Background: Counterexample-Guided Abstraction Refinement (CEGAR) is a prominent technique to generate Cartesian abstractions for guiding search in cost-optimal planning. The core idea is to start from the trivial abstraction—an abstract state representing all concrete states—and iteratively refine it in a loop by splitting one abstract state into two. Each iteration of the loop searches an optimal abstract plan and replicates it into the concrete state space until finding a flaw—and splitting such abstract state—or returning a plan for the task if no flaw is found. Previous work finds only a single flaw in progression, by executing the abstract plan from the initial state and stopping when execution cannot be continued. Objectives: A theoretical framework for identifying different flaws of abstract plans, analysing their properties and using them to refine abstractions in different ways leading to higher-quality heuristics. Methods: We show that alternative types of flaw can be defined. Specifically, we search flaws in regression from the goals—resulting in higher heuristic values—and identify sequence flaws along the whole abstract plan by searching them in a Cartesian relaxation of the task after the first flaw, which greatly increases the flexibility of refinements in CEGAR. Results: Our experiments show that across existing benchmarks numerous sequence flaws exist in most abstract plans. We observe that the selected flaw has a high impact on the heuristic, and we propose several strategies that generate more informed abstractions. Overall, this greatly improves the performance of the baseline that only used the first progression flaw. Conclusions: Guiding the CEGAR process by analysing multiple flaws of an abstract plan trace and selecting the best refinement can improve its performance as a tool to generate admissible heuristics in planning. Thus, using our new types of flaw and flaw selection strategies, we get stronger heuristics than the state-of-the-art planners based on Cartesian abstractions.
Gaussian process (GP) regression with a single global GP (GP-glo) incurs cubic computational cost, limiting scalability to large datasets. Product-of-experts GP models (GP-pro), which combine local GP models to capture global correlations, alleviate this computational burden. However, training local experts on disjoint data subsets can lead to overestimated posterior variances. We propose GP-pro-c, a product-of-experts GP model that calibrates these variances using an information-based method. The method exploits the monotonicity and submodularity of information gain in GPs to define a calibration ratio that reduces the posterior variance of individual local GP models. We evaluate GP-pro-c using negative log-likelihood (NLL), root mean squared error (RMSE), and expected normalised calibration error (ENCE). Experiments on four synthetic functions and six regression datasets show that GP-pro-c achieves average reductions of 2.3
Background: In declarative constraint solving, a user formulates a constraint model in terms of variables and constraints, and uses a generic, off-the-shelf solver to solve the problem. Constraint Programming (CP) is one such constraint-solving paradigm, which has a wide support for many types of constraints, including global constraints. Global constraints capture complex relations between several decision variables, and CP solvers have specialized propagators to solve them efficiently. Objectives: While CP solvers support a wide range of global constraints, few solvers support them in a reified or even halfreified context. Hence, for most CP solvers, reified global constraints must be decomposed into non-global constraints. This bypasses the global constraint propagator, which can considerably slow the solving process, suppressing one of the key benefits of modeling with global constraints: a faster solve-time. This is a problem for generic CP-modeling, as reified constraints are often introduced by the modeling system during translation and flattening of compound constraints. Additionally, half-reified global constraints are also used extensively in eXplainable Constraint Programming techniques (XCP). Therefore, XCP techniques suffer from scalability issues when global constraints occur in the model. In this paper, we aim to alleviate this bottleneck, allowing the use of the propagators of global constraints when modeling their half-reification, for all CP-solvers. Methods: We propose a set of reformulation rules that allow the use of half-reification of a global constraint with any CP solver that supports the “normal” global constraint propagator. This is achieved by introducing auxiliary variables for the decision variables in the global constraint and the use of a reified channeling constraint, which most CP solvers support. Additionally, we show how to reduce the overhead of these auxiliary variables, by limiting the number of variables introduced, and by fixing their value when unconstrained. Finally, we prove the propagation strength of our reformulation for a variety of global constraint families. Results: We experimentally evaluate the reformulations on a variety of global constraints and applications where reified constraints can occur. Our results show that this reformulation is much faster compared to decomposing the global constraint, and in some cases, even outperforms solver-level propagation routines for reified global constraints. Conclusions: Using the reformulations proposed in this paper, we make the use of reified global constraints easily available for any CP solver. Hence, we expand the range of available solvers and constraint models that can be used in XCP techniques or for solving CSPs with compound constraints.
