Title: Online Experimental Design With Estimation-Regret Trade-off Under Network Interference
Venue: NeurIPS 2025
Accepted: yes
Keywords: Online experimental design

Causal inference

Network interference

Multi-armed bandits
Abstract: Network interference has attracted significant attention in the field of causal inference, encapsulating various sociological behaviors in which the treatment assigned to one individual within a network
may affect the outcomes of others, such as their neighbors. A key challenge in this setting is that
standard causal inference methods often assume independent treatment effects among individuals,
which may not hold in networked environments. To estimate interference-aware causal effects, a
traditional approach is to inherit the independent settings, where practitioners randomly assign experimental participants to different groups and compare their outcomes. Although effective in offline
settings, this strategy becomes problematic in sequential experiments, where suboptimal decisions persist, leading to substantial regret. To address this issue, we introduce a unified interference-aware framework for online experimental design. Compared to existing studies, we extend the
definition of arm space using the statistical concept of exposure mapping, which allows for
a more flexible and context-aware representation of treatment effects in network settings. Crucially, we establish a Pareto-optimal trade-off between estimation accuracy and regret under the
network concerning both time period and arm space, which remains superior to baseline models
even without network interference. Furthermore, we propose an algorithmic implementation and
discuss its generalization in different learning settings and network topology.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper studies sequential experimental design under network interference. The core contribution is to introduce a multi-armed bandit framework (\"MAB-N\") that incorporates arbitrary exposure mappings and allows the researcher to formalize trade-offs between estimation precision (for causal effect estimands, here ATE across exposure arms) and regret minimization (i.e., reward optimization for the experimental population). The authors define a family of exposure mappings generalizing existing designs (e.g., global proportion, cluster-randomized Bernoulli, unit-level assignments), define the feasible super-arm space induced by these mappings, and study a minimax trade-off problem indexed by time horizon T and number of exposure arms |UE|. They provide a lower bound on the product of regret and estimation error, and propose an algorithm (UCB-TSN) that achieves matching upper bounds. The result is extended to an adversarial bandit setting using an EXP3-based variant.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The paper is clearly and accurately situation in relation to the most relevant literature. You can tell the authors are well-read up on this research area.\n\n2. The framework appears to be modular and flexible, unifying several previously distinct formulations (cluster-randomized experiments, global interference designs, local neighborhood exposure mappings) via an abstraction based on exposure mappings. The distinction between the original super arm space and the reduced exposure arm space is clearly formalized.\n\n3. The core trade-off result (Thm 1) is interesting and seems to extends prior work on estimation-regret trade-offs (e.g., Simchi-Levi & Wang 2024) to the interference setting and general exposure mappings. \n\n\nWeaknesses:\n\n4. The paper’s contribution is primarily in generalization, not in introducing fundamentally new algorithmic or statistical ideas. The key trade-off result follows a similar form as existing results in the non-interference setting. While extending it to interference is nontrivial, the conceptual gain beyond the generality of the exposure mapping is somewhat limited. In particular, there is no significant conceptual advance in interference-aware estimation itself; rather, the interference structure is encoded in the exposure mapping and treated as black-box from that point onward.\n\n5. The algorithmic contribution is not obvious to me. The UCB-TSN algorithm is essentially UCB run after a fixed exploration phase over the exposure arms. The EXP3-TSN algorithm is only briefly sketched and seems to follow standard ideas. There is no adaptive or data-driven tuning of the exposure mapping, and no exploration of what happens when the exposure mapping is misspecified or learned.\n\n6. The claim of \"bridging estimation and regret via Pareto-optimality\" is slightly overstated. The definition of Pareto front (Definition 1) is not operationalized in the design of the algorithm. In practice, it seems to me the user still has to pick $T_1$ manually. There is no procedure that selects the allocation adaptively based on observed data to balance the objectives. So while the theory is elegant, its practical impact may be limited. Please correct me if I missed something.\n\n7. The writing could be improved. For one, it is sometimes a bit too abstract. For example, the formal definition of the Pareto front (Def 1) is not necessary; the concept could be explained more directly in terms of a constrained optimization trade-off. Similarly, the distinction between different exposure mappings is clear but not especially novel. The generality could be preserved with a shorter exposition. Second, the paper would benefit from removing some material in exchange for providing more intuition and dividing up their paragraphs into multiple shorter ones. It is quite tough to read as-is.\n\n8. The exposition of key assumptions is vague in some parts. For example, it is not clearly stated whether the exposure mapping $S$ is assumed to satisfy some form of partial interference (e.g., unit i’s outcome depends only on the treatment assignments of units in a neighborhood of i). This may be needed for identification, especially if $|\\mathcal U_{\\mathcal E}|$ is to be small relative to $KN$. The discussion of Condition 1 $(2 \\leq |\\mathcal U_{\\mathcal E}| \\leq T)$ is too brief and gives the impression that the exposure mapping can be chosen arbitrarily, without concern for identifiability.