Research map / Bandits and online learning / Multi-armed bandits
Combinatorial Multi-Armed Bandit with General Reward Functions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace UCB-style mean estimates with stochastically dominant CDF confidence bounds (SDCB) for general nonlinear rewards | Combinatorial MAB with general reward functions · theoretical analysis (distribution-dependent and distribution-independent regret) | regret bound | Helped |
| Discretize outcome distributions onto s=ceil(sqrt(T)) equally spaced support points (Lazy-SDCB) | SDCB · theoretical analysis (time and space complexity) | worst-case running time and memory: Time O(T^{3/2}) and space O(sqrt(T)) instead of Theta(T^2) time and Theta(T) space | Helped |
| Use PTAS as offline oracle for K-MAX (versus greedy (1-1/e) oracle) | K-MAX bandit with SDCB · theoretical analysis (approximation regret) | (1-epsilon)-approximation regret bound | Helped |
| Apply SDCB to summation reward (linear CMAB) instead of general reward | SDCB · theoretical analysis | regret bound | No clear effect |
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