arXiv subjects

Maurits Kaptein

Publications and source records attributed to Maurits Kaptein.

At least 19 recordsLinked to original sources

arXiv2026

Runtime Governance for AI Agents: Policies on Paths

AI agents -- systems that plan, reason, and act using large language models -- produce non-deterministic, path-dependent behavior that cannot be fully governed at design time, where with governed we mean striking the right balance between as high as possible successful task completion rate and the legal, data-breach, reputational and other costs associated with running agents. We argue that the execution path is the central object for effective runtime governance and formalize compliance policies as deterministic functions mapping agent identity, partial path, proposed next action, and organizational state to a policy violation probability. We show that prompt-level instructions (and "system prompts"), and static access control are special cases of this framework: the former shape the distribution over paths without actually evaluating them; the latter evaluates deterministic policies that ignore the path (i.e., these can only account for a specific subset of all possible paths). In our view, runtime evaluation is the general case, and it is necessary for any path-dependent policy. We develop the formal framework for analyzing AI agent governance, present concrete policy examples (inspired by the AI act), discuss a reference implementation, and identify open problems including risk calibration and the limits of enforced compliance.

cs.AI↗

arXiv2025

Incorporating structural uncertainty in causal decision making

Practitioners making decisions based on causal effects typically ignore structural uncertainty. We analyze when this uncertainty is consequential enough to warrant methodological solutions (Bayesian model averaging over competing causal structures). Focusing on bivariate relationships ($X \rightarrow Y$ vs. $X \leftarrow Y$), we establish that model averaging is beneficial when: (1) structural uncertainty is moderate to high, (2) causal effects differ substantially between structures, and (3) loss functions are sufficiently sensitive to the size of the causal effect. We prove optimality results of our suggested methodological solution under regularity conditions and demonstrate through simulations that modern causal discovery methods can provide, within limits, the necessary quantification. Our framework complements existing robust causal inference approaches by addressing a distinct source of uncertainty typically overlooked in practice.

cs.LG↗

arXiv2025

A Verifier Hierarchy

We investigate the trade-off between certificate length and verifier runtime. We prove a Verifier Trade-off Theorem showing that reducing the inherent verification time of a language from $f(n)$ to $g(n)$, where $f(n) \ge g(n)$, requires certificates of length at least $\Omega(\log(f(n) / g(n)))$. This theorem induces a natural hierarchy based on certificate complexity. We demonstrate its applicability to analyzing conjectured separations between complexity classes (e.g., $\np$ and $\exptime$) and to studying natural problems such as string periodicity and rotation detection. Additionally, we provide perspectives on the $\p$ vs. $\np$ problem by relating it to the existence of sub-linear certificates.

cs.LG↗

arXiv2024

Rethinking Knowledge Transfer in Learning Using Privileged Information

In supervised machine learning, privileged information (PI) is information that is unavailable at inference, but is accessible during training time. Research on learning using privileged information (LUPI) aims to transfer the knowledge captured in PI onto a model that can perform inference without PI. It seems that this extra bit of information ought to make the resulting model better. However, finding conclusive theoretical or empirical evidence that supports the ability to transfer knowledge using PI has been challenging. In this paper, we critically examine the assumptions underlying existing theoretical analyses and argue that there is little theoretical justification for when LUPI should work. We analyze LUPI methods and reveal that apparent improvements in empirical risk of existing research may not directly result from PI. Instead, these improvements often stem from dataset anomalies or modifications in model design misguidedly attributed to PI. Our experiments for a wide variety of application domains further demonstrate that state-of-the-art LUPI approaches fail to effectively transfer knowledge from PI. Thus, we advocate for practitioners to exercise caution when working with PI to avoid unintended inductive biases.

cs.LG↗

arXiv2024

Efficient Exploration in Average-Reward Constrained Reinforcement Learning: Achieving Near-Optimal Regret With Posterior Sampling

