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About this paper
Shubhada Agrawal, Sandeep Juneja, Wouter M. Koolen
The KL$_{inf}$-UCB algorithm provides an asymptotically optimal solution for regret minimization in stochastic multi-armed bandits, effectively handling heavy-tailed reward distributions by assuming only a bounded (1+epsilon)-th moment. This algorithm offers tighter confidence intervals and outperforms robust mean-based UCB methods in numerical experiments.
Key insights
- Optimal regret minimization in heavy-tailed bandit settings is achievable under the weaker assumption of a uniformly bounded (1+epsilon)-th moment.
- Novel non-asymptotic concentration inequalities based on the KL$_{inf}$ functional provide tighter confidence intervals for heavy-tailed means than traditional robust estimators.
- A controlled trade-off between computational efficiency and statistical optimality is possible through batching, making complex optimal algorithms practical.
Summary by alphaXiv.
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