Online Network Source Optimization with Graph-Kernel MAB
Laura Toni Pascal Frossard
We propose Grab-UCB, a graph-kernel multi-arms bandit algorithm to learn
online the optimal source placement in large scale networks, such that the
reward obtained from a priori unknown network processes is maximized. The
uncertainty calls for online learning, which suffers however from the curse of
dimensionality. To achieve sample efficiency, we describe the network processes
with an adaptive graph dictionary model, which typically leads to sparse
spectral representations. This enables a data-efficient learning framework,
whose learning rate scales with the dimension of the spectral representation
model instead of the one of the network. We then propose Grab-UCB, an online
sequential decision strategy that learns the parameters of the spectral
representation while optimizing the action strategy. We derive the performance
guarantees that depend on network parameters, which further influence the
learning curve of the sequential decision strategy We introduce a
computationally simplified solving method, Grab-arm-Light, an algorithm that
walks along the edges of the polytope representing the objective function.
Simulations results show that the proposed online learning algorithm
outperforms baseline offline methods that typically separate the learning phase
from the testing one. The results confirm the theoretical findings, and further
highlight the gain of the proposed online learning strategy in terms of
cumulative regret, sample efficiency and computational complexity.