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Nathan Kallus

Publications and source records attributed to Nathan Kallus.

At least 37 records · Page 2Linked to original sources
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

Semiparametric Preference Optimization: Your Language Model is Secretly a Single-Index Model

Policy alignment to preference data typically assumes a known link function between observed preferences and latent rewards (e.g., Bradley-Terry model / logistic link). Misspecification of this link can bias inferred rewards and misalign learned policies. We study policy alignment under an unknown and unrestricted link function. We formulate an $f$-divergence-constrained reward maximization problem and show that realizability in a policy class induces a semiparametric single-index binary choice model, where a scalar policy-induced index captures all dependence on demonstrations and the remaining preference distribution is unrestricted. Rather than impose identifiability of structural parameters of such a model and estimate them, as in econometrics, we develop methods that directly learn policies, with the reward function implicit, analyzing error to the optimal policy and allowing for unidentifiable and nonparametric indices. We prove link-agnostic convergence guarantees in terms of generic function complexity measures and validate the methods and theory empirically. Code is available at https://github.com/causalml/spo/.

cs.LG↗
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

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

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

Inverse Reinforcement Learning with Just Classification and a Few Regressions

Inverse reinforcement learning (IRL) aims to infer rewards from observed behavior, but rewards are not identified from the policy alone: many reward--value pairs can rationalize the same actions. Meaningful reward recovery therefore requires a normalization, yet existing normalized IRL methods often rely on anchor-action restrictions or specialized neural architectures. We study reward recovery in the maximum-entropy, or Gumbel-shock, model under a broad class of statewise affine normalizations, with anchor-action constraints as a special case. This yields Generalized Policy-to-$Q$-to-Reward (GenPQR), a modular procedure that estimates the behavior policy, evaluates its soft $Q$-function through the Bellman equation, and recovers the normalized reward. Both stages can be implemented with off-the-shelf classification and regression methods. We prove modular finite-sample guarantees under general function approximation, with separate policy-estimation and $Q$-estimation errors. As a concrete instantiation, we study GenPQR with fitted $Q$-evaluation, reducing IRL to policy estimation followed by regression. Experiments show that GenPQR matches or improves reward recovery relative to DeepPQR while remaining simpler and more modular. Compared with DeepPQR, our theory goes beyond anchor actions, accommodates large and continuous action spaces, makes coverage requirements explicit, and is not tied to a specific neural-network architecture or training procedure.

cs.LG↗
arXiv2026

Bellman Calibration for $V$-Learning in Offline Reinforcement Learning

Reliable long-horizon value prediction is difficult in offline reinforcement learning because fitted value methods combine bootstrapping, function approximation, and distribution shift, while standard guarantees often require Bellman completeness or realizability. We introduce Bellman calibration, a weak reliability criterion requiring that states assigned similar predicted values have average Bellman targets that agree with those predictions. This criterion yields a scalar calibration error for diagnosing systematic numerical miscalibration, which we estimate from off-policy data using doubly robust Bellman target estimates. We then propose Iterated Bellman Calibration, a model-agnostic post-hoc procedure that recalibrates any learned value predictor by fitting a one-dimensional map of its original prediction, with histogram and isotonic variants. We prove finite-sample guarantees showing that Bellman calibration error is controlled at one-dimensional nonparametric rates without Bellman completeness or value-function realizability. Our value-error bounds separate statistical estimation, finite-iteration, and approximation errors, clarifying when calibration improves value prediction and when its gains are limited by the information in the original predictor or insufficient coverage.

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

Entropy After for reasoning model early exiting

Reasoning LLMs show improved performance with longer chains of thought. However, recent work has highlighted their tendency to overthink, continuing to revise answers even after reaching the correct solution. We quantitatively confirm this inefficiency from the distribution dynamics perspective by tracking Pass@1 for answers averaged over a large number of rollouts and find the model often begins to always produce the correct answer early in the reasoning, making extra reasoning tokens wasteful. To detect and prevent overthinking, we propose a simple and inexpensive novel signal, Entropy After (EAT), for monitoring and deciding whether to exit reasoning early. By appending a stop thinking token ( ) and monitoring the entropy of the following token as the model reasons, we obtain a trajectory that decreases and stabilizes when Pass@1 plateaus; thresholding its variance under an exponential moving average yields a practical stopping rule. Importantly, our approach enables adaptively allocating compute based on the EAT trajectory, allowing us to spend compute in a more efficient way compared with fixing the token budget for all questions. Empirically, on MATH500 and AIME2025, EAT reduces token usage by 12 - 22% without harming accuracy. EAT also remains effective in black box settings where logits from the reasoning model are not accessible, and EAT is computed with proxy models: We verified the feasibility via early stopping Llama 70B with a 1.5B model and Claude 3.7 with a local 4B model.

