Adaptive Weight Module (AWM) that learns to infer an adaptive weight assignment between different skill priors and uses them to guide policy learning for downstream tasks via weighted Kullback-Leibler divergences. Our experiments demonstrate that ASPiRe can significantly accelerate the learning of new downstream tasks in the presence of multiple priors and show improvement on competitive baselines.Comment: 36th Conference on Neural Information Processing Systems (NeurIPS 2022