Regret Tail Characterization of Optimal Bandit Algorithms with Generic Rewards

2026-04-16 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new study investigates the tail behavior of regret in stochastic multi-armed bandits, specifically for algorithms that achieve asymptotic optimality in expectation. While minimizing expected regret is a standard goal, prior research indicates that even these algorithms can exhibit heavy regret tails, leading to substantial regret with considerable probability. This work extends the KLinf-UCB algorithm to a broad nonparametric class of reward distributions, establishing its asymptotic optimality in expectation. The research then analyzes the regret's tail behavior, deriving a novel upper bound on the regret tail probability. This framework recovers regret-tail guarantees for both bounded-support and heavy-tailed bandit models, and for finitely-supported reward distributions, the upper bound precisely matches the known lower bound, offering a unified and tight characterization of regret tails for KL-based UCB algorithms beyond parametric models.

Key takeaway

For research scientists developing or deploying multi-armed bandit algorithms, you should prioritize analyzing regret tail behavior in addition to expected regret. This work demonstrates that even asymptotically optimal algorithms can incur large regret with non-negligible probability, especially in nonparametric settings. Incorporating the extended KLinf-UCB algorithm and its tail characterization can lead to more robust and predictable system performance.

Key insights

Asymptotically optimal bandit algorithms can still exhibit heavy regret tails, necessitating tail behavior analysis.

Principles

• Regret tail behavior is crucial for bandit algorithm robustness.
• Nonparametric reward distributions require generalized analysis.

Method

The KLinf-UCB algorithm is extended to nonparametric reward distributions, followed by deriving a novel upper bound on regret tail probability to characterize its behavior.

In practice

• Evaluate bandit algorithms beyond expected regret.
• Consider KLinf-UCB for nonparametric reward settings.

Topics

• Stochastic Multi-Armed Bandits
• Regret Tail Characterization
• KLinf-UCB Algorithm
• Nonparametric Reward Distributions
• Asymptotic Optimality

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.