Tootfinder

Scenario-based Decision-making Using Game Theory for Interactive Autonomous Driving: A Survey
Zhihao Lin, Zhen Tian
https://arxiv.org/abs/2509.05777 https://

Scenario-based Decision-making Using Game Theory for Interactive Autonomous Driving: A Survey
Game-based interactive driving simulations have emerged as versatile platforms for advancing decision-making algorithms in road transport mobility. While these environments offer safe, scalable, and engaging settings for testing driving strategies, ensuring both realism and robust performance amid dynamic and diverse scenarios remains a significant challenge. Recently, the integration of game-based techniques with advanced learning frameworks has enabled the development of adaptive decision-mak…

A Review On Safe Reinforcement Learning Using Lyapunov and Barrier Functions
Dhruv S. Kushwaha, Zoleikha A. Biron
https://arxiv.org/abs/2508.09128 https://…

A Review On Safe Reinforcement Learning Using Lyapunov and Barrier Functions
Reinforcement learning (RL) has proven to be particularly effective in solving complex decision-making problems for a wide range of applications. From a control theory perspective, RL can be considered as an adaptive optimal control scheme. Lyapunov and barrier functions are the most commonly used certificates to guarantee system stability for a proposed/derived controller and constraint satisfaction guarantees, respectively, in control theoretic approaches. However, compared to theoretical gua…

Procedural Mixture Sets
Hendrik Rommeswinkel
https://arxiv.org/abs/2508.07588 https://arxiv.org/pdf/2508.07588

Procedural Mixture Sets
The paper characterizes the Shannon (1948) and Tsallis (1988) entropies in a standard framework of decision theory, mixture sets. Procedural mixture sets are introduced as a variant of mixture sets in which it is not necessarily true that a mixture of two identical elements yields the same element. This allows the process of mixing itself to have an intrinsic value. The paper proves the surprising result that simply imposing the standard axioms of von Neumann-Morgenstern on preferences on a pro…

Decision Theoretic Subgroup Detection With Bayesian Machine Learning
Entejar Alam, Poorbita Kundu, Antonio R. Linero
https://arxiv.org/abs/2509.05832 https://

Decision Theoretic Subgroup Detection With Bayesian Machine Learning
We consider the problem of identifying promising subpopulations in terms of treatment effectiveness or treatment effect heterogeneity, from a Bayesian decision theoretic perspective. We first show that a straight-forward application of Bayesian decision theory to subgroup detection leads to a counter-intuitive risk-seeking (RS) behavior. Motivated by this observation, we introduce the Bayesian Risk-Aware Inference and Detection of Subgroups (BRAIDS) utility and use it to perform subgroup select…

AI Darwin Awards
Honouring Those Who Asked "Can We?" Without Ever Asking "Should We?"
Named after Charles Darwin's theory of natural selection, the original Darwin Awards celebrated those who "improved the gene pool by removing themselves from it" through spectacularly stupid acts. Well, guess what? Humans have evolved! We're now so advanced that we've outsourced our poor decision-making to machines. […]
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AI Darwin Awards 2025 - Celebrating Spectacularly Bad AI Decisions
Honouring those who use artificial intelligence in spectacularly reckless ways. Submit nominations for the most catastrophically ill-advised AI deployments of 2025.

Replaced article(s) found for cs.FL. https://arxiv.org/list/cs.FL/new
[1/1]:
- Decision Procedure for A Theory of String Sequences
Denghang Hu, Taolue Chen, Philipp R\"ummer, Fu Song, Zhilin Wu

Collaboration and Conflict between Humans and Language Models through the Lens of Game Theory
Mukul Singh, Arjun Radhakrishna, Sumit Gulwani
https://arxiv.org/abs/2509.04847 htt…

Collaboration and Conflict between Humans and Language Models through the Lens of Game Theory
Language models are increasingly deployed in interactive online environments, from personal chat assistants to domain-specific agents, raising questions about their cooperative and competitive behavior in multi-party settings. While prior work has examined language model decision-making in isolated or short-term game-theoretic contexts, these studies often neglect long-horizon interactions, human-model collaboration, and the evolution of behavioral patterns over time. In this paper, we investig…

