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Nathan Kallus

Publications and source records attributed to Nathan Kallus.

At least 19 recordsLinked to original sources
arXiv2026

A positive resolution of the gap-entropy conjecture

We prove the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in $[0,1]$, and a unique optimal arm. For each suboptimal arm $i$, let $\Delta_i=\mu_*-\mu_i$ be its gap from the optimal mean, and write $H=\sum_{i\ne *}\Delta_i^{-2}$. Let $p_r$ be the fraction of $H$ contributed by arms with $2^{-(r+1)}<\Delta_i\le2^{-r}$, and let $\mathrm{Ent}(I)=\sum_{r:p_r>0} p_r\log(1/p_r)$. Among all algorithms that identify the optimal arm with probability at least $1-\delta$ on every Gaussian instance, the optimal expected number of samples on a given instance, averaged over all permutations of the arm labels, is within absolute constant factors of $H(\log(1/\delta)+\mathrm{Ent}(I))$. Moreover, there is an algorithm, independent of the instance, whose expected number of samples is bounded by a constant multiple of this quantity plus $g^{-2}\log\log(e^e/g)$, where $g=\min_{i\ne *}\Delta_i$ is the gap to the closest competitor.

cs.LG↗
arXiv2026

Bellman Calibration for Marginalized Importance Weighting in Offline Reinforcement Learning

Marginalized importance weighting evaluates a target policy by reweighting offline state-action samples with its discounted occupancy ratio, characterized by an adjoint Bellman equation. Existing minimax, primal-dual, and fitted fixed-point estimators can leave residual occupancy-balance violations because of function-class approximation, regularization, or incomplete optimization. These violations are difficult to diagnose and reduce because the objectives generally lack a direct supervised validation loss for hyperparameter tuning, model selection, and early stopping. We introduce isotonic Bellman calibration, a one-dimensional, model-agnostic post-processing method that reduces these violations while preserving the ranking information in any initial occupancy-ratio estimate. The method corrects the estimate's scale and shape by applying fitted occupancy-ratio evaluation (FORE) over a one-dimensional class of nondecreasing transformations. We characterize Bellman calibration as a conditional fixed-point property equivalent to occupancy-balance against every test function of the calibrated ratio. More generally, we derive a calibration-refinement bound showing that any fitted ratio with small calibration error performs nearly as well as the best post-processing based on its fitted values. For isotonic Bellman calibration, we establish finite-sample calibration guarantees and a KL oracle inequality relative to the best monotone transformation of the initial estimate. Consequently, isotonic Bellman calibration achieves small calibration error and KL risk within statistical error of the best monotone correction, with guarantees for downstream target-occupancy functionals, including policy-value estimation.

cs.LG↗
arXiv2026

Recommendation Quality and the Concentration of Consumption: Experimental Evidence from Netflix

We study an experiment with 8.5 million users on Netflix's recommender system to measure how improvements in recommendation technology affect the set of products that get consumed. Improvements increase total consumption and users' reliance on recommendations while diffusing recommendations and consumption away from the most popular titles (``superstars") toward a larger number of moderately popular titles (``middle-tail"), with minimal effects on the most niche titles (``long-tail"). Our results challenge the notion that recommender systems polarize consumption -- raising the consumption shares of the head and tail at the expense of the middle -- and suggest that the returns to investing in middle-tail products grow as algorithms improve and platforms scale.

