3 research outputs found
Learning in Congestion Games with Bandit Feedback
In this paper, we investigate Nash-regret minimization in congestion games, a
class of games with benign theoretical structure and broad real-world
applications. We first propose a centralized algorithm based on the optimism in
the face of uncertainty principle for congestion games with (semi-)bandit
feedback, and obtain finite-sample guarantees. Then we propose a decentralized
algorithm via a novel combination of the Frank-Wolfe method and G-optimal
design. By exploiting the structure of the congestion game, we show the sample
complexity of both algorithms depends only polynomially on the number of
players and the number of facilities, but not the size of the action set, which
can be exponentially large in terms of the number of facilities. We further
define a new problem class, Markov congestion games, which allows us to model
the non-stationarity in congestion games. We propose a centralized algorithm
for Markov congestion games, whose sample complexity again has only polynomial
dependence on all relevant problem parameters, but not the size of the action
set.Comment: 34 pages, Thirty-sixth Conference on Neural Information Processing
Systems (NeurIPS 2022
Polynomial Convergence of Bandit No-Regret Dynamics in Congestion Games
We introduce an online learning algorithm in the bandit feedback model that,
once adopted by all agents of a congestion game, results in game-dynamics that
converge to an -approximate Nash Equilibrium in a polynomial number
of rounds with respect to , the number of players and the number of
available resources. The proposed algorithm also guarantees sublinear regret to
any agent adopting it. As a result, our work answers an open question from
arXiv:2206.01880 and extends the recent results of arXiv:2306.15543 to the
bandit feedback model. We additionally establish that our online learning
algorithm can be implemented in polynomial time for the important special case
of Network Congestion Games on Directed Acyclic Graphs (DAG) by constructing an
exact -barycentric spanner for DAGs