We present a new algorithm based on posterior sampling for learning in Constrained Markov Decision Processes (CMDP) in the infinite-horizon undiscounted setting. The algorithm achieves near-optimal regret bounds while being advantageous empirically compared to the existing algorithms. Our main theoretical result is a Bayesian regret bound for each cost component of $\tilde{O} (DS\sqrt{AT})$ for any communicating CMDP with $S$ states, $A$ actions, and diameter $D$. This regret bound matches the lower bound in order of time horizon $T$ and is the best-known regret bound for communicating CMDPs achieved by a computationally tractable algorithm. Empirical results show that our posterior sampling algorithm outperforms the existing algorithms for constrained reinforcement learning.

cs.LG↗

arXiv2023

Making accurate and interpretable treatment decisions for binary outcomes

Optimal treatment rules can improve health outcomes on average by assigning a treatment associated with the most desirable outcome to each individual. Due to an unknown data generation mechanism, it is appealing to use flexible models to estimate these rules. However, such models often lead to complex and uninterpretable rules. In this article, we introduce an approach aimed at estimating optimal treatment rules that have higher accuracy, higher value, and lower loss from the same simple model family. We use a flexible model to estimate the optimal treatment rules and a simple model to derive interpretable treatment rules. We provide an extensible definition of interpretability and present a method that - given a class of simple models - can be used to select a preferred model. We conduct a simulation study to evaluate the performance of our approach compared to treatment rules obtained by fitting the same simple model directly to observed data. The results show that our approach has lower average loss, higher average outcome, and greater power in identifying individuals who can benefit from the treatment. We apply our approach to derive treatment rules of adjuvant chemotherapy in colon cancer patients using cancer registry data. The results show that our approach has the potential to improve treatment decisions.

stat.ME↗

arXiv2023

Provably Efficient Exploration in Constrained Reinforcement Learning:Posterior Sampling Is All You Need

We present a new algorithm based on posterior sampling for learning in constrained Markov decision processes (CMDP) in the infinite-horizon undiscounted setting. The algorithm achieves near-optimal regret bounds while being advantageous empirically compared to the existing algorithms. Our main theoretical result is a Bayesian regret bound for each cost component of \tilde{O} (HS \sqrt{AT}) for any communicating CMDP with S states, A actions, and bound on the hitting time H. This regret bound matches the lower bound in order of time horizon T and is the best-known regret bound for communicating CMDPs in the infinite-horizon undiscounted setting. Empirical results show that, despite its simplicity, our posterior sampling algorithm outperforms the existing algorithms for constrained reinforcement learning.

cs.LG↗

arXiv2023

A novel framework extending cause-effect inference methods to multivariate causal discovery

We focus on the extension of bivariate causal learning methods into multivariate problem settings in a systematic manner via a novel framework. It is purposive to augment the scale to which bivariate causal discovery approaches can be applied since contrast to traditional causal discovery methods, bivariate methods render estimation in the form of a causal Directed Acyclic Graph (DAG) instead of its complete partial directed acyclic graphs (CPDAGs). To tackle the problem, an auxiliary framework is proposed in this work so that together with any bivariate causal inference method, one could identify and estimate causal structure over variables more than two from observational data. In particular, we propose a local graphical structure in causal graph that is identifiable by a given bivariate method, which could be iteratively exploited to discover the whole causal structure under certain assumptions. We show both theoretically and experimentally that the proposed framework can achieve sound results in causal learning problems.

stat.ME↗

arXiv2023

On efficient covariate adjustment selection in causal effect estimation

In order to achieve unbiased and efficient estimators of causal effects from observational data, covariate selection for confounding adjustment becomes an important task in causal inference. Despite recent advancements in graphical criterion for constructing valid and efficient adjustment sets, these methods often rely on assumptions that may not hold in practice. We examine the properties of existing graph-free covariate selection methods with respect to both validity and efficiency, highlighting the potential dangers of producing invalid adjustment sets when hidden variables are present. To address this issue, we propose a novel graph-free method, referred to as CMIO, adapted from Mixed Integer Optimization (MIO) with a set of causal constraints. Our results demonstrate that CMIO outperforms existing state-of-the-art methods and provides theoretically sound outputs. Furthermore, we present a revised version of CMIO capable of handling the scenario in the absence of causal sufficiency and graphical information, offering efficient and valid covariate adjustments for causal inference.