Replaced article(s) found for cs.PL. https://arxiv.org/list/cs.PL/new
[1/1]:
- Decision Procedure for A Theory of String Sequences
Denghang Hu, Taolue Chen, Philipp R\"ummer, Fu Song, Zhilin Wu

Using causal abstractions to accelerate decision-making in complex bandit problems
Joel Dyer, Nicholas Bishop, Anisoara Calinescu, Michael Wooldridge, Fabio Massimo Zennaro
https://arxiv.org/abs/2509.04296

Using causal abstractions to accelerate decision-making in complex bandit problems
Although real-world decision-making problems can often be encoded as causal multi-armed bandits (CMABs) at different levels of abstraction, a general methodology exploiting the information and computational advantages of each abstraction level is missing. In this paper, we propose AT-UCB, an algorithm which efficiently exploits shared information between CMAB problem instances defined at different levels of abstraction. More specifically, AT-UCB leverages causal abstraction (CA) theory to explo…

Causality and Decision-making: A Logical Framework for Systems and Security Modelling
Pinaki Chakraborty, Tristan Caulfield, David Pym
https://arxiv.org/abs/2508.01758 https://

Causality and Decision-making: A Logical Framework for Systems and Security Modelling
Causal reasoning is essential for understanding decision-making about the behaviour of complex `ecosystems' of systems that underpin modern society, with security -- including issues around correctness, safety, resilience, etc. -- typically providing critical examples. We present a theory of strategic reasoning about system modelling based on minimal structural assumptions and employing the methods of transition systems, supported by a modal logic of system states in the tradition of van Benthe…

Breaking New Ground in Software Defect Prediction: Introducing Practical and Actionable Metrics with Superior Predictive Power for Enhanced Decision-Making
Carlos Andr\'es Ram\'irez Cata\~no, Makoto Itoh
https://arxiv.org/abs/2508.04408

Breaking New Ground in Software Defect Prediction: Introducing Practical and Actionable Metrics with Superior Predictive Power for Enhanced Decision-Making
Software defect prediction using code metrics has been extensively researched over the past five decades. However, prediction harnessing non-software metrics is under-researched. Considering that the root cause of software defects is often attributed to human error, human factors theory might offer key forecasting metrics for actionable insights. This paper explores automated software defect prediction at the method level based on the developers' coding habits. First, we propose a framework for…

Downside Risk-Aware Equilibria for Strategic Decision-Making
Oliver Slumbers, Benjamin Patrick Evans, Sumitra Ganesh, Leo Ardon
https://arxiv.org/abs/2510.03446 https://

Downside Risk-Aware Equilibria for Strategic Decision-Making
Game theory has traditionally had a relatively limited view of risk based on how a player's expected reward is impacted by the uncertainty of the actions of other players. Recently, a new game-theoretic approach provides a more holistic view of risk also considering the reward-variance. However, these variance-based approaches measure variance of the reward on both the upside and downside. In many domains, such as finance, downside risk only is of key importance, as this represents the potentia…

Global Optimality in Multi-Flyby Asteroid Trajectory Optimization: Theory and Application Techniques
Zhong Zhang, Xiang Guo, Di Wu, Hexi Baoyin, Junfeng Li, Francesco Topputo
https://arxiv.org/abs/2508.02904

Global Optimality in Multi-Flyby Asteroid Trajectory Optimization: Theory and Application Techniques
Designing optimal trajectories for multi-flyby asteroid missions is scientifically critical but technically challenging due to nonlinear dynamics, intermediate constraints, and numerous local optima. This paper establishes a method that approaches global optimality for multi-flyby trajectory optimization under a given sequence. The original optimal control problem with interior-point equality constraints is transformed into a multi-stage decision formulation. This reformulation enables direct a…

Decision Procedure for A Theory of String Sequences
Denghang Hu, Taolue Chen, Philipp R\"ummer, Fu Song, Zhilin Wu
https://arxiv.org/abs/2509.00948 https://

