Title: Efficient Adaptive Experimentation with Noncompliance
Venue: NeurIPS 2025
Accepted: yes
Keywords: adaptive experimentation

instrumental variables

causal inference

semiparametric efficiency

multiply robust estimation

sequential design
Abstract: We study the problem of estimating the average treatment effect (ATE) in adaptive experiments where treatment can only be encouraged—rather than directly assigned—via a binary instrumental variable. Building on semiparametric efficiency theory, we derive the efficiency bound for ATE estimation under arbitrary, history-dependent instrument-assignment policies, and show it is minimized by a variance-aware allocation rule that balances outcome noise and compliance variability. Leveraging this insight, we introduce AMRIV—an **A**daptive, **M**ultiply-**R**obust estimator for **I**nstrumental-**V**ariable settings with variance-optimal assignment. AMRIV pairs (i) an online policy that adaptively approximates the optimal allocation with (ii) a sequential, influence-function–based estimator that attains the semiparametric efficiency bound while retaining multiply-robust consistency. We establish asymptotic normality, explicit convergence rates, and anytime-valid asymptotic confidence sequences that enable sequential inference. Finally, we demonstrate the practical effectiveness of our approach through empirical studies, showing that adaptive instrument assignment, when combined with the AMRIV estimator, yields improved efficiency and robustness compared to existing baselines.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the problem of estimating the Average Treatment Effect (ATE) in a sequential experiment where treatment assignment is endogenous. To tackle this, the authors propose a covariate-dependent instrument assignment strategy using historical data. The derived efficient influence function leads to a doubly robust ATE estimator, which enhances estimation robustness. Theoretical guarantees, including asymptotic normality and consistency rates, are established for the proposed method.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- The paper provides a well-defined and motivated problem statement.\n- The authors conduct a thorough investigation, integrating estimation theory with experimental design considerations. \n- The proposed covariate-dependent instrument assignment and doubly robust estimator are rigorously derived, with theoretical guarantees.\n\nWeaknesses\n- The literature review in the main text is inadequate, particularly concerning adaptive experimental design in sequential settings. \n- The paper does not clearly articulate how it addresses or advances prior work. As currently presented, the main results appear to be derivable easily from established literature, raising questions about the incremental contribution. \n- The simulation study does not explore important practical scenarios, such as the presence of always-takers and never-takers. \n- The estimation procedure assumes access to the complete historical data up to time $t$, which may not be realistic in certain applications. It would be valuable to discuss whether and how the method could be adapted to scenarios where only summary statistics of the historical data are available\n\nQUESTIONS:\n- The parameter $\\epsilon$ in Equation (6) is used in both the simulation studies and real data analysis. How sensitive is the proposed method to the choice of $\\epsilon$? \n    \n- How does the method perform with different choices or dynamics of the variance term $k_t$ in Equation (7)? \n\n- For the variance estimation step, would it be possible to use a simple empirical variance estimator that avoids producing negative estimates?\n\nLIMITATIONS:\nSee Weaknesses and Questions sections for limitations.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-20"}

comments: SUMMARY:
A new estimator AMRIV is introduced for adaptive experiments in noncompliance scenarios. The paper derives the optimal assignment policy by minimizing estimator variance, and proposes an efficient estimator using influence functions. The method supports valid sequential inference and outperforms some baselines in simulations.

STRENGTHS AND WEAKNESSES:
This paper does a very good job in providing the motivation for adaptive experimentation and non-compliance. AE is a growing topic in causal inference and experimentation and non-compliance is very common in real life. The problem statement is very clear and the connection/contribution to related work is also articulated. A semiparametric efficiency bound and optimal policy is derived on optimal instrument assignment, and the toy example in Figure 1 illustrates how the optimal policy reacts under different compliance scores. Although the proposed AMRIV integrates recent advances of adaptive nuisance estimation, sample splitting, policy truncation and time-uniform inference and hence might be considered incremental, the paper provides a thorough theoretical analysis that is not in previous work. The experimental evaluation is also strong, two studies involving both synthetic and semi-synthetic data and many  non-adaptive and oracle baselines.

For (minor) weakness, see questions below.

QUESTIONS:
There is only one minor question from me. The (R)EIF estimator in Equation 9 kind of comes out of nowhere and I cannot find any explanation or reference. Could the authors briefly describle the motivation of eq 9, or point to the reference if it was part of previos work on nuisance function estimation?