stat.ME↗

arXiv2022

Bayesian multilevel multivariate logistic regression for superiority decision-making under observable treatment heterogeneity

In medical, social, and behavioral research we often encounter datasets with a multilevel structure and multiple correlated dependent variables. These data are frequently collected from a study population that distinguishes several subpopulations with different (i.e., heterogeneous) effects of an intervention. Despite the frequent occurrence of such data, methods to analyze them are less common and researchers often resort to either ignoring the multilevel and/or heterogeneous structure, analyzing only a single dependent variable, or a combination of these. These analysis strategies are suboptimal: Ignoring multilevel structures inflates Type I error rates, while neglecting the multivariate or heterogeneous structure masks detailed insights. To analyze such data comprehensively, the current paper presents a novel Bayesian multilevel multivariate logistic regression model. The clustered structure of multilevel data is taken into account, such that posterior inferences can be made with accurate error rates. Further, the model shares information between different subpopulations in the estimation of average and conditional average multivariate treatment effects. To facilitate interpretation, multivariate logistic regression parameters are transformed to posterior success probabilities and differences between them. A numerical evaluation compared our framework to less comprehensive alternatives and highlighted the need to model the multilevel structure: Treatment comparisons based on the multilevel model had targeted Type I error rates, while single-level alternatives resulted in inflated Type I errors. Further, the multilevel model was more powerful than a single-level model when the number of clusters was higher. ...

stat.ME↗

arXiv2022

An Empirical Evaluation of Posterior Sampling for Constrained Reinforcement Learning

We study a posterior sampling approach to efficient exploration in constrained reinforcement learning. Alternatively to existing algorithms, we propose two simple algorithms that are more efficient statistically, simpler to implement and computationally cheaper. The first algorithm is based on a linear formulation of CMDP, and the second algorithm leverages the saddle-point formulation of CMDP. Our empirical results demonstrate that, despite its simplicity, posterior sampling achieves state-of-the-art performance and, in some cases, significantly outperforms optimistic algorithms.

cs.LG↗

arXiv2022

The Impact of Batch Learning in Stochastic Linear Bandits

We consider a special case of bandit problems, named batched bandits, in which an agent observes batches of responses over a certain time period. Unlike previous work, we consider a more practically relevant batch-centric scenario of batch learning. That is to say, we provide a policy-agnostic regret analysis and demonstrate upper and lower bounds for the regret of a candidate policy. Our main theoretical results show that the impact of batch learning is a multiplicative factor of batch size relative to the regret of online behavior. Primarily, we study two settings of the stochastic linear bandits: bandits with finitely and infinitely many arms. While the regret bounds are the same for both settings, the former setting results hold under milder assumptions. Also, we provide a more robust result for the 2-armed bandit problem as an important insight. Finally, we demonstrate the consistency of theoretical results by conducting empirical experiments and reflect on optimal batch size choice.

cs.LG↗

arXiv2022

Bayesian multivariate logistic regression for superiority and inferiority decision-making under observable treatment heterogeneity

The effects of treatments may differ between persons with different characteristics. Addressing such treatment heterogeneity is crucial to investigate whether patients with specific characteristics are likely to benefit from a new treatment. The current paper presents a novel Bayesian method for superiority decision-making in the context of randomized controlled trials with multivariate binary responses and heterogeneous treatment effects. The framework is based on three elements: a) Bayesian multivariate logistic regression analysis with a P\'olya-Gamma expansion; b) a transformation procedure to transfer obtained regression coefficients to a more intuitive multivariate probability scale (i.e., success probabilities and the differences between them); and c) a compatible decision procedure for treatment comparison with prespecified decision error rates. Procedures for a priori sample size estimation under a non-informative prior distribution are included. A numerical evaluation demonstrated that decisions based on a priori sample size estimation resulted in anticipated error rates among the trial population as well as subpopulations. Further, average and conditional treatment effect parameters could be estimated unbiasedly when the sample was large enough. Illustration with the International Stroke Trial dataset revealed a trend towards heterogeneous effects among stroke patients: Something that would have remained undetected when analyses were limited to average treatment effects.

