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2017 Volume 32
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ORIGINAL RESEARCH   Open Access    

Limits and limitations of no-regret learning in games

  • Engineering Systems & Design Pillar, 8 Somapah Road

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  • Abstract: We study the limit behavior and performance of no-regret dynamics in general game theoretic settings. We design protocols that achieve both good regret and equilibration guarantees in general games. We also establish a strong equivalence between them and coarse correlated equilibria (CCE). We examine structured game settings where stronger properties can be established for no-regret dynamics and CCE. In congestion games with non-atomic agents (each contributing a fraction of the flow), as we decrease the individual flow of agents, CCE become closely concentrated around the unique equilibrium flow of the non-atomic game. Moreover, we compare best/worst case no-regret learning behavior to best/worst case Nash equilibrium (NE) in small games. We prove analytical bounds on these inefficiency ratios for 2×2 games and unboundedness for larger games. Experimentally, we sample normal form games and compute their measures of inefficiency. We show that the ratio distribution has sharp decay, in the sense that most generated games have small ratios. They also exhibit strong anti-correlation between each other, that is games with large improvements from the best NE to the best CCE present small degradation from the worst NE to the worst CCE.
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  • Cite this article

    Barnabé Monnot, Georgios Piliouras. 2017. Limits and limitations of no-regret learning in games. The Knowledge Engineering Review 32(1), doi: 10.1017/S0269888917000133
    Barnabé Monnot, Georgios Piliouras. 2017. Limits and limitations of no-regret learning in games. The Knowledge Engineering Review 32(1), doi: 10.1017/S0269888917000133
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ORIGINAL RESEARCH   Open Access    

Limits and limitations of no-regret learning in games

  • Engineering Systems & Design Pillar, 8 Somapah Road

  • Published online: 13 October 2017
The Knowledge Engineering Review  32,  2017, 32(1)  |  Cite this article

Abstract: Abstract: We study the limit behavior and performance of no-regret dynamics in general game theoretic settings. We design protocols that achieve both good regret and equilibration guarantees in general games. We also establish a strong equivalence between them and coarse correlated equilibria (CCE). We examine structured game settings where stronger properties can be established for no-regret dynamics and CCE. In congestion games with non-atomic agents (each contributing a fraction of the flow), as we decrease the individual flow of agents, CCE become closely concentrated around the unique equilibrium flow of the non-atomic game. Moreover, we compare best/worst case no-regret learning behavior to best/worst case Nash equilibrium (NE) in small games. We prove analytical bounds on these inefficiency ratios for 2×2 games and unboundedness for larger games. Experimentally, we sample normal form games and compute their measures of inefficiency. We show that the ratio distribution has sharp decay, in the sense that most generated games have small ratios. They also exhibit strong anti-correlation between each other, that is games with large improvements from the best NE to the best CCE present small degradation from the worst NE to the worst CCE.

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    Acknowledgments

    • The authors would like to thank Harald Bernhard for his helpful comments and suggestions. B. M. would like to acknowledge a SUTD Presidential Graduate Fellowship. G. P. would like to acknowledge SUTD grant SRG ESD 2015 097 and MOE AcRF Tier 2 Grant 2016-T2-1-170.

    • We will assume that all involved probabilities are rational. Since the set of coarse correlated equilibria is a convex polytope defined Ax⩽b where all entries of A, b are rational every correlated equilibrium involves rational probabilities or can be approximated with arbitrarily high accuracy by using rational probabilities.

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    Barnabé Monnot, Georgios Piliouras. 2017. Limits and limitations of no-regret learning in games. The Knowledge Engineering Review 32(1), doi: 10.1017/S0269888917000133
    Barnabé Monnot, Georgios Piliouras. 2017. Limits and limitations of no-regret learning in games. The Knowledge Engineering Review 32(1), doi: 10.1017/S0269888917000133
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