Research map / Bandits and online learning / Online convex optimization and games
Parameter-Free Online Learning via Model Selection
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MultiScaleFTPL aggregation with expert-specific loss scales and a prior | Online prediction with expert advice · Experts with losses bounded by individual scales c_i | regret: O\prn*{c_i\sqrt{n\log\prn*{nc_i/\pi_i}}} | Helped |
| Aggregate Mirror Descent instances over norm balls using MultiScaleOCO | Online convex optimization in uniformly convex Banach spaces · Lipschitz online convex losses | regret: O\prn*{L\cdot{}(\nrm{w}+1)\sqrt{n\cdot{}\log\prn*{(\nrm{w}+1)Ln}/\lambda{}}} | Helped |
| Aggregate sub-algorithms for multiple norms simultaneously | Online learning in R^d · All p in [1+δ,2] | regret: O\prn*{(\nrm{w}_{p}+1)L_{p}\sqrt{n\log\prn*{(\nrm{w}_{p}+1)L_{p}\log(d)n}/(p-1)}} | Helped |
| Aggregate rank-specific online PCA strategies | Online PCA · Ranks k in [d/2] | regret: \wt{O}\prn*{k\sqrt{n}} | Helped |
| Aggregate Matrix Multiplicative Weights strategies across trace-norm scales | Matrix prediction · Positive semidefinite comparators | regret: (\nrm*{W}_{\Sigma}+1)\sqrt{n\log{}d\log((\nrm*{W}_{\Sigma}+1)n)} | Helped |
| Apply multi-scale aggregation to arbitrary nonlinear hypothesis classes with efficient class-specific algorithms | Online supervised learning · Online penalized risk minimization | regret: O\prn*{L\cdot{}\mathbf{Rad}_{n}(\F_{k})\cdot{}\sqrt{\log(L\cdot\mathbf{Rad}_{n}(\F_{k})\cdot{}k)}} | Helped |
| Aggregate algorithms across reproducing kernel Hilbert spaces | Multiple kernel learning · Kernel classes H_k | regret: O\prn*{LB_{k}(\nrm*{f}_{\mc{H}_k}+1)\sqrt{\log(LB_kkn(\nrm*{f}_{\mc{H}_k}+1))}} | Helped |
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