econ.GN↗
arXiv2026

Evaluating for the long term: Learnings from industry

Online platforms prioritize long-term business outcomes, yet typical experiments are far too short to measure these outcomes directly. Our goal in this paper is to collect and share industry knowledge on how to make decisions from short-term experiments that are better aligned with long-term outcomes. Based on a daylong workshop with 26 experts from 15 online platforms and 4 universities, we formulate a series of propositions that reflect current industry knowledge. Participants largely agreed that reversals of sign from short-run to long-run treatment effects are rare, with reversals concentrating in specific cases such as treatments involving content quality signals, hyper-monetization, and pricing. Although the magnitude of treatment effects can shift over time, a "univariate autosurrogate", corresponding to the short-run treatment effect on the long-run metric of interest, is often hard to beat. A recurring theme was the importance of surrogates that are not only (or even primarily) unbiased for true long-run outcomes, but that improve decision-making. Thus, participants generally agreed that simple, interpretable surrogates were generally preferable to elaborate but hard-to-explain surrogate indices. Participants also agreed that, due to concerns about confounding and transportability, experimentally-learned surrogates are generally preferable to observationally-learned surrogates. However, the drawback is that learning good surrogates from experiments typically requires a large, representative portfolio of long-run experiments that few platforms possess. We conclude that there is no substitute for a well-run long-term experiment, whether for learning surrogates or validating them, and we highlight open challenges including evolving treatments, persistent treatments not fully mediated by short-term proxies, and mismatch between experimental samples and the target population.

stat.AP↗
arXiv2026

A Human-Augmenting Agentic Workflow for Observational Causal Inference

Data analysis agents are becoming increasingly common tools for applied and scientific research. Yet, for highly specialized tasks such as Observational Causal Inference (OCI), human oversight remains necessary to ensure the validity of results. We introduce `oci-agent`, an open-source Python package that implements a human-in-the-loop agentic workflow for observational causal inference. `oci-agent` is designed to automate vital but laborious aspects of applied causal inference, such as covariate balance checking, propensity score trimming, and sensitivity analysis, so that humans can focus on more nuanced tasks, such as framing questions, scrutinizing assumptions, and evaluating diagnostics and results. We initially open-sourced `oci-agent` in June 2026 with support for doubly robust learning of the average treatment effect of a single binary treatment. Since then, we have added support for heterogeneous treatment effect estimation and for multiple continuous treatments via partially linear models. In this paper, we describe the principles behind `oci-agent` and offer internal Netflix case studies and evaluations on public data of its capabilities. Across numerous evaluations, `oci-agent` outperforms less structured baselines while remaining competitive with hand-tuned benchmarks. `oci-agent` is used extensively for causal inference at Netflix and has orchestrated more than 100 analyses per month since its release in June.

stat.CO↗
arXiv2026

Semiparametric inference on identification sets in choice modeling

In a discrete choice model, choice probabilities observed for a finite collection of choice sets may not identify a counterfactual choice probability under an unobserved choice set. We represent this counterfactual probability as a linear functional of a mixing distribution. Because the target is a functional of a distribution whose support is not restricted to a finite set, the parameter space is infinite-dimensional, while the data impose only finitely many moment restrictions. Therefore, observed choice probabilities need not point identify such a target. The identified set is defined as the set of target values compatible with observed choice probabilities. Rather than imposing conditions to ensure point identification, we characterize the identified set, and conduct inference on its lower and upper endpoints. We represent each endpoint as the value of a linear program over probability measures, and give conditions to obtain pathwise differentiability of the identification bounds. As a consequence, we are able to prove asymptotic normality of plug-in endpoint estimators. Finally, we provide an Expectation-Maximization-like algorithm for certifying membership of candidate values in the identified set and establish local convergence guarantees.

math.ST↗
arXiv2026

Fitted Occupancy-Ratio Evaluation without Bellman Completeness

Occupancy ratios correct distribution shift in offline reinforcement learning and are central to off-policy evaluation. Existing primal-dual and minimax methods typically estimate these ratios by enforcing occupancy-balance moments over a critic class. We propose fitted occupancy-ratio evaluation (FORE), a fitted fixed-point method that characterizes the discounted occupancy ratio through an adjoint Bellman recursion. At each iteration, FORE solves a single-level density-ratio objective on one-step-transition data, thereby projecting the adjoint Bellman image onto a log-ratio class in Kullback-Leibler (KL) divergence. Unlike analyses of fitted Q-evaluation, which typically require value-function realizability together with Bellman completeness or projected-operator stability, our central approximation condition is just realizability of the discounted occupancy ratio itself. Under this condition, the population KL-projected recursion contracts in relative entropy toward the true ratio by virtue of the adjoint Bellman operator being a KL-contraction. For the empirical recursion, we establish finite-sample regret bounds that yield convergence in KL up to approximation error and a statistical error governed by the complexity of the ratio hypothesis class. When full coverage fails, we introduce coverage-stopped FORE, which targets the discounted occupancy accumulated before the first uncovered state-action pair and yields a conservative lower bound on target-policy value for nonnegative rewards. The fitted ratio supports direct value estimation by reward reweighting, occupancy-weighted fitted Q-evaluation, and doubly robust estimation that combines the fitted ratio with a fitted Q-function. Together, these results identify discounted occupancy-ratio realizability as a sufficient condition for offline policy evaluation without any completeness assumptions.