Decision Procedure for A Theory of String Sequences
The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation, forming sub-sequences and updating elements. Strings and sequences are intimately related; many operations, e.g., matching a string according to a regular expression, splitting strings, or joining strings in a sequence, are frequently used in string-manipulat…

Decision Theory For Large Scale Outlier Detection Using Aleatoric Uncertainty: With a Note on Bayesian FDR
Ryan Warnick
https://arxiv.org/abs/2508.01988 https://

Decision Theory For Large Scale Outlier Detection Using Aleatoric Uncertainty: With a Note on Bayesian FDR
Aleatoric and Epistemic uncertainty have achieved recent attention in the literature as different sources from which uncertainty can emerge in stochastic modeling. Epistemic being intrinsic or model based notions of uncertainty, and aleatoric being the uncertainty inherent in the data. We propose a novel decision theoretic framework for outlier detection in the context of aleatoric uncertainty; in the context of Bayesian modeling. The model incorporates bayesian false discovery rate control for…

Covariate balance under Bayesian decision theory
Andr\'e A. F. Fumis, Victor Fossaluza, Rafael B. Stern
https://arxiv.org/abs/2509.01828 https://arxiv.…

Covariate balance under Bayesian decision theory
We study optimal sample allocation between treatment and control groups under Bayesian linear models. We derive an analytic expression for the Bayes risk, which depends jointly on sample size and covariate mean balance across groups. Under a flat conditional prior, the covariate mean balance term simplifies to the Mahalanobis distance. Our results reveal that the optimal allocation does not always correspond to equal sample sizes, and we provide sufficient conditions under which equal allocatio…

Foundational theory for optimal decision tree problems. II. Optimal hypersurface decision tree algorithm
Xi He
https://arxiv.org/abs/2509.12057 https://arx…

Foundational theory for optimal decision tree problems. II. Optimal hypersurface decision tree algorithm
Decision trees are a ubiquitous model for classification and regression tasks due to their interpretability and efficiency. However, solving the optimal decision tree (ODT) problem remains a challenging combinatorial optimization task. Even for the simplest splitting rules--axis-parallel hyperplanes--it is NP-hard to optimize. In Part I of this series, we rigorously defined the proper decision tree model through four axioms and, based on these, introduced four formal definitions of the ODT prob…

The Geodesics Less Traveled: Nonminimal RT Surfaces and Holographic Scattering
Jacqueline Caminiti, Caroline Lima, Robert C. Myers
https://arxiv.org/abs/2509.03597 https://

The Geodesics Less Traveled: Nonminimal RT Surfaces and Holographic Scattering
The connected wedge theorem states that in order to have a scattering process in the bulk, it is necessary to have O(1/G) mutual information between certain "decision" regions in the boundary theory. While this large mutual information is not generally sufficient to imply scattering, Caminiti et al. (2024) showed that for a certain class of geometries, bulk scattering is implied by a certain relation between two (possibly non-minimal) Ryu-Takayanagi surfaces. Here, we show that the 2-to-2 versi…

Extreme Value Theory-enhanced Radio Maps for Handovers in Ultra-reliable Communications
Dian Echevarr\'ia P\'erez, Onel L. Alcaraz L\'opez, Hirley Alves
https://arxiv.org/abs/2509.22547

Extreme Value Theory-enhanced Radio Maps for Handovers in Ultra-reliable Communications
Efficient handover (HO) strategies are essential for maintaining the stringent performance requirements of ultra-reliable communication (URC) systems. This work introduces a novel HO framework designed from a physical-layer perspective, where the decision-making process focuses on determining the optimal time and location for performing HOs. Leveraging extreme value theory (EVT) and statistical radio maps, the proposed method predicts signal behaviour and enables efficient resource allocation. …

A Category Theoretic Approach to Approximate Game Theory
Neil Ghani (MSP Group, University of Strathclyde)
https://arxiv.org/abs/2509.20932 https://arxiv.o…

A Category Theoretic Approach to Approximate Game Theory
This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal decision is in a given scenario. Thus approximate game theory asks what is an approximately optimal decision in a given scenario. This is important in practice as -- just like in much of computing -- exact answers maybe too difficult to compute or even impossible …

