Research map / Learning theory and algorithms / Submodular and game algorithms
Follow-the-Regularized-Leader Routes to Chaos in Routing Games
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase normalized demand a beyond a_b | FoReL in an asymmetric two-link linear congestion game · Two-link linear congestion game, b ≠ 1/2 | chaotic dynamics: periodic orbits of all periods, positive topological entropy and Li-Yorke chaos | Helped |
| Increase normalized demand a beyond a_b | FoReL in a symmetric two-link linear congestion game · Two-link linear congestion game, b=1/2 | convergence to Nash equilibrium: all points from (0,1) (except countably many points) are attracted by periodic attracting orbits | Hurt |
| Increase normalized demand a | FoReL in a two-link linear congestion game · Two-link linear congestion game | time-average flow: the averages ... converge to b | No clear effect |
| Replace the Shannon regularizer with the specified perturbed log-barrier regularizer (ablation) | FoReL in a two-link game with b=0.61 and a=3.25 · Two-link linear congestion game | topological entropy: positive | Helped |
| Use the log-barrier regularizer | FoReL in a two-link game with b=0.61 · Two-link linear congestion game | chaotic attractor: a between 146.97 and 147 | Mixed |
| Use the Havrda-Charvát-Tsallis regularizer with q=0.5 (ablation) | FoReL in a two-link game with b=0.61 · Two-link linear congestion game | chaotic attractor: as a increases from 39.915 to 39.93 | Mixed |
| Increase a through the reported bifurcation range | FoReL with log-barrier regularizer · Two-link game with b=0.61 | chaotic behavior: a between 10 and 190 | Mixed |
| Increase a within the range where Ψ'''<0 and the Nash equilibrium is attracting | FoReL with a regularizer whose Ψ'''<0 · Two-link linear congestion game | global convergence to Nash equilibrium: a ∈ (0, -2·Ψ'(b)) | Helped |
| Allow a regularizer for which Ψ'''<0 does not hold (ablation) | FoReL in a two-link linear congestion game · Two-link linear congestion game | coexistence of chaos and an attracting Nash equilibrium: a=3.25; b=0.61 | Helped |
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