Research map / Multi-agent systems and games / Games and equilibria
Estimating $α$-Rank from A Few Entries with Low Rank Matrix Completion
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use low-rank matrix completion (OptSpace) on a random subset of pairs before alpha-rank, noise-free | OptEval-1 · Bern(100) and Soccer meta-game | ranking/pi error with few pairs | Helped |
| Use noisy low-rank completion with RG-UCB sampling on subset of pairs | OptEval-2 · Gaussian(15) noisy | pi error, ranking error, convergence error: reduces interactions by 60% vs full pairs | Helped |
| Lower rank r=1 for OptEval-2 (ablation) | OptEval-2 · Gaussian(15) noisy | fit to payoff matrix | Hurt |
| Increase rank from 2 to 4 for OptEval-2 (ablation) | OptEval-2 · Gaussian(15) noisy | convergence speed | Hurt |
| Choose rank r=2 instead of full rank for noisy completion (ablation) | OptEval-2 · Bern(100) noisy | sampled pairs and alpha-Conv: sampled pairs reduced by 40% vs RG-UCB | Helped |
| Use repeated-agent structure (rank 4) in noisy completion | OptEval-2 · Soccer meta-game noisy | sampled pairs: 75% reduction in pairs vs RG-UCB | Helped |
| Apply low-rank completion to real-world games with full or high rank payoffs | OptEval-1 · 12 real-world games (OpenSpiel) | alpha-rank ranking error | Mixed |
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