Theory-informed neural networks for particle physics
Barry M. Dillon, Michael Spannowsky
https://arxiv.org/abs/2507.13447 https://arx…

Theory-informed neural networks for particle physics
We present a theory-informed reinforcement-learning framework that recasts the combinatorial assignment of final-state particles in hadron collider events as a Markov decision process. A transformer-based Deep Q-Network, rewarded at each step by the logarithmic change in the tree-level matrix element, learns to map final-state particles to partons. Because the reward derives solely from first-principles theory, the resulting policy is label-free and fully interpretable, allowing every reconstru…

Verification Cost Asymmetry in Cognitive Warfare: A Complexity-Theoretic Framework
Joshua Luberisse
https://arxiv.org/abs/2507.21258 https://arxiv.org/pdf/…

Verification Cost Asymmetry in Cognitive Warfare: A Complexity-Theoretic Framework
Human verification under adversarial information flow operates as a cost-bounded decision procedure constrained by working memory limits and cognitive biases. We introduce the Verification Cost Asymmetry (VCA) coefficient, formalizing it as the ratio of expected verification work between populations under identical claim distributions. Drawing on probabilistically checkable proofs (PCP) and parameterized complexity theory, we construct dissemination protocols that reduce verification for truste…

Secondary Bounded Rationality: A Theory of How Algorithms Reproduce Structural Inequality in AI Hiring
Jia Xiao
https://arxiv.org/abs/2507.09233 https://…

Secondary Bounded Rationality: A Theory of How Algorithms Reproduce Structural Inequality in AI Hiring
AI-driven recruitment systems, while promising efficiency and objectivity, often perpetuate systemic inequalities by encoding cultural and social capital disparities into algorithmic decision making. This article develops and defends a novel theory of secondary bounded rationality, arguing that AI systems, despite their computational power, inherit and amplify human cognitive and structural biases through technical and sociopolitical constraints. Analyzing multimodal recruitment frameworks, we …

Leaf it to renewal: Improved predictive maintenance policies via renewal theory and decision trees
Daniel Koutas, Daniel Straub
https://arxiv.org/abs/2509.20145 https://

Leaf it to renewal: Improved predictive maintenance policies via renewal theory and decision trees
We propose a general method for deriving prognostics-based predictive maintenance policies. The method takes into account the available decision options at hand, the information on the future state of the system provided by a prognostic model, as well as the costs of the underlying renewal-reward process. It results in heuristic policies with only a few parameters, which can be determined based on theoretical considerations or by optimization from run-to-failure data. We show the potential of t…

Dynamical Systems Perspective for a Real-Time Response to a Marine Oil Spill
V. J. Garcia-Garrido, A. Ramos, A. M. Mancho, J. Coca, S. Wiggins
https://arxiv.org/abs/2509.01615 h…

Dynamical Systems Perspective for a Real-Time Response to a Marine Oil Spill
This paper discusses the combined use of tools from dynamical systems theory and remote sensing techniques and shows how they are effective instruments which may greatly contribute to the decision making protocols of the emergency services for the real-time management of oil spills. This work presents the successful interplay of these techniques for a recent situation, the sinking of the Oleg Naydenov fishing ship that took place in Spain, close to the Canary Islands, in April 2015.

Geometric Theory of Ising Machines
Andrew G. Moore, Zachary Richey, Isaac K. Martin
https://arxiv.org/abs/2507.12626 https://arxiv.or…

Geometric Theory of Ising Machines
We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a physical system allows efficient and distributed computation, but the design of the energy function is a difficult puzzle. We introduce a diagrammatic device that allows us to visualize the decision boundaries for Ising circuits. It is then used to prove two results…

Encoding and Reasoning About Arrays in Set Theory
Maximiliano Cristi\'a, Gianfranco Rossi
https://arxiv.org/abs/2508.11447 https://arxiv.org/pdf/2508.1…

Encoding and Reasoning About Arrays in Set Theory
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is used to give the specifications of a non-trivial class of programs with arrays. In this way, array reasoning becomes set reasoning. Furthermore, a decision procedure for this fragment is also provided and implemented as part of the {log} (read 'setlog') tool. {…