Background: Large Language Model (LLM)-based systems, such as conversational agents, are usually designed with monolithic, static architectures that rely on a single, general-purpose LLM to handle all user queries. However, these systems may be inefficient as different queries may require different levels of reasoning, domain knowledge or pre-processing. While generalist LLMs (e.g. GPT-4o, Claude-Sonnet) perform well across a wide range of tasks, they may incur significant financial, energy and computational costs. These costs may be disproportionate for simpler queries, resulting in unnecessary resource utilisation. A routing mechanism can therefore be employed to route queries to more appropriate components, such as smaller or specialised models, thereby improving efficiency and optimising resource consumption. Objectives: This survey aims to provide a comprehensive overview of routing strategies in LLM-based systems. Specifically, it reviews when, why, and how routing should be integrated into LLM pipelines to improve efficiency, scalability, and performance. Methods: We structure the survey by defining the objectives to optimise, such as cost minimisation and performance maximisation; the timing of routing within the LLM workflow, whether it occurs before or after generation; and the various implementation strategies, including similarity-based, supervised, reinforcement learning-based, and generative methods. Practical considerations such as industrial applications and current limitations are also examined, like standardising routing experiments, accounting for non-financial costs, and designing adaptive strategies. Results: There is a wide range of routing strategies, from lightweight, similarity-based and supervised methods, to more complex approaches involving LLM fine-tuning and reinforcement learning. Most current strategies adopt a pre-generation approach, which is generally more resource-efficient. This survey demonstrates that some low-resource solutions can provide generalisation capabilities. Conclusions: Routing offers a practical way to improve the efficiency of LLM-based systems. By formalising routing as a performance-cost optimisation problem, this survey provides tools and directions to guide future research and development of adaptive low-cost LLM-based systems.
Designing Artificial Intelligence (AI)-based interactive systems for law enforcement poses unique socio-technical and ethical challenges, particularly when such systems must support real-time decision-making in dynamic, high-stakes environments. Despite their potential, AI-supported interactive systems in policing require carefully elicited domain-specific requirements to ensure effective use while being Ethical by Design. However, methods for such requirement elicitation remain limited. This paper presents a participatory approach for identifying the requirements of AI-driven Mixed Reality (MR) systems in law enforcement contexts. The introduced methodology builds on two of our previous EU projects: the Erasmus+ project "Trustworthy AI", which provided educational material to teach key principles of Trustworthy AI, and AI4EU, which developed an abbreviated assessment tool for evaluating AI systems. In collaboration with police education units and law enforcement agencies in Sweden and Catalonia, we conducted a multi-phase study involving two preparatory workshops—one focused on educating participants in Trustworthy AI, and another involving hands-on MR use in standard police training scenarios. This reflects the view that it is not enough to simply ask people about new technologies—they must also be educated to critically assess their implications. After the workshops, we collected structured feedback using quantitative and qualitative methods. To analyze risk levels of the elicited requirements, we applied the AI4EU-based assessment tool. Our findings highlight key challenges and opportunities for designing AI-based systems with MR interfaces that enhance decision-making in real-time police operations while ensuring transparency, safety, and human oversight.
Virtualization is the mechanism of creating virtual representations of physical resources. It is ubiquitously used in data centers and cloud computing services. The objective of virtualization is to ensure that the physical resources are managed efficiently and effectively. This goal induces the Virtual Network Embedding (VNE) problem: the cornerstone task of properly allocating the physical resources of a network to satisfy requests for resources under various constraints while ensuring the quality of service and maximizing resource utilization. Combinatorially, the VNE problem is a problem in resource management that is NP-hard to solve optimally. In this article, we adapt the Conflict-Based Search (CBS) framework for solving the VNE problem, inspired by its success in the Multi-Agent Path Finding (MAPF) domain. We create two algorithms: VNE-CBS and its improved version Improved VNE-CBS (iVNE-CBS). These algorithms not only successfully address the unique challenges in applying the CBS framework to the VNE problem but also import powerful algorithmic techniques, such as disjoint splitting, bypassing conflicts, and conflict avoidance tables, from the MAPF domain. We show that iVNE-CBS significantly outperforms popular baseline VNE algorithms: It scales to networks with several hundred vertices and thousands of edges—significantly larger than the scale of the networks previously used in the VNE literature—while also producing better-quality solutions. The success of our approach might pave the way for overcoming a crucial issue in Internet ossification via heuristic search methods.