LIMITATIONS:
The authors have discussed their limitations and broader impacts in Appendix.
TITLE: Official Review
CLARITY: 3
IMPACT: 4
ORIGINALITY: 3
DATE: 2025-06-23

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper studies the problem of estimating the average treatment effect (ATE) in instrumental-variable (IV) settings when the researcher can adaptively allocate the instrument. Under a strong “no-confounding compliance” assumption that ensures point identification of the ATE, the authors derive an influence-function lower bound on the asymptotic variance and propose a sequential experimental design that attains this bound. Their strategy adaptively chooses the distribution of the instrument based on past data to minimize estimator variance. The paper provides both the theoretical derivations and a simulation study illustrating variance reduction compared to non-adaptive designs.\n\nSTRENGTHS AND WEAKNESSES:\nOverall the paper is well organized and clearly motivated. Definitions, assumptions, and the statement of the main theorem are clearly separated, and the adaptive algorithm is described in pseudocode. The asymptotic efficiency analysis is rigorous. The derivation of the influence-function bound follows established semiparametric methods and is presented clearly, with all regularity conditions stated. They introduce adaptive instrument allocation to minimize variance addresses an important practical challenge when instruments are costly or limited. It extends classical IV estimation by adding an experimental-design layer. Combining semiparametric efficiency theory with adaptive online experimental design in an IV context is novel.\n\nWeakness:  \nPractical Aspect: Under what real-world scenarios is it credible to assume both (a) the researcher can fully control the instrument distribution, and (b) there is genuine motivation to tune that distribution solely to reduce estimator variance?\nTheoretical aspect: 1) In the broader IV literature, identification typically dominates focus. Because the paper assumes point identification via a strong, untestable restriction, some may view the variance-optimization objective as a secondary concern. The work’s impact hinges on the prevalence of settings where such an assumption is plausible and the instrument is manipulable. 2) All variance guarantees are asymptotic. No finite-sample (non-asymptotic) variance bounds are provided, which limits practical guidance for moderate sample sizes. Also, influence function-based arguments only hold for iid sampling, so whether it’s the optimal variance that an adaptive policy can achieve remains unknown.\n\nQUESTIONS:\n1. Practical Motivation for Assumptions\nAs claimed in the weakness part, it’s not intuitive to think about scenario where the experimenter can actively control the instruments, willing to do that to reduce variance and also accept the strong assumption made.  Clarifying this will help justify the paper’s focus and demonstrate its applicability beyond toy settings.\n2. Partial Identification and Trade-Offs\n   If the “no-confounding compliance” assumption is violated or misspecified, can you characterize the resulting partial identification bounds for the ATE? Would your adaptive allocation ever widen these bounds (trading off identification tightness against variance)? This analysis would illuminate possible trade-offs when the key assumption fails.\n3. Finite-Sample Variance Bounds\n   Can you derive finite-sample (non-asymptotic) upper bounds on the mean-squared error of your estimator under the proposed adaptive design? Providing such guarantees would significantly strengthen the practical relevance for moderate sample sizes.\n4. Optimality under Adaptive Policies\n   Your influence-function lower bound applies under IID sampling. Does the same asymptotic variance lower bound hold when restricting to all history-dependent adaptive policies? In other words, is your algorithm provably optimal within that broader class?\nThe paper [1] addresses similar questions in the randomized-treatment setting. Can you explicitly map their finite-sample and asymptotic results to your IV framework? Such a comparison would clarify which aspects generalize and where new technical challenges arise.\nA clear answer to these questions will likely lead to higher score.\n\n[1] Li, J., Simchi-Levi, D., & Zhao, Y. (2024). Optimal adaptive experimental design for estimating treatment effect.\n\nLIMITATIONS:\nSee above", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-28"}

comments: SUMMARY:
This paper considers ATE estimation in the context of indirect treatment (instrumental variables) and adaptive experimentation. In this context, the authors derive a semi-parametric efficiency bound and use this to justify a specific adaptive experimentation strategy. Their approach is therefore an extension of MRIV to the adaptive setting. The instrument assignment policy used plugs data estimators for $\\sigma^2(0, X),\\sigma^2(1,X)$ into the formula of equation (4). These are computed by fitting several regression models as outlined on page 5. Theoretical guarantees are provided. Experimental validation on synthetic data shows that AMRIV performs better than several alternatives.

STRENGTHS AND WEAKNESSES:
# Strengths
- non-compliance in experiments is a common set-up that warrants study
- the paper provides an extremely detailed exposition
- assumptions are clearly stated
- a semiparametric efficiency bound is derived for adaptive instrument assignment
- thorough theoretical treatment is provided giving asymptotic normality of the estimator, convergence rates and consistency, and confidence sets based on anytime-valid approaches

# Weaknesses
- the write-up is rather notation heavy. Perhaps consider including a glossary in the appendix so that we can easily find e.g. the definition of $\\delta$ on line 132 more quickly
- little is said about which nuisance estimators are to be preferred, despite these being an absolutely crucial part of the algorithm. Perhaps some empirical investigation could have been presented here to help ground the practitioner.

QUESTIONS:
- you say that $k$-NN, kernel smoother, random forest and neural net regressors can be used. How would one make this determination in practice?

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-02