Transient-Stability-Aware Frequency Provision in IBR-Rich Grids via Information Gap Decision Theory and Deep Learning
Amin Masoumi, Mert Korkali
https://arxiv.org/abs/2507.13265

Transient-Stability-Aware Frequency Provision in IBR-Rich Grids via Information Gap Decision Theory and Deep Learning
This paper introduces a framework to address the critical loss of transient stability caused by reduced inertia in grids with high inverter-based resource (IBR) penetration. The proposed method integrates a predictive deep learning (DL) model with information gap decision theory (IGDT) to create a risk-averse dispatch strategy. By reformulating the conventional virtual inertia scheduling (VIS) problem, the framework uses early predictions of post-fault dynamics to proactively redispatch resourc…

Confirmation Bias as a Cognitive Resource in LLM-Supported Deliberation
Sander de Jong, Rune M{\o}berg Jacobsen, Niels van Berkel
https://arxiv.org/abs/2509.14824 https://

Confirmation Bias as a Cognitive Resource in LLM-Supported Deliberation
Large language models (LLMs) are increasingly used in group decision-making, but their influence risks fostering conformity and reducing epistemic vigilance. Drawing on the Argumentative Theory of Reasoning, we argue that confirmation bias, often seen as detrimental, can be harnessed as a resource when paired with critical evaluation. We propose a three-step process in which individuals first generate ideas independently, then use LLMs to refine and articulate them, and finally engage with LLMs…

Quantum-like representation of neuronal networks' activity: modeling "mental entanglement"
Andrei Khrennikov, Makiko Yamada
https://arxiv.org/abs/2509.16253 https:…

Quantum-like representation of neuronal networks' activity: modeling "mental entanglement"
Quantum-like modeling (QLM) - quantum theory applications outside of physics - are intensively developed with applications in biology, cognition, psychology, and decision-making. For cognition, QLM should be distinguished from quantum reductionist models in the spirit of Hameroff and Penrose and well as Umezawa and Vitiello. QLM is not concerned with just quantum physical processes in the brain but also QL information processing by macroscopic neuronal structures. Although QLM of cognition and …

Uncertainty Quantification for Regression using Proper Scoring Rules
Alexander Fishkov, Kajetan Schweighofer, Mykyta Ielanskyi, Nikita Kotelevskii, Mohsen Guizani, Maxim Panov
https://arxiv.org/abs/2509.26610

Uncertainty Quantification for Regression using Proper Scoring Rules
Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a firm basis of learning with proper scoring rules. However, these advances were focused on classification, while extending these ideas to regression remains challenging. In this work, we introduce a unified UQ framework for regression based on proper scoring r…

A Characterization Framework for Stable Sets and Their Variants
Athanasios Andrikopoulos, Nikolaos Sampanis
https://arxiv.org/abs/2508.09798 https://arxiv.…

A Characterization Framework for Stable Sets and Their Variants
The theory of optimal choice sets offers a well-established solution framework in social choice and game theory. In social choice theory, decision-making is typically modeled as a maximization problem. However, when preferences are cyclic -- as can occur in economic processes -- the set of maximal elements may be empty, raising the key question of what should be considered a valid choice. To address this issue, several approaches -- collectively known as general solution theories -- have been p…

Distance Between Stochastic Linear Systems
Venkatraman Renganathan, Sei Zhen Khong
https://arxiv.org/abs/2509.04014 https://arxiv.org/pdf/2509.04014…

Distance Between Stochastic Linear Systems
This manuscript proposes a distance measure between stochastic linear dynamical systems. While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the field. As a first step, a distance measure between two linear time invariant stochastic dynamical systems is proposed here, extending the existing distance metrics betwee…

Research on Conversational Recommender System Considering Consumer Types
Yaying Luo, Hui Fang, Zhu Sun
https://arxiv.org/abs/2508.13209 https://arxiv.org/p…

Research on Conversational Recommender System Considering Consumer Types
Conversational Recommender Systems (CRS) provide personalized services through multi-turn interactions, yet most existing methods overlook users' heterogeneous decision-making styles and knowledge levels, which constrains both accuracy and efficiency. To address this gap, we propose CT-CRS (Consumer Type-Enhanced Conversational Recommender System), a framework that integrates consumer type modeling into dialogue recommendation. Based on consumer type theory, we define four user categories--depe…