This survey provides a comprehensive synthesis of research on automatic poetry generation and evaluation from 2017 to 2025. We examine computational approaches that leverage pre-trained LLMs, multimodal architectures, and specialized algorithms for handling poetic constraints such as meter, rhyme, and stanza structure. In addition to surveying generative methods, we analyze practices in data engineering, including corpus construction, annotation, and preprocessing tools tailored to poetry. Evaluation receives particular attention: we review automatic metrics, LLM-as-a-judge methods, and human-centered protocols, discussing their strengths and limitations. Compared with prior surveys, our work emphasizes (1) the dominant role of LLMs in both generation and evaluation, (2) a taxonomy of poetry generation tasks categorized by interaction modality, (3) systematic coverage of dataset engineering challenges, and (4) a comprehensive analysis of automatic and human evaluation approaches, highlighting their drawbacks. By consolidating advances across diverse research lines, we show how poetry serves as a challenging benchmark for controllable text generation, multimodal grounding, and human-aligned evaluation. Building on this perspective, the survey summarizes current methods and open challenges in the generation, control, and evaluation of poetic and lyrical text.
Revising what an agent knows in response to new information is a central problem in formal epistemology. In doxastic logics such as KD45, belief revision proceeds by reordering plausibility: the agent simply re-ranks which worlds it considers most credible. This strategy fails for S5 knowledge. Because knowledge is factive (Kqp-qp), an agent cannot come to know qp merely by finding qp-worlds more plausible; if the actual world falsifies qp, then Kqp remains unsatisfiable regardless of any reordering. Accommodating new modal information in S5 therefore requires genuine model transformation: adjusting the equivalence-based accessibility structure, the valuation, or both. We develop R-Mod, a selection-based revision operator that realizes this transformation as minimal structural repair. Given an S5 model and a target formula, R-Mod searches for a closest model-measured by a bisimulation-aware distance on quotient structures-that satisfies the formula while preserving S5 constraints. At the skeptical level, R-Mod satisfies success, consistency preservation, and deductive closure; classical AGM postulates such as Inclusion and Superexpansion fail due to permissible structural amplification, though we identify conditions under which they re-emerge. Computationally, the decision problem is NP-complete, and we provide tractable fragments exploiting structural locality. While recent work has advanced AGM-style postulate analysis for S5 and topological semantics via simplicial complexes, these approaches do not provide goal-driven optimization with algorithmic guarantees. R-Mod fills this gap by combining modal invariance, explicit distance minimization, and fine-grained complexity analysis. Our results reframe revision in S5 as knowledge-model revision rather than belief revision, offering a foundation for algorithmic implementations and extensions to richer epistemic semantics.
The widespread adoption of deep neural network (DNN)-based learning systems in safety-critical applications requires exceptional reliability. However, this reliability could be compromised by perturbations in model parameters, such as variations in neural network weights caused by hardware vulnerabilities and environmental factors, which can lead to mispredictions and compromise system safety. To address this, we propose ‘ModelStar’, an innovative framework leveraging reachability analysis to evaluate the robustness of DNNs against weight perturbations. ModelStar employs a linear set propagation technique to analyze the impact of an infinite family of parameter variations on DNN outputs. Our comprehensive analysis demonstrates that ModelStar not only establishes tighter robustness bounds but also verifies DNN robustness for up to 60% more samples from image classification datasets compared to existing methods. Furthermore, ModelStar extends safety verification to convolutional layers, advancing the state-of-the-art in neural network safety verification. These results highlight ModelStar’s efficacy in improving the reliability of DNNs in real-world, safety-critical scenarios.
We study multivariate decision trees (MDTs), in particular, classes of MDTs determined by the language of relations that can be used to split feature space. An abductive explanation (AXp) of the classification of a particular instance, viewed as a set of feature-value assignments, is a minimal subset of the instance which is sufficient to lead to the same decision. We investigate when finding a single AXp is tractable. We identify tractable languages for real, integer and boolean features. Indeed, in the case of boolean languages, we provide a P/NP-hard dichotomy. We extend this dichotomy to languages defined by formulas whose literals correspond to splits of ordered domains of arbitrary finite size. Experiments indicate that MDTs can provide more compact models than classical decision trees while conserving accuracy and explainability.