cs.LG↗
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

Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands

We develop a unified framework for automatic debiased machine learning (autoDML) for inference on a broad class of statistical parameters. The framework applies to any smooth functional of a nonparametric M-estimand, defined as the minimizer of a population risk over an infinite-dimensional linear space. Examples include counterfactual regression, quantile, and survival functions, as well as conditional average treatment effects. Rather than requiring manual derivation of influence functions, our approach automates the construction of debiased estimators using three ingredients: the gradient and Hessian of the loss function and a linear approximation of the target functional. Estimation reduces to solving two risk minimization problems, one for the M-estimand and one for a Riesz representer. The framework accommodates Neyman-orthogonal loss functions that depend on nuisance parameters and extends to vector-valued M-estimands through joint risk minimization. We characterize the efficient influence function and construct efficient autoDML estimators via one-step correction, targeted minimum loss estimation, and sieve-based plug-in methods. Under quadratic risk, these estimators satisfy double robustness for linear functionals. We further show that they are robust to mild misspecification of the M-estimand model, incurring only second-order bias. We illustrate the method by estimating long-term survival probabilities under a semiparametric two-parameter beta-geometric failure model.

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

Rank-GRPO: Training LLM-based Conversational Recommender Systems with Reinforcement Learning

Large language models (LLMs) are reshaping the recommender system paradigm by enabling users to express preferences and receive recommendations through conversations. Yet, aligning LLMs to the recommendation task remains challenging: pretrained LLMs often generate out-of-catalog items, violate required output formats, and their ranking quality degrades sharply toward the end of the generated list. To this end, we propose ConvRec-R1, a two-stage framework for end-to-end training of LLM-based conversational recommender systems. In Stage 1, we construct a behavioral-cloning dataset with a Remap-Reflect-Adjust pipeline, which produces high-quality, catalog-grounded demonstrations from powerful blackbox LLMs to warm-start the RL training. In Stage 2, we propose Rank-GRPO, a principled extension of group relative policy optimization (GRPO) tailored to tasks with rank-style outputs. Rank-GRPO treats each rank in the recommendation list as the unit instead of token (too fine-grained) or sequence (too coarse), redefining rewards to remove non-causal credit assignment and introducing a rank-level importance ratio based on the geometric mean of rank-wise token probabilities to stabilize policy updates. Experiments on the public Reddit-v2 dataset show that ConvRec-R1 converges faster and achieves higher Recall and NDCG than GRPO-style baselines. Code and datasets are released at https://github.com/yaochenzhu/Rank-GRPO.

cs.IR↗
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↗
arXiv2026

DiFFPO: Training Diffusion LLMs to Reason Fast and Furious via Reinforcement Learning

We propose DiFFPO, Diffusion Fast and Furious Policy Optimization, a unified framework for training masked diffusion large language models (dLLMs) to reason not only better (furious), but also faster via reinforcement learning (RL). We first unify the existing baseline approach such as d1 by proposing to train surrogate policies via off-policy RL, whose likelihood is much more tractable as an approximation to the true dLLM policy. This naturally motivates a more accurate and informative two-stage likelihood approximation combined with importance sampling correction, which leads to generalized RL algorithms with better sample efficiency and superior task performance. Second, we propose a new direction of joint training efficient samplers/controllers of dLLMs policy. Via RL, we incentivize dLLMs' natural multi-token prediction capabilities by letting the model learn to adaptively allocate an inference threshold for each prompt. By jointly training the sampler, we yield better accuracies with lower number of function evaluations (NFEs) compared to training the model only, obtaining the best performance in improving the Pareto frontier of the inference-time compute of dLLMs. We showcase the effectiveness of our pipeline by training open source large diffusion language models over benchmark math and planning tasks.

cs.LG↗
arXiv2026

Nonparametric Instrumental Variable Inference with Many Weak Instruments

We study inference on linear functionals in the nonparametric instrumental variable (NPIV) problem with a discretely-valued instrument under a many-weak-instruments asymptotic regime, where the number of instrument values grows with the sample size. A key motivating example is estimating long-term causal effects in a new experiment with only short-term outcomes, using past experiments to instrument for the effect of short- on long-term outcomes. Here, the assignment to a past experiment serves as the instrument: we have many past experiments but only a limited number of units in each. Since the structural function is nonparametric but constrained by only finitely many moment restrictions, point identification typically fails. To address this, we consider linear functionals of the minimum-norm solution to the moment restrictions, which is always well-defined. As the number of instrument levels grows, these functionals define an approximating sequence to a target functional, replacing point identification with a weaker asymptotic notion suited to discrete instruments. Extending the Jackknife Instrumental Variable Estimator (JIVE) beyond the classical parametric setting, we propose npJIVE, a nonparametric estimator for solutions to linear inverse problems with many weak instruments. We construct automatic debiased machine learning estimators for linear functionals of both the structural function and its minimum-norm projection, and establish their efficiency in the many-weak-instruments regime. To do so, we develop a general semiparametric efficiency theory for regular estimators under weak identification and many-weak-instrument asymptotics.

stat.ME↗