Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper studies the federated generalized linear bandits problem where each client faces a generalized linear bandits model. The parameters and the link functions across clients are the same. The learning objective is to minimize the cumulative regret of those clients. The paper proposes an algorithm called FedGLB-UCB with regret bound $O(d\sqrt{T})$ and communication cost at most $O(dN^2\sqrt{T})$, where $d$ is the dimension of parameter space, $T$ is the time horizon, and $N$ is the number of clients. Experiments are performed on both synthetic and real world dataset. 
strengths_and_weaknesses: The GLB setting introduces new challenges in the federated setting, since the estimation of the parameter does not have closed form and should be iteratively updated. This imposes challenges for efficient communication, and causes drifting issues at local updates.

The proposed FedGLB-UCB algorithm addresses such challenges by combining online local updating and offline regression for global update. It rigorously proves that  FedGLB-UCB achieves the same learning regret order as in the centralized setting, with a sublinear communication cost. The paper is in general well written and easy to follow.

Although  the communication cost is sub-linear, the order of $O(N^2\sqrt{T})$ still seems a little bit large, since federated linear bandits can achieve $O(N\log(T))$. 

questions: FedGLB-UCB adopts online regression for local update. While this reduces the computation complexity in each round, it may lead to larger estimation error. Is it possible to relace online regression with offline regression in each round for local update? Meanwhile, the global update takes many iterations of communications for each update. If the local update is already offline, can the computation complexity (hence the communication cost) for global update be reduced?

As mentioned above, the communication cost scales in $O(\sqrt{T})$ other than $\log(T)$. Is it possible to further reduce the communication cost to $O(\log(T))$ under federated generalized linear bandits? The scaling in $N$ is also not promising, as it increases as $N$ increases, which limits the scalability of the algorithm. Can this be reduced as well?

In Li, et al, (2017), it assumes that the link function is strictly increasing. Does this paper have similar assumption?

Is there applicable lower bound on regret for this problem?

limitations: The paper discusses limitations of current analysis and potential future directions.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper studies the generalized linear bandit in the federated setting. In contrast to prior work on federated/distributed bandits that consider the linear bandit setting, the generalized linear bandit is more challenging since the lack of a closed-form solution prevents naively broadcasting sufficient statistics in the generalized linear bandit. The authors propose a novel algorithm $\texttt{FedGLB-UCB}$ for the generalized linear bandit in the federated setting that combines offline and online regression in order to balance communication and computation. The authors demonstrate that $\texttt{FedGLB-UCB}$ obtains competitive regret with a moderate communication budget, and also demonstrate its efficiency on a synthetic and real-world benchmark.
strengths_and_weaknesses: Strengths:
- Federated bandits are an upcoming area of interest within the bandit community, and hence the topic of this paper is very relevant to that community.
- The authors are correct in that most prior work focuses on linear bandits in the federated setting, and extending those algorithms to the generalized linear bandit is non-trivial and hence this is an important challenge. 
- The paper is well-written and easy to understand. The central algorithm design components are easy to grasp.
- The presented algorithm is no-regret with efficient communication and works well on benchmarks, outperforming prior work.

Weaknesses:
- The authors do not discuss optimality within the problem setting: what is the optimal level of communication for no-regret learning in federated generalized linear bandits?
- It appears that the suboptimality (e.g., compared to the linear bandit) arises from the global update communication. Do the authors have any concrete remarks regarding this? The update does nullify the value in local updates (as pointed out by the authors in the conclusion as well), are there any assumptions that can allow reusing local updates in the global aggregation step?
questions: Please see above for questions.
limitations: The authors have discussed their limitations in the conclusion, however it would be great if they could provide more substantial remarks in those directions.
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: This paper considers federated learning for generalized linear bandits. The key difference compared to federated linear bandits is that it requires an iterative process for the global update rather than relying on sufficient statistics. The authors propose an efficient algorithm that is able to achieve a trade-off between communication and regret. Some variants of the proposed algorithm are also studied. Experiments are also conducted to corroborate the theoretical results.
strengths_and_weaknesses: **Strengths**
- A first study on the new problem
- Both theoretical results and empirical experiments

**Weaknesses**
- Technical contributions are limited
- The presentation may be improved
questions: The reviewer has the following concerns.
- The first one is about the technical contributions. It seems to me that this paper is a simple combination of existing techniques. That is, online-to-confidence bound + distributed optimization. The authors might need to highlight the new technical challenges in this paper. 
- The authors point out the issue of filtration in existing work (e.g., Lemma H.1 [28]) in the appendix. But it seems to the reviewer that the current explanation is not clear. Can the authors elaborate on this possible gap?
- The presentation for the main part, especially Section 4.2 needs improvement. The current presentation makes readers difficult to appreciate new insights in this paper compared to existing work [2,12]. The authors can try to only give an informal version of the lemma and results by only highlighting the key terms and discarding all other similar terms in [2,12]. 
- Another question is about the measure of the communication overhead. It would also be important to measure the cost in terms of real numbers rather than the communication times.
- Also, the current communication is a synchronized one, i.e., when one local client triggered it, all the clients need to communicate. This could be impractical. Can the authors comment on how to handle an asynchronous communication scheme?
limitations: Yes.
review_title: null

Meta-review: metareview: Federated bandits are a current area of interest within the community and the paper provides valuable contributions. In particular, the authors deal with the rather general GLM setting, provide algorithms, and study the regret. It would be useful if the authors would use the discussions with the reviewers and the reviewers' comments to improve and polish the paper.
confidence: Less certain
Decision: Accept