Title: A Near-optimal, Scalable and Parallelizable Framework for Stochastic Bandits Robust to Adversarial Corruptions and Beyond
Venue: NeurIPS 2025
Accepted: yes
Keywords: multi-armed bandits

adversarial corruption

multi-agent bandits

batched bandits

graph bandits

semi-bandits
Abstract: We investigate various stochastic bandit problems in the presence of adversarial corruptions. A seminal work for this problem is the BARBAR~\cite{gupta2019better} algorithm, which achieves both robustness and efficiency. However, it suffers from a regret of $O(KC)$, which does not match the lower bound of $\Omega(C)$, where $K$ denotes the number of arms and $C$ denotes the corruption level. In this paper, we first improve the BARBAR algorithm by proposing a novel framework called BARBAT, which eliminates the factor of $K$ to achieve an optimal regret bound up to a logarithmic factor. We also extend BARBAT to various settings, including multi-agent bandits, graph bandits, combinatorial semi-bandits and batched bandits. Compared with the Follow-the-Regularized-Leader framework, our methods are more amenable to parallelization, making them suitable for multi-agent and batched bandit settings, and they incur lower computational costs, particularly in semi-bandit problems. Numerical experiments verify the efficiency of the proposed methods.


Peer reviews:
comments: SUMMARY:
The paper focused on the stochastic bandits under the adversarial corruption problem. Based on the limitations of the previous BARBAR algorithm, the authors proposed a new framework called BARBAT based on the elimination idea. Based on the framework, they can get a better regret bound. They also showed the framework on different specific bandit settings, such as multi-agent bandits, graph bandits,
combinatorial semi-bandits and batched bandits, and provided both theoretical and experimental results for these settings.

STRENGTHS AND WEAKNESSES:
Strengths:
The paper improved the previous regret bound for the problem and provided both solid theoretical results and interesting experimental results.

Weaknesses:
The main concern is the novelty of the algorithm since it is based on BARBAR.

QUESTIONS:
1. You provided a lower bound in section 4.2 but how about other settings? Is it possible to provide a lower bound for other settings? 
2. From Table 1, the results seem to be a little outperforming previous work. For example, for d-set semmi-bandits, your result is worse than others on the order of $\log T$. Please discuss it.
3. You mentioned the different definition of regret: $R(T)$ and $\tilde{R}(T)$. In the whole paper, you work on $R(T)$, not $\tilde{R}(T)$. Please discuss the motivation for choosing the definition.

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-06-22

comments: SUMMARY:
This paper proposes BARBAT, an improved algorithmic framework for stochastic bandits robust to adversarial corruptions. Based on the BARBAR algorithm, BARBAT achieves a near-optimal regret bound of $O(C+ \sum_{\Delta_k>0} \log T^2/\Delta_k)$, removing the suboptimal $O(KC)$ term. The paper also extends BARBAT to settings including multi-agent, graph-structured, semi-bandits, and batched bandits, which is a naturally generalization for successive elimination algorithms.

STRENGTHS AND WEAKNESSES:
Strengths:
This paper is well-written and easy to follow, with clear and precise technical discussions. It extends the core framework to a wide range of bandit settings and is supported by extensive numerical experiments. The breadth of the work reflects a commendable level of effort and thoroughness by the authors.

Weaknesses:
The proposed BARBAT algorithm appears structurally similar to BARBAR, with the main change being in the change of epoch lengths. If achieving the improved regret bounds requires nontrivial technical innovations beyond modifying this aspect, I encourage the authors to highlight and clarify them. One of the primary advantages claimed is BARBAT's scalability and parallelizability, which are indeed important. However, these properties are common to many elimination-based methods, and it is unclear whether they stem from novel design choices in BARBAT. If direct generalization is not sufficient for the multiple settings considered, it would be helpful for the authors to elaborate on the challenges involved and the innovations introduced. Overall, while the work is executed with care, its contributions feel somewhat incremental.