\n\nQUESTIONS:\n1. The regret bounds scale in $\\sqrt{|\\mathcal U_{\\mathcal E}| T}$, and the estimation error scales in $\\sqrt{|\\mathcal U_{\\mathcal E}| T_1}$. Is there any way to adaptively choose $T_1$ based on online variance estimation or confidence bounds on $\\hat \\Delta$, rather than fixing $T_1$ ex ante?\n\n2. Can the exposure mapping $S(\\cdot)$ be learned or optimized from data? For example, if the mapping $S$ is unknown but satisfies some low-complexity/interference structure (e.g., depends only on local neighborhoods), could one select among candidate exposure mappings to improve trade-off performance?\n\n3. Are there settings where the optimal action under full-information differs across units (i.e., no single exposure arm $S^*$)? The regret definition assumes a globally optimal $S^*, but in general with interference, optimal actions may be heterogeneous across clusters or individuals.\n\n4. In what sense does this framework allow generalization to real-world experiments? Can the authors describe a concrete application (beyond simulations) where the proposed UCB-TSN or EXP3-TSN could be used in practice, with a discussion of what assumptions would be required to justify the exposure mapping used?\n\n5. There is no empirical comparison on realistic graphs or real-world networks. Are the conclusions robust to heterogeneous degree distributions or violations of the exposure mapping assumptions (e.g., exposure misclassification due to incomplete network information)?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors present a bandit-style tradeoff between estimation and optimization when experiments are repeatedly run (and there is interference).\n\nSTRENGTHS AND WEAKNESSES:\nThis setting is extremely strange. I don't believe its accurate to even refer to this experimental design method as \"online\". Typically, an \"online\" design would entail individual units entering the experiment, choosing how to assign them treatment and perhaps performing inference as those units enter the test. For examples of this kind of work, see [1, 2, 3]. In contrast, this work entails repeated running an entire experiment on all N units, T times. The approach in this paper is more like [4], which repeats an experiment multiple times so as to learn about the structure of interference through a model of equilibrium behavior. The setup here is so strange to traditional practice that it merits some form of justification. Why would anyone actually be doing this?\n\nThe setup is a bit confused. Typical work in causality makes one of two assumptions: fixed potential outcomes for each unit or random outcomes. The authors here essentially set out both of these: l113 indicates particular fixed potential outcomes for each unit (based only on the _treatment_ of other units in the test) while l115 follows the super-population setting in which the _reward_ comes from a super-population through the additively separable Gaussian noise. This is a strange mixing of typical settings that will probably not make anyone particularly happy. The difference in setting here is meaningful, as in the distinction between the theoretical results in [5] and [6].\n\nProposition 1 is nice, and not surprising from a causal perspective: it is fairly well understood that the problem of causal inference under interference is the combiniatoric explosion of potential outcomes. The angle that merits further discussion is why the solution here isn't something along the lines of graph-cluster-randomization [7,8] with a bandit on top of that. Or perhaps that is the solution proposed? If so, the connection needs to be spelled out much more explicitly.\n\n[1] https://arxiv.org/abs/2103.06476\n[2] https://arxiv.org/abs/2311.05794\n[3] https://arxiv.org/abs/2203.02025\n[4] https://arxiv.org/abs/1903.02124\n[5] https://arxiv.org/abs/2411.14341\n[6] https://arxiv.org/abs/2305.17187\n[7] https://arxiv.org/abs/1305.6979\n[8] https://arxiv.org/abs/1404.7530\n\nQUESTIONS:\nThe most important question is on whether the setting makes sense (above).\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors characterize the Pareto front for the tradeoff between inference and exposure-map-based regret in MAB with network interference. With a long enough time horizon, their proposed algorithm---sampling each pull within the exposure map once and applying UCB---is shown to be on this Pareto front.\n\nSTRENGTHS AND WEAKNESSES:\nIt is not clear to me what the key technical contributions are. Overall, I am struggling to understand why these exposure-map-based theorems differ in any substantial way to their counterparts in the classical MAB problem. \n\nFor instance I find the discussion and proof of Theorem 1 hard to follow. In the \"challenge of the proof\" section, point (i) appears to have been addressed already in Simchi-Levi and Wang (2024) while network interference is already widely studied, which appears to cover (ii) and (iii). The proof of Theorem 1 is unclear because notation such as the bivariate function Rad( , ) is used without definition, either in the main text or appendix. \n\nThe algorithm proposed by the authors appears not to differ from the classical MAB and relies upon the exposure mapping being small. An algorithm with the flexibility of sampling any point on the Pareto front using a tuneable trade-off parameter may have been more novel. \n\nPlease address these concerns and I will reconsider my score. I may have simply misunderstood some technical aspects.\n\nQUESTIONS:\nThe authors should address the concerns raised above and provide a clearer description of their approach's novelty and technical challenges. \n\nThe theorem proofs need to be described clearly, without using undefined terminology. \n\nOne line of investigation that could greatly improve the originality of the work is a comparison between network interference and the structural causal bandits setup, whereby downstream readouts can be used to learn the causal structure that leads to the interference.\n\nLIMITATIONS:\nPlease see the above sections.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