stat.ML↗
arXiv2026

Mult-DPO: Multinomial Direct Preference Optimization for Recommender Systems

Direct preference optimization (DPO) is a simple and effective alignment strategy for large language models (LLMs) based on pairwise preferences. In recommender systems, however, user feedback is rarely pairwise. For a given context, e.g., a user, a session, or a conversation, we typically observe set-wise preferences with multiple positive items, where every positive item should outrank every unobserved or explicitly negative item, with no prescribed order among the positives or the negatives themselves. A natural generalization is to use the Plackett-Luce (PL) reward model, which extends the Bradley-Terry reward model underlying vanilla DPO from pairwise preferences to full rankings of candidates. However, we show that adapting the PL model to set-wise preferences requires marginalizing over all positive orderings, where the resulting expression is combinatorial in complexity. To address this fundamental challenge, we propose Mult-DPO, a novel DPO objective with a tractable multinomial surrogate likelihood over set-wise preference events for the user-preference alignment of LLM-based recommender systems. The multinomial construction is not itself a ranking distribution, but it is defined on the same reward-induced weight space and admits a closed-form DPO-style objective, enabling direct alignment of LLMs with multiple candidates through a classification-style objective. In addition, we prove that the multinomial DPO loss is a tractable upper bound on the marginalized PL DPO loss when optimizing against the set-wise preference data. We further characterize the tightness of this bound in terms of the relative total weight of positives versus negatives, which provides insights into tightening the bound with richer or harder negatives. Finally, we extend Mult-DPO to the alignment of LLMs with multiple preference levels. Code is available at https://github.com/yaochenzhu/Mult_DPO

cs.IR↗
arXiv2026

Reward Transfer from Inverse Reinforcement Learning: A Coupled Minimax Approach

We study the transfer of rewards learned using inverse reinforcement learning from expert demonstrations in one environment to reinforcement learning in a new, different environment. This arises naturally when demonstrations are collected in a controlled environment. We formulate the problem as a joint system of Bellman equations across the source and target environments and develop minimax estimators for the target soft-$q$-function. Whereas a sequential solution approach first estimates the source reward and then plugs it into the target control problem, a coupled approach solves the source and target system of equations jointly. We show that, in contrast to the sequential approach, the coupled approach removes the first-order influence of source Bellman residual error. We characterize the local behavior of each approach, develop finite-sample soft-$q$-function error bounds, and prove regret guarantees for the resulting soft-control policy. An empirical investigation using a sepsis simulator validates the theoretical comparison.

cs.LG↗
arXiv2026

Semiparametric Efficient Bilevel Gradient Estimation

Functional bilevel methods estimate a lower-level function and plug it into a hypergradient, but this plug-in gradient can retain first-order bias when the lower-level problem is learned nonparametrically. To remove this bias, we develop a semiparametric debiasing theory for population bilevel gradients based on the efficient influence function. This perspective leads to a cross-fitted orthogonal hypergradient estimator for which we establish asymptotic normality together with uniform control over the outer parameter. Under quadratic losses, the estimator reduces to a simple doubly robust score based on conditional mean nuisances. On synthetic bilevel benchmarks with known ground truth, the method tracks the oracle efficient-gradient benchmark and improves over plug-in functional hypergradients and regularized kernel bilevel baselines.