Background: Multi-Agent Planning (MAP) involves coordinating the actions of multiple autonomous agents to achieve shared objectives. A prevalent formalism for MAP is the Multi-Agent Planning Domain Definition Language (MA-PDDL). While effective, existing MA-PDDL solvers typically require complete access to agents’ action models—specifically their preconditions and effects. However, manually creating these models is often intractable, requiring exhaustive domain expertise. Objectives: This work explores an alternative approach: automatically learning agents’ action models from observed transitions. Since learned models may be inaccurate, planning with them can yield invalid or non-executable sequences. To mitigate this, we formalize a requirement for safety, ensuring that plans generated via the learned model remain sound with respect to the real unknown action model. Methods: Previous research introduced the Safe Action Model Learning (SAM) algorithm for single-agent domains. However, SAM is not suitable for MA-PDDL environments where observations include concurrently executed actions, since it cannot naturally disambiguate the individual contributions of the agents to the observed effects. To address this, we introduce Multi-Agent Safe Action Model Learning (MA-SAM), a safe action model learning algorithm designed to handle concurrent multi-agent observations. For scenarios where individual action effects remain ambiguous, we further propose MA-SAM+ , which learns the preconditions and effects of macro-actions representing concurrent execution of subsets of actions. We evaluate both algorithms on domains from the Competition of Distributed and Multi-Agent Planners (CoDMAP) benchmarks and a novel MAP domain inspired by the game Overcooked. Results: We establish a theoretical lower bound on the sample complexity for learning safe action models in multi-agent settings. We prove that MA-SAM does not achieve this lower bound in all cases, identifying specific conditions under which its sample complexity may become unbounded. Empirically, both MA-SAM and MA-SAM+ significantly outperform SAM-based baselines in coverage and applicability rates. While their performance is comparable in many settings, MA-SAM+ highly outperforms MA-SAM in some of the evaluated domains. Conclusions: We present the first algorithms capable of learning safe MA-PDDL action models from concurrently executed actions, providing both theoretical foundations and empirical validation across diverse planning benchmarks
There is a well-known approach to cope with NP-hard problems in practice: reduce the given problem to SAT or MAX-SAT and run a SAT or a MAX-SAT solver. This method is very efficient since SAT/MAX-SAT solvers are extremely well-studied, as well as the complexity of these problems. At IJCAI-2011, Li et al. proposed an alternative to this approach and suggested the Partial Minimum Satisfiability problem as a reduction target for NP-hard problems. They developed the MinSatz solver and showed that reducing to PARTIAL MIN-SAT and using MinSatz is in some cases more efficient than reductions to SAT or MAX-SAT. Since then many results connected to the PARTIAL MIN-SAT problem were published. However, to the best of our knowledge, the worst-case complexity of PARTIAL MIN-SAT has not been studied up until now. Our goal is to fix the issue and show a O & lowast;( (2-e)m) lower bound under the SETH assumption (here m is the total number of clauses), as well as several other lower bounds and parameterized exact algorithms with better-than-trivial running time.
Background: Compositional symbol-forming and symbol-relating behaviors in deep learning or neuro-symbolic systems have been repeatedly recommended as part of a solution to the shortcomings of current state-of-the-art artificial intelligence. Studying how compositional languages can emerge between tabula rasa deep learning agents may help us understand how to make artificial neural networks represent unstructured, continuous input data in terms of combinations of discrete symbols. Objectives: We aim present a comprehensive overview of recent research into compositional languages emerging between deep learning agents, in a manner that will be accessible to machine learning researchers who are not already aware of emergent communication and emergent languages. Methods: We review roughly ten years of emergent language research, particularly focusing on contributions after 2019 that pertain to measuring or eliciting compositionality in emergent languages. Results: Systematic generalization and topographic similarity (topsim) are the most dominant measures of compositionality in recent literature. “Productivity pressure”, forcing agents to use vocabularies smaller than the number of meanings they need to communicate, is clearly necessary for compositionality to emerge. Regularizing or periodically resetting receiver/listener agents is an effective way of encouraging more compositional languages, perhaps because it creates a pressure for the speaker to create languages that can be learned more efficiently. The relative benefits of various neural network architectures, particularly the Transformer architecture dominant in other areas of deep learning, remains an underexplored topic. As other authors have noted, the field relies heavily on small-scale models and simple, often symbolic environments, which may hinder the generality of current conclusions. Conclusions: Emergent language research provides a testbed for encouraging emergent compositionality in deep learning models, which may in future contribute to the development of safer, more interpretable, and more sample-efficient neuro-symbolic foundational models. We advocate that future research converges on topsim and generalization as the standard approaches to measuring compositionality, but also works to expand topsim into a family of metrics that can detect compositionality in languages displaying forms of linguistic variation such as free word order and synonymy. We also call upon researchers to test promising techniques at larger scales, with a greater range of agent architectures, and with more complex, multi-modal referents.
