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Following the Leader and Fast Rates in Linear Prediction: Curved Constraint Sets and Other Regularities
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Curvature of constraint set boundary (principal curvature bounded below by lambda_0) with mean loss norm bounded away from zero | FTL on linear losses · adversarial linear prediction over C^2 convex body | regret | Helped |
| Polytope constraint set: regret bounded by number of leader switches | FTL on polytope domain, stochastic i.i.d. losses · stochastic i.i.d. losses over polytope | expected regret | Helped |
| Combine FTL and FTRL via (A,B)-prod meta-algorithm | linear prediction over general domains · worst-case and easy data | regret | Helped |
| Shrinkage of FTL prediction (follow the shrunken leader) on unit ball | FTL on unit ball · unit ball, bounded-away-from-zero Theta_t | regret | Helped |
| FTRL with eta_t=1/sqrt(t-1) on unit ball for stochastic data with nonzero mean | FTRL · unit ball, i.i.d. losses with mean mu != 0 | expected regret | Helped |
| Half-adversarial data with L=0.1 on unit ball: FTL vs FTRL | FTL · half-adversarial linear game, unit ball | regret growth | Helped |
| Stochastic data with L=0 (zero mean): curvature-based FTL advantage absent | FTL · 4-dim ellipsoid stochastic, L=0 | regret | No clear effect |
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