Research map / Bandits and online learning / Online convex optimization and games
Adaptive Online Estimation of Piecewise Polynomial Trends
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Ada-VAW with wavelet-based interval detection and polynomial VAW predictions | Online forecasting of TV^k(C_n) sequences · TV^k(C_n) online forecasting | dynamic regret: \tilde{O}\left(n^{1/(2k+3)}C_n^{2/(2k+3)}\right); lower bound: \Omega\left(n^{1/(2k+3)}C_n^{2/(2k+3)}\right) | Helped |
| Use Ada-VAW instead of ARROWS | Online forecasting of TV^k(C_n) sequences · TV^k(C_n) online forecasting | dynamic regret: \tilde{O}\left(n^{1/(2k+3)}C_n^{2/(2k+3)}\right) vs. \tilde{O}\left(n^{1/3}C_n^{2/3}\right) | Helped |
| Use Ada-VAW instead of MA/OGD/Ader | Online forecasting of TV^k(C_n) sequences · TV^k(C_n) online forecasting | dynamic regret: \tilde{O}\left(n^{1/(2k+3)}C_n^{2/(2k+3)}\right) vs. \tilde{O}\left(\sqrt{nC_n}\right) | Helped |
| Apply Ada-VAW to sequences with at most J_n nonzero (k+1)th differences | Ada-VAW · Exact sparsity E^{k+1}(J_n) | dynamic regret: \tilde{O}\left(J_n\right); lower bound: \Omega(J_n) | Helped |
| Apply Ada-VAW to a higher-order Sobolev sequence class | Ada-VAW · Higher-order Sobolev class S^{k+1}(C_n') | dynamic regret: \tilde{O}\left(n^{\frac{2}{2k+3}}[C_n']^{\frac{2}{2k+3}}\right) | Helped |
| Apply Ada-VAW to Holder-smooth sequences enclosed within a higher-order TV ball | Ada-VAW · Higher-order Holder class H^{k+1}(L_n') | dynamic regret: \tilde{O}\left(n^{\frac{1}{2k+3}}C_n^{\frac{2}{2k+3}}\right) | Helped |
| Use zero padding rather than the packing strategy before the wavelet transform | Ada-VAW · Higher-order TV^k online forecasting | dynamic regret | Hurt |
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