comments: SUMMARY:
The paper proposes a unified framework (MAB‑N) for running sequential A/B tests on a network where users’ treatments spill over to their neighbours. It shows there is an unavoidable \sqrt(|exposure‑arms|) trade‑off between regret while the test runs and precision of the estimated treatment effect, and supplies two simple two‑stage algorithms (UCB‑TSN for stochastic rewards, EXP3‑TSN for adversarial noise) that exactly hit that frontier.

STRENGTHS AND WEAKNESSES:
Pros: 
- This submission prove you can’t beat the \sqrt ∣U_E​∣ ​ regret × error frontier and then hit it with a two-stage algorithm that’s basically “round-robin for T_1 ​ rounds, then UCB/EXP3.” No fancy optimisation needed.
- For a theory-heavy study, the writing is unusually clear—every equation is introduced in context, then followed by a plain-language explanation, so the math never feels abrupt or opaque.

Cons: 
- The paper collapses each node’s neighbourhood into a single summary label, but real interference can depend on far subtler patterns (e.g., distance-weighted influence, repeated contacts, directionality). It would be reassuring to see the algorithm tested on richer synthetic scenarios, where the neighbourhood effect is not expressible by a single coarse bin.
- The optimal schedule demands a uniform-exploration phase of T 1 ​ = \sqrt ∣U_E∣T. As soon as the exposure mapping becomes more detailed, ∣U_E∣ explores, and Phase 1 can eat up a large fraction of the total horizon, diluting the promised regret savings.

QUESTIONS:
It has been resolved.

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 4
IMPACT: 4
ORIGINALITY: 3
DATE: 2025-07-03