Adaptive Linear Estimating Equations

Summary

The authors propose a general method for constructing debiased estimator called Adaptive Linear Estimating Equations (ALEE) estimator, which achieves asymptotic normality even in sequential data collection. To obtain valid statistical inference, the online debiasing concept is used. The online debiasing procedure guarantees asymptotic reduction of bias to zero, but the convergence speed is slow. However, the ALEE estimator solves the slowly decreasing bias problem. In this paper, the stable weights of ALEE are proved through equations for three cases: multi-arm bandits, autoregressive time series, and contextual bandits. A comparison of the ALEE method confirms that it performs better than the previous method.

Strengths

- ALEE provides point and interval estimation based on the central limit theorem, which enables stable estimation. It also prove the stability condition of ALEE through formulas for stable weights in three cases (Multi-arm bandits, Autoregressive time series, and Contextual bandits), which increases the efficiency of ALEE. Based on this stability and efficiency, we expect that it can be applied to various models. - ALEE's training algorithm has fast convergence. The authors provide theoretical performance guarantees and demonstrate ALEE's effectiveness on distributed time series forecasting problems with several examples.

Weaknesses

- In the numerical experiments, the results are only shown using parameter values of 0.3 and 1 for the two-armed bandit setting and the contextual bandit setting. It would be better if used the various values for the parameters. - Lack of explanation for Table 1.

Questions

Table 1: OLEE typo (ALEE), and Table 1 seems to lack explanation.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

-

Summary

This paper considers the problem of least squares when the data is collected sequentially. It proposes a form of weighted least squares where the weights are designed to lead to estimates that are asymptotically normal and nearly optimal variance. The appropriate weights are derived for the multi-arm bandit, autoregressive, and context bandit settings. Experimental results on some toy datasets confirm the theory.

Strengths

1. The proposed estimator is simple and nearly efficient. 2. Therefore, I think it would be useful for practitioners. 3. The problem is well-motivated. I am not familiar with the literature on this problem, so I cannot comment on originality.

Weaknesses

1. The presentation is somewhat confusing at times. The matrix $A$ from Section 2 does not appear in Section 3. The general construction strategy in Section 3.1 does not seem to be applied in Section 3.3 and it's not clear why. 2. The examples used in the experiments are all very simple. It would strengthen the work to, for example, vary the number of arms/dimension.

Questions

Please see above.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

2 fair

Contribution

3 good

Limitations

The paper is largely theoretical, so I think it's fine that the authors don't include a broader impacts section. However, I think the authors should include something about the limitations of the current work (see previous sections).

Summary

This paper proposes an estimator (ALEE) for adaptively collected data generated from adaptive linear models, describes its construction such that asymptotic normality holds for practically relevant examples, and demonstrates its desirable properties in numerical experiments.

Strengths

I enjoy reading this paper. It reads well. - The problem of inference for adaptive data is practically relevant - Theoretical guarantees assume somewhat weaker assumptions than previous works - The proposed method provides an improvement over other approaches, at least in the numerical experiments shown

Weaknesses

I don't think this submission lacks anything for a NeurIPS paper

Questions

- One novelty of the paper is that Eq (3) is weaker than sub-Gaussian, yet all experiments are for Gaussian noise. I would be more convinced if the numerical simulations shows the same desirable properties for non-Gaussian noise. - Perhaps refer to Fig 1 from the main text? Some minor typos I find: - Refs 14&15 are identical - l51 - _debaising_ → debiasing - l98 - _Slutsy's theorem_ → Slutsky's theorem

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

N/A

Summary

This paper introduces a general method for constructing debiased estimator within the context of sequential data collection. The proposed methodology is applied explicitly to multi-arm bandits, autoregressive time series, and contextual bandits. Experiments are conducted in these three domains to verify the applicability and effectiveness.

Strengths

1. The proposed method is able to achieve asymptotic normality without knowing the data collection algorithm and can obtain a faster convergence rate of the bias term. 2. Pointwise and interval estimates can therefore be generated.

Weaknesses

The experiment section only contains synthetic results. Considering the broad application of sequential data collection, it would greatly enhance the study if the authors could validate their framework using real-world datasets. This could provide more practical insight into the effectiveness of the proposed method.

Questions

In Figures 2 and 3, what do “lower tail coverage” and “upper tail coverage” represent?

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

1: Your assessment is an educated guess. The submission is not in your area or the submission was difficult to understand. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

Limitations are not mentioned, and the potential negative societal impact is not addressed.

Thanks for the reply

I am satisfied with the response. I am keeping my rating as is.

Thanks to the authors for the rebuttal

After reading it and the other reviews, I have decided to keep the same score.

Thanks for the Authors' response

The authors' response is promising to me. I will keep my score as it is.