QUESTIONS:
See weaknesses

LIMITATIONS:
See weaknesses
TITLE: Official Review
CLARITY: 4
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-06-25

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes BARBAT, a novel algorithmic framework for stochastic multi-armed bandits (MABs) under adversarial corruptions. BARBAT improves upon the BARBAR algorithm [1]  by eliminating the suboptimal corruption-dependent term $\\mathcal{O}(KC)$  in favor of a near-optimal $\\mathcal{O}(C)$ regret bound up to logarithmic factors, where $K$ is the number of arms and $C$ is the corruption budget. The authors further demonstrate the versatility of the framework by extending it to multi-agent, batched, strongly observable graph, and d-set semi-bandit settings, providing tailored algorithms and regret analyses for each. The theoretical results are complemented by empirical validations, showing that BARBAT and its extensions outperform prior methods in several regimes.\n\n[1] Anupam Gupta, Tomer Koren, and Kunal Talwar. Better algorithms for stochastic bandits with adversarial corruptions. In Conference on Learning Theory, pages 1562–1578. PMLR, 2019.\n\nSTRENGTHS AND WEAKNESSES:\nBelow is a summary of the paper’s main strengths and weaknesses.\n\n**Strengths**:\n\n1) The paper successfully generalizes BARBAT to four complex and practically relevant settings. The algorithmic adjustments for each extension are thoughtfully designed and maintain the core advantages of the framework. For each setting, the paper provides tight regret upper bounds.\n\n2)  BARBAT avoids the need to solve per-round convex optimization problems (as required by FTRL-based methods), making it computationally efficient.\n\n3) The introduction of BB-BARBAT constitutes the first theoretical analysis of batched bandits under adversarial corruptions, along with a corresponding lower bound. This fills a meaningful gap in the literature.\n\n4)  The experimental results across multiple settings consistently demonstrate that BARBAT-based methods outperform baseline algorithms. The results also show robustness to increasing corruption budgets, further supporting the theoretical claims.\n\n**Weaknesses**:\n\n1) The core BARBAT algorithm is closely related to DRAA [2], with the primary distinction being the use of epoch-varying failure probabilities. While this yields slightly improved regret bounds, this improvement is quite incremental.\n\n\n2) The multi-agent setting assumes instantaneous, reliable, and cost-free broadcasts. This assumption, while common in theory, limits the practical relevance of the results, especially since the authors claim their method to be highly parallelizable. There is no discussion of asynchronous or faulty communication scenarios, which are common in real-world systems.  Could the framework be extended to handle asynchronous message passing?\n\n3) While a lower bound is provided for batched bandits, no new lower bounds are given for other extensions (e.g., multi-agent or semi-bandits), making it unclear how tight the regret is in these settings.  Is it possible to derive lower bounds for these setting?\n\n[2] Fatemeh Ghaffari, Xuchuang Wang, Jinhang Zuo, and Mohammad Hajiesmaili. Multi-agent stochastic bandits robust to adversarial corruptions. arXiv preprint arXiv:2411.08167, 2024\n\nQUESTIONS:\nPlease see the Weaknesses section for related questions and concerns.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

comments: SUMMARY:
This study investigates the problem of stochastic bandits with adversarial corruptions. The authors refine the BARBAR algorithm and resolve an open issue presented in Gupta et al. Under the refined algorithm, the regret bounds are improved across various settings. The advantage of this algorithm, compared with other algorithms such as Tsallis-INF, lies in its computational efficiency.

STRENGTHS AND WEAKNESSES:
The authors provide a general framework for stochastic bandits with adversarial corruptions. Although several algorithms have been proposed, many of them are computationally costly, which is undesirable for settings such as graph or batched bandits. For example, $(1/2)$-Tsallis-INF requires solving an optimization problem at every step, which makes parallelization difficult.

BARBAR was proposed by Gupta et al. and is known to be computationally efficient. However, its regret does not match the lower bound with respect to the number of arms $K$ and the corruption level $C$. The authors refine the BARBAR algorithm and extend it to the settings mentioned above. They show that the new algorithm achieves favorable performance while retaining computational efficiency.

I believe the authors’ contribution is worth accepting to the conference; however, I still have some concerns. The main issue is that the regret bound is not tight in $T$. For example, if the algorithm incurs $\log(T)^2$ regret in the stochastic bandit setting, one could instead use Shannon-FTRL, which also achieves $\log(T)^2$ regret and is computationally efficient.

Minor comment: In the abstract, the authors use $K$ and $C$ without definition. Although the meaning can be inferred, it may be confusing.

QUESTIONS:
See above.

LIMITATIONS:
N/A.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-01