A Decision Procedure for Probabilistic Kleene Algebra with Angelic Nondeterminism
Shawn Ong, Dexter Kozen
https://arxiv.org/abs/2507.10980 https://

A Decision Procedure for Probabilistic Kleene Algebra with Angelic Nondeterminism
We give a decision procedure and proof of correctness for the equational theory of probabilistic Kleene algebra with angelic nondeterminism introduced in Ong, Ma, and Kozen (2025).

Evaluating the Infinite
Toby Ord
https://arxiv.org/abs/2509.19389 https://arxiv.org/pdf/2509.19389

Evaluating the Infinite
I present a novel mathematical technique for dealing with the infinities arising from divergent sums and integrals. It assigns them fine-grained infinite values from the set of hyperreal numbers in a manner that refines the standard theories of summation and integration. This has implications in statistics (helping us work with distributions whose mean or variance is infinite), decision theory (allowing comparison of options with infinite expected values), economics (allowing evaluation of infi…

RoboSeek: You Need to Interact with Your Objects
Yibo Peng, Jiahao Yang, Shenhao Yan, Ziyu Huang, Shuang Li, Shuguang Cui, Yiming Zhao, Yatong Han
https://arxiv.org/abs/2509.17783

RoboSeek: You Need to Interact with Your Objects
Optimizing and refining action execution through exploration and interaction is a promising way for robotic manipulation. However, practical approaches to interaction driven robotic learning are still underexplored, particularly for long-horizon tasks where sequential decision-making, physical constraints, and perceptual uncertainties pose significant chal lenges. Motivated by embodied cognition theory, we propose RoboSeek, a framework for embodied action execution that leverages in…

A decision-theoretic framework for uncertainty quantification in epidemiological modelling
Nicholas Steyn, Freddie Bickford Smith, Cathal Mills, Vik Shirvaikar, Christl A Donnelly, Kris V Parag
https://arxiv.org/abs/2509.20013

A decision-theoretic framework for uncertainty quantification in epidemiological modelling
Estimating, understanding, and communicating uncertainty is fundamental to statistical epidemiology, where model-based estimates regularly inform real-world decisions. However, sources of uncertainty are rarely formalised, and existing classifications are often defined inconsistently. This lack of structure hampers interpretation, model comparison, and targeted data collection. Connecting ideas from machine learning, information theory, experimental design, and health economics, we present a fi…

Probabilistic Graphical Models: A Concise Tutorial
Jacqueline Maasch, Willie Neiswanger, Stefano Ermon, Volodymyr Kuleshov
https://arxiv.org/abs/2507.17116

Probabilistic Graphical Models: A Concise Tutorial
Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant body of theory that bridges two mathematical traditions: probability and graph theory. This framework provides compact yet expressive representations of joint probability distributions, yielding powerful generative models for probabilistic reasoning. This tut…

Trust Region Algorithm for Stochastic Minimax Problems with Decision-Dependent Distributions
Yan Gao, Yongchao Liu, Zili Luo
https://arxiv.org/abs/2509.12868 https://

Trust Region Algorithm for Stochastic Minimax Problems with Decision-Dependent Distributions
Stochastic minimax optimization has drawn much attention over the past decade due to its broad applications in machine learning, signal processing and game theory. In some applications, the probability distribution of uncertainty depends on decision variables, as the environment may respond to decisions. In this paper, we propose a trust region algorithm for finding the stationary points of stochastic minimax problems with decision-dependent distributions. At each iteration, the algorithm local…

Unified Field-integral Thermodynamics of Bose Mixtures: Stability and Critical Behavior
Yuan-Hong Chen, Renyuan Liao
https://arxiv.org/abs/2508.11263 https://

Unified Field-integral Thermodynamics of Bose Mixtures: Stability and Critical Behavior
We establish a unified thermodynamic framework for Bose mixtures at finite temperatures based on the functional field integral, within which the decision on whether to discard the anomalous densities, when determining the density configuration and stability matrix, yields distinct theories. Beyond the existing Hartree-Fock approximation and Ota-Giorgini-Stringari theory, retaining the anomalous densities throughout will provide a completely self-consistent thermodynamic description, requiring t…