stat.ML↗
arXiv2026

The Context Gathering Decision Process: A POMDP Framework for Agentic Search

Large Language Model (LLM) agents are deployed in complex environments -- such as massive codebases, enterprise databases, and conversational histories -- where the relevant state far exceeds their context windows. To navigate these spaces, an agent must iteratively explore the environment to find relevant information. However, without explicit infrastructure, an agent's working memory can degrade into lossy representations of the search state, resulting in redundant work (e.g. repetitive looping) and premature stopping. In this work, we formalize this challenge as the Context Gathering Decision Process (CGDP), a specialized Partially Observable Markov Decision Process, where an agent's objective is to adaptively refine its belief state to isolate the necessary information for a task. We model an LLM's behavior as approximate Thompson Sampling within this CGDP, and introduce a predicate-based method that decomposes an LLM's implicit search into explicit and modular operations. We then derive two plug-and-play interventions for iterative LLM agents: a persistent, predicate-based belief state that bounds context while preserving multi-hop reasoning, and a programmatic exhaustion gate that halts unproductive search without premature stopping. Across four methods and three question-answering domains, we empirically validate that replacing an LLM's implicit state with our CGDP-motivated belief state improves multi-hop reasoning by up to $11.4\%$; while the modular programmatic exhaustion detection saves up to $39\%$ of tokens without any degradation in agent performance. Ultimately, we argue that framing the LLM agent loop as a CGDP can guide the design of modular, non-interfering improvements to agentic search harnesses.

cs.AI↗
arXiv2026

Nonparametric Instrumental Variable Analysis Without Structural Equations: Debiased Inference on Functionals of Inverse Problems with No Solutions

We consider debiased inference on finite-dimensional functionals of infinite-dimensional least-squares solutions to inverse problems as a way to avoid having to assume exact solutions exist. Such assumptions are substantive and not innocuous, and their failure may imperil inference when we impose them on the statistical model. Our approach instead allows us to conduct inference on a quantity that is defined regardless of solutions existing and coincides with the usual estimands when they do. For the case of instrumental variables, this means we can motivate the analysis with structural models but these do not need to hold exactly for the semiparametric inferential procedure to remain valid.

stat.ML↗
arXiv2026

Functional Natural Policy Gradients

We propose a cross-fitted debiasing device for policy learning from offline data. A key consequence of the resulting learning principle is $\sqrt N$ regret even for policy classes with complexity greater than Donsker, provided a product-of-errors nuisance remainder is $O(N^{-1/2})$. The regret bound factors into a plug-in policy error factor governed by policy-class complexity and an environment nuisance factor governed by the complexity of the environment dynamics, making explicit how one may be traded against the other.

stat.ML↗
arXiv2026

Design-Based Anytime-Valid Inference for Randomized Experiments with Delayed Outcomes and Staggered Entry

Delayed outcomes are ubiquitous in online experimentation: treatment can affect whether an outcome occurs, when it occurs, and its realized value. To accommodate staggered entry while remaining robust to environmental nonstationarity and unit-level heterogeneity, we adopt a design-based perspective and target the sample cumulative reward in each arm as a function of calendar time. Our confidence sequences allow practitioners to continuously monitor the counterfactual incremental reward, such as revenue, that would have been realized by calendar time $t$ had all entered units been assigned to treatment rather than control. The main technical challenge is the choice of design-based filtration, complicated by the presence of asynchronous potential outcome times. We show that the IPW treatment-effect estimation error is not a martingale with respect to any filtration, while each arm-specific IPW estimation error is a martingale with respect to a carefully chosen arm-specific event-time filtration. We therefore construct a confidence sequence for the treatment effect by combining two arm-level confidence sequences with a union bound, and further demonstrate that this can outperform the traditional design-based variance upper bound. Finally, we characterize the class of augmentations for which the per-arm AIPW estimation error remains a martingale.

