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arXiv · 1810.01925

Bandit learning in concave $N$-person games

Mario Bravo·David S. Leslie·Panayotis Mertikopoulos
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Abstract

This paper examines the long-run behavior of learning with bandit feedback in non-cooperative concave games. The bandit framework accounts for extremely low-information environments where the agents may not even know they are playing a game; as such, the agents' most sensible choice in this setting would be to employ a no-regret learning algorithm. In general, this does not mean that the players' behavior stabilizes in the long run: no-regret learning may lead to cycles, even with perfect gradient information. However, if a standard monotonicity condition is satisfied, our analysis shows that no-regret learning based on mirror descent with bandit feedback converges to Nash equilibrium with probability $1$. We also derive an upper bound for the convergence rate of the process that nearly matches the best attainable rate for single-agent bandit stochastic optimization.

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Mario Bravo, David S. Leslie, Panayotis Mertikopoulos. 2018-10-03. Bandit learning in concave $N$-person games. https://arxiv.org/abs/1810.01925

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