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Online mirror descent and dual averaging: keeping pace in the dynamic case
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add dual stabilization with γ_t = η_{t+1}/η_t to OMD | OMD with dynamic learning rates · Online convex optimization with unbounded Bregman divergence | regret: Ω(T) -> O(√T) | Helped |
| Use dual stabilization with η_t = 2 √(ln(n) / t) | OMD · Prediction with expert advice, ĝ_t ∈ [0,1]^n | regret: Regret(T,z) ≤ √(T ln n) | Helped |
| Use a self-confident learning rate based on the learner's past cost | Dual-stabilized OMD · Prediction with expert advice, ĝ_t ∈ [0,1]^n | first-order regret: Regret(T,z) ≤ 2√(ln(n) L_T^*) + 8 ln n | Helped |
| Use the standard OMD update instead of adding stabilization | OMD with dynamic learning rates · Online convex optimization with unbounded Bregman divergence | regret: Ω(T) | Hurt |
| Use dual stabilization with the same decreasing learning rates as dual averaging | OMD · Online convex optimization, strongly convex mirror map | regret: Regret(T, z) ≤ ∑_{t=1}^T η_t ||ĝ_t||_*^2/(2ρ) + D_Φ(z, x_1)/η_{T+1} | No clear effect |
| Use the proximal composite update without linearizing Ψ | Dual-stabilized OMD · Composite online convex optimization | Ψ-regret | Mixed |
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