# Near-optimal Per-Action Regret Bounds for Sleeping Bandits

arXiv: https://arxiv.org/abs/2403.01315 · HTML: https://mlsanity.com/paper/2403.01315/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 39 references that are in the map.
- First posted on arXiv 2 Mar 2024.

## Builds on (most cited first, 9 of 9)

- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Explore no more: Improved high-probability regret bounds for non-stochastic bandits](https://mlsanity.com/paper/1506.03271/) (2015)
- [Strongly Adaptive Online Learning](https://mlsanity.com/paper/1502.07073/) (2015)
- [A Second-order Bound with Excess Losses](https://mlsanity.com/paper/1402.2044/) (2014)
- [Efficient Contextual Bandits in Non-stationary Worlds](https://mlsanity.com/paper/1708.01799/) (2017)
- [Fighting Bandits with a New Kind of Smoothness](https://mlsanity.com/paper/1512.04152/) (2015)
- [Improved Sleeping Bandits with Stochastic Actions Sets and Adversarial Rewards](https://mlsanity.com/paper/2004.06248/) (2020)
- [Dynamic Ad Allocation: Bandits with Budgets](https://mlsanity.com/paper/1306.0155/) (2013)
- [One Arrow, Two Kills: An Unified Framework for Achieving Optimal Regret Guarantees in Sleeping Bandits](https://mlsanity.com/paper/2210.14998/) (2022)

## Built on by (most cited first, 3 of 3)

- [Beyond Minimax Rates in Group Distributionally Robust Optimization via a Novel Notion of Sparsity](https://mlsanity.com/paper/2410.00690/) (2024)
- [Prior-Agnostic Incentive-Compatible Exploration](https://mlsanity.com/paper/2602.20465/) (2026)
- [Counterfactual Regret for Reflective Agents with Lean-Verified Guarantees](https://mlsanity.com/paper/2610.14790/) (2026)

## Abstract (arXiv)

We derive near-optimal per-action regret bounds for sleeping bandits, in which both the sets of available arms and their losses in every round are chosen by an adversary. In a setting with K total arms and at most A available arms in each round over T rounds, the best known upper bound is O(K√TAlnK), obtained indirectly via minimizing internal sleeping regrets. Compared to the minimax Omega(√TA) lower bound, this upper bound contains an extra multiplicative factor of KlnK. We address this gap by directly minimizing the per-action regret using generalized versions of EXP3, EXP3-IX and FTRL with Tsallis entropy, thereby obtaining near-optimal bounds of order O(√TAlnK) and O(√T√AK). We extend our results to the setting of bandits with advice from sleeping experts, generalizing EXP4 along the way. This leads to new proofs for a number of existing adaptive and tracking regret bounds for standard non-sleeping bandits. Extending our results to the bandit version of experts that report their confidences leads to new bounds for the confidence regret that depends primarily on the sum of experts' confidences. We prove a lower bound, showing that for any minimax optimal algorithms, there exists an action whose regret is sublinear in T but linear in the number of its active rounds.