Co-Investment with Payoff-Sharing Mechanism for Cooperative Decision-Making in Network Design Games
Mingjia He, Andrea Censi, Emilio Frazzoli, Gioele Zardini
https://arxiv.org/abs/2508.12059

Co-Investment with Payoff-Sharing Mechanism for Cooperative Decision-Making in Network Design Games
Network-based systems are inherently interconnected, with the design and performance of subnetworks being interdependent. However, the decisions of self-interested operators may lead to suboptimal outcomes for users and the overall system. This paper explores cooperative mechanisms that can simultaneously benefit both operators and users. We address this challenge using a game-theoretical framework that integrates both non-cooperative and cooperative game theory. In the non-cooperative stage, w…

Bellman Optimality of Average-Reward Robust Markov Decision Processes with a Constant Gain
Shengbo Wang, Nian Si
https://arxiv.org/abs/2509.14203 https://a…

Bellman Optimality of Average-Reward Robust Markov Decision Processes with a Constant Gain
Learning and optimal control under robust Markov decision processes (MDPs) have received increasing attention, yet most existing theory, algorithms, and applications focus on finite-horizon or discounted models. The average-reward formulation, while natural in many operations research and management contexts, remains underexplored. This is primarily because the dynamic programming foundations are technically challenging and only partially understood, with several fundamental questions remaining…

Minmax Exclusivity Classes for Power-Type Loss Functions
Stanis{\l}aw M. S. Halkiewicz
https://arxiv.org/abs/2507.12447 https://arxiv…

Minmax Exclusivity Classes for Power-Type Loss Functions
In statistical decision theory, the choice of loss function fundamentally shapes which estimators qualify as optimal. This paper introduces and develops the general concept of exclusivity classes of loss functions: subsets of loss functions such that no estimator can be optimal (according to a specified notion) for losses lying in different classes. We focus on the case of minmax optimality and define minmax exclusivity classes, demonstrating that the classical family of power-type loss functio…

Coarse Addition and the St. Petersburg Paradox: A Heuristic Perspective
Takashi Izumo
https://arxiv.org/abs/2507.12475 https://arxiv.…

Coarse Addition and the St. Petersburg Paradox: A Heuristic Perspective
The St. Petersburg paradox presents a longstanding challenge in decision theory. It describes a game whose expected value is infinite, yet for which no rational finite stake can be determined. Traditional solutions introduce auxiliary assumptions, such as diminishing marginal utility, temporal discounting, or extended number systems. These methods often involve mathematical refinements that may not correspond to how people actually perceive or process numerical information. This paper explores …

Informative Post-Hoc Explanations Only Exist for Simple Functions
Eric G\"unther, Bal\'azs Szabados, Robi Bhattacharjee, Sebastian Bordt, Ulrike von Luxburg
https://arxiv.org/abs/2508.11441

Informative Post-Hoc Explanations Only Exist for Simple Functions
Many researchers have suggested that local post-hoc explanation algorithms can be used to gain insights into the behavior of complex machine learning models. However, theoretical guarantees about such algorithms only exist for simple decision functions, and it is unclear whether and under which assumptions similar results might exist for complex models. In this paper, we introduce a general, learning-theory-based framework for what it means for an explanation to provide information about a deci…

Distributed Functional Optimization and Learning on Banach Spaces: Generic Frameworks
Zhan Yu, Zhongjie Shi, Deming Yuan, Daniel W. C. Ho
https://arxiv.org/abs/2509.17554 https:…

Distributed Functional Optimization and Learning on Banach Spaces: Generic Frameworks
In this paper, we establish a distributed functional optimization (DFO) theory based on time-varying multi-agent networks. The vast majority of existing distributed optimization theories are developed based on Euclidean decision variables. However, for many scenarios in machine learning and statistical learning, such as reproducing kernel spaces or probability measure spaces that use functions or probability measures as fundamental variables, the development of existing distributed optimization…