stat.ME↗

arXiv2021

The Impact of Batch Learning in Stochastic Bandits

We consider a special case of bandit problems, namely batched bandits. Motivated by natural restrictions of recommender systems and e-commerce platforms, we assume that a learning agent observes responses batched in groups over a certain time period. Unlike previous work, we consider a more practically relevant batch-centric scenario of batch learning. We provide a policy-agnostic regret analysis and demonstrate upper and lower bounds for the regret of a candidate policy. Our main theoretical results show that the impact of batch learning can be measured in terms of online behavior. Finally, we demonstrate the consistency of theoretical results by conducting empirical experiments and reflect on the optimal batch size choice.

cs.LG↗

arXiv2020

Continuous-Time Birth-Death MCMC for Bayesian Regression Tree Models

Decision trees are flexible models that are well suited for many statistical regression problems. In a Bayesian framework for regression trees, Markov Chain Monte Carlo (MCMC) search algorithms are required to generate samples of tree models according to their posterior probabilities. The critical component of such an MCMC algorithm is to construct good Metropolis-Hastings steps for updating the tree topology. However, such algorithms frequently suffering from local mode stickiness and poor mixing. As a result, the algorithms are slow to converge. Hitherto, authors have primarily used discrete-time birth/death mechanisms for Bayesian (sums of) regression tree models to explore the model space. These algorithms are efficient only if the acceptance rate is high which is not always the case. Here we overcome this issue by developing a new search algorithm which is based on a continuous-time birth-death Markov process. This search algorithm explores the model space by jumping between parameter spaces corresponding to different tree structures. In the proposed algorithm, the moves between models are always accepted which can dramatically improve the convergence and mixing properties of the MCMC algorithm. We provide theoretical support of the algorithm for Bayesian regression tree models and demonstrate its performance.

stat.ML↗

arXiv2020

contextual: Evaluating Contextual Multi-Armed Bandit Problems in R

Over the past decade, contextual bandit algorithms have been gaining in popularity due to their effectiveness and flexibility in solving sequential decision problems---from online advertising and finance to clinical trial design and personalized medicine. At the same time, there are, as of yet, surprisingly few options that enable researchers and practitioners to simulate and compare the wealth of new and existing bandit algorithms in a standardized way. To help close this gap between analytical research and empirical evaluation the current paper introduces the object-oriented R package "contextual": a user-friendly and, through its object-oriented structure, easily extensible framework that facilitates parallelized comparison of contextual and context-free bandit policies through both simulation and offline analysis.

cs.LG↗

arXiv2019

Exploring Offline Policy Evaluation for the Continuous-Armed Bandit Problem

The (contextual) multi-armed bandit problem (MAB) provides a formalization of sequential decision-making which has many applications. However, validly evaluating MAB policies is challenging; we either resort to simulations which inherently include debatable assumptions, or we resort to expensive field trials. Recently an offline evaluation method has been suggested that is based on empirical data, thus relaxing the assumptions, and can be used to evaluate multiple competing policies in parallel. This method is however not directly suited for the continuous armed (CAB) problem; an often encountered version of the MAB problem in which the action set is continuous instead of discrete. We propose and evaluate an extension of the existing method such that it can be used to evaluate CAB policies. We empirically demonstrate that our method provides a relatively consistent ranking of policies. Furthermore, we detail how our method can be used to select policies in a real-life CAB problem.

cs.LG↗

arXiv2018

StreamingBandit; Experimenting with Bandit Policies

A large number of statistical decision problems in the social sciences and beyond can be framed as a (contextual) multi-armed bandit problem. However, it is notoriously hard to develop and evaluate policies that tackle these types of problem, and to use such policies in applied studies. To address this issue, this paper introduces StreamingBandit, a Python web application for developing and testing bandit policies in field studies. StreamingBandit can sequentially select treatments using (online) policies in real time. Once StreamingBandit is implemented in an applied context, different policies can be tested, altered, nested, and compared. StreamingBandit makes it easy to apply a multitude of bandit policies for sequential allocation in field experiments, and allows for the quick development and re-use of novel policies. In this article, we detail the implementation logic of StreamingBandit and provide several examples of its use.

cs.HC↗