Research map / Bandits and online learning / Online convex optimization and games
Tight Bounds on Minimax Regret under Logarithmic Loss via Self-Concordance
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use self-concordance instead of truncating predicted probabilities | Sequential probability assignment under log loss · Expert classes with sequential entropy Θ(γ^-p) | minimax regret: O(n^{\frac{p}{p+1}}) | Helped |
| Use the general entropy-based bound for infinite-dimensional linear predictors | Sequential probability assignment under log loss · Infinite-dimensional linear predictors on the Hilbert unit ball | minimax regret: \tilde\cO(n^{2/3}) versus \tilde\cO(n^{1/2}) | Mixed |
| Use a single-scale discretization rather than multiple-scale chaining | The proposed minimax-regret analysis · Rich expert classes under log loss | minimax regret: O(n^{\frac{p}{p+1}}) | Helped |
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