stat.ME↗
arXiv2026

Efficient Inference after Directionally Stable Adaptive Experiments

We study inference on scalar-valued pathwise differentiable targets after adaptive data collection, such as a bandit algorithm. We introduce a novel target-specific condition, directional stability, which is strictly weaker than previously imposed target-agnostic stability conditions. Under directional stability, we show that estimators that would have been efficient under i.i.d. data remain asymptotically normal and semiparametrically efficient when computed from adaptively collected trajectories. The canonical gradient has a martingale form, and directional stability guarantees stabilization of its predictable quadratic variation, enabling high-dimensional asymptotic normality. We characterize efficiency using a convolution theorem for the adaptive-data setting, and give a condition under which the one-step estimator attains the efficiency bound. We verify directional stability for LinUCB, yielding the first semiparametric efficiency guarantee for a regular scalar target under LinUCB sampling.

stat.ML↗
arXiv2026

GAAVI: Global Asymptotic Anytime Valid Inference for the Conditional Mean Function

Inference on the conditional mean function (CMF) is central to tasks from adaptive experimentation to optimal treatment assignment and algorithmic fairness auditing. In this work, we provide a novel asymptotic anytime-valid test for a CMF global null (e.g., that all conditional means are zero) and contrasts between CMFs, enabling experimenters to make high confidence decisions at any time during the experiment beyond a minimum sample size. We provide mild conditions under which our tests achieve (i) asymptotic type-I error guarantees, (i) power one, and, unlike past tests, (iii) optimal sample complexity relative to a Gaussian location testing. By inverting our tests, we show how to construct function-valued asymptotic confidence sequences for the CMF and contrasts thereof. Experiments on both synthetic and real-world data show our method is well-powered across various distributions while preserving the nominal error rate under continuous monitoring.

stat.ME↗
arXiv2026

Causal Inference on Networks under Misspecified Exposure Mappings: A Partial Identification Framework

Estimating treatment effects in networks is challenging, as each potential outcome depends on the treatments of all other nodes in the network. To overcome this difficulty, existing methods typically impose an exposure mapping that compresses the treatment assignments in the network into a low-dimensional summary. However, if this mapping is misspecified, standard estimators for direct and spillover effects can be severely biased. We propose a novel partial identification framework for causal inference on networks to assess the robustness of treatment effects under misspecifications of the exposure mapping. Specifically, we derive sharp upper and lower bounds on direct and spillover effects under such misspecifications. As such, our framework presents a novel application of causal sensitivity analysis to exposure mappings. We instantiate our framework for three canonical exposure settings widely used in practice: (i) weighted means of the neighborhood treatments, (ii) threshold-based exposure mappings, and (iii) truncated neighborhood interference in the presence of higher-order spillovers. Furthermore, we develop orthogonal estimators for these bounds and prove that the resulting bound estimates are valid, sharp, and efficient. Our experiments show the bounds remain informative and provide reliable conclusions under misspecification of exposure mappings.

cs.LG↗
arXiv2025

Exploration in the Limit

In fixed-confidence best arm identification (BAI), the objective is to quickly identify the optimal option while controlling the probability of error below a desired threshold. Despite the plethora of BAI algorithms, existing methods typically fall short in practical settings, as stringent exact error control requires using loose tail inequalities and/or parametric restrictions. To overcome these limitations, we introduce a relaxed formulation that requires valid error control asymptotically with respect to a minimum sample size. This aligns with many real-world settings that often involve weak signals, high desired significance, and post-experiment inference requirements, all of which necessitate long horizons. This allows us to achieve tighter optimality, while better handling flexible nonparametric outcome distributions and fully leveraging individual-level contexts. We develop a novel asymptotic anytime-valid confidence sequences over arm indices, and we use it to design a new BAI algorithm for our asymptotic framework. Our method flexibly incorporates covariates for variance reduction and ensures approximate error control in fully nonparametric settings. Under mild convergence assumptions, we provide asymptotic bounds on the sample complexity and show the worst-case sample complexity of our approach matches the best-case sample complexity of Gaussian BAI under exact error guarantees and known variances. Experiments suggest our approach reduces average sample complexities while maintaining error control.

cs.LG↗