Deep neural networks (DNNs) deployed on edge devices often suffer from severe performance degradation when exposed to dynamic and continually shifting environments. Test-time adaptation (TTA) has emerged as a promising solution by updating models online with incoming test data. However, edge deployment poses unique challenges: limited computational resources, latency caused by adaptation delays, and knowledge isolation across devices. The situation becomes even more complex in open-world scenarios, where the presence of unknown categories further disrupts adaptation. To overcome these limitations, we propose TeamTTA, a cloud-integrated framework designed for efficient multi-device collaboration open-set test-time adaptation. Specifically, TeamTTA aggregates reliable samples from multiple edge devices through crowdsourcing, uploads them to the cloud, and maintains a memory buffer for continual adaptation. A large vision model (LVM) in the cloud leverages its zero-shot generalization ability to filter out open-set samples and acts as a teacher model, distilling its knowledge into a replicated student edge model stored in the cloud. The adapted model parameters, or alternatively global statistics under poor network conditions, are then transmitted back to the edge devices for efficient inference. Extensive experiments on standard public TTA benchmarks, including corrupted and open-set datasets, show that TeamTTA achieves superior adaptation accuracy, robustness to distribution shifts, and communication efficiency, outperforming state-of-the-art TTA baselines. These results validate the effectiveness of integrating cloud-edge collaboration and LVM-driven knowledge distillation for real-world edge intelligence.
Fragments of propositional logic, i.e., tailored sub-languages designed for neatly structured data, are relevant in many practical settings. This paper studies belief update in fragments (e.g., Horn, Krom, affine) that obey a desirable semantic closure condition. We assume update is guided by the well-known Katsuno-Mendelzon (KM) postulates, which in full propositional logic characterize update operators as choice functions guided by total or partial preorders over possible worlds. Because many useful fragments cannot express every connective (e.g., they often lack closure under disjunction), the KM axioms must be rephrased and supplemented to keep updates rational in these less expressive environments. Our main result is a set of representation theorems: once the KM postulates are adjusted, they capture exactly the update operators generated by suitably constrained total or partial preorders within the fragment. In addition, we clarify how revision works in fragments when partial preorders are allowed and also present concrete, fragment-friendly update operators.
We consider the Anonymous Multi-Agent Path-Finding (AMAPF) problem where the agents are confined to a graph, a set of goal vertices is given, and each of these vertices has to be reached by some agent. The problem is to find an assignment of the goals to the agents as well as the collision-free paths, and we seek solutions that minimize either the sum of costs of all paths (SOC) or the maximum path cost (makespan). Two assumptions are usually used for the agents’ behavior after reaching the goals. The first assumption is that agents stay at the goals after reaching them and wait for the other agents to reach their goals, while the second assumption is that agents disappear upon arrival at goal vertices. We refer to the AMAPF problem under the first assumption and to the problem under the second assumption as AMAPF and AMAPFD, respectively. AMAPF can be solved in polynomial time with respect to the makespan objective (although existing approaches have a critical bottleneck in one part of the solving process). For the SOC objective, the known optimal approaches have worst-case exponential complexity. For AMAPFD with the SOC objective, to the best of our knowledge, no dedicated optimal solver has been reported. To this end, in this paper, we enhance the existing solution of the AMAPF-makespan problem and introduce a novel solution to AMAPFD-SOC. Specifically, for the AMAPF-makespan problem, the polynomial approach to solving this problem is to reduce it to a special type of a graph search problem, i.e., to the problem of finding a Maximum Flow on an auxiliary graph induced by the input one. The size of the former graph may be very large and the search on it may become a bottleneck for the standard Maximum Flow solvers. We suggest a specific search algorithm (called Bulk Search) that leverages the idea of exploring the search space not through considering separate search states but rather bulks of them simultaneously. That is, we implicitly compress, store, and expand bulks of the search states as single states, reducing the runtime and memory consumption. Empirically, the resulting AMAPF solver outperforms the competing approach based on the standard MF solver, and solves all publicly available MAPF instances from the MovingAI benchmark in less than 30 seconds. For the AMAPFD-SOC problem, we suggest a method to reduce the problem to a Minimum-Cost Maximum-Flow (MCMF) problem on a similar auxiliary graph used in the AMAPF problem but now with non-zero edge costs. After that, we propose a modified version of Bulk Search, called Generalized Bulk Search to help solve the MCMF problem efficiently. As a result, the AMAPFD-SOC problem is solved by an efficient solver that could solve 98.5% of all MovingAI benchmark instances in less than 30 seconds.
Weighted gradual semantics provide an acceptability degree to each argument representing its final strength, computed based on factors including the argument's background evidence, and taking into account interactions between the argument and others. We introduce five important problems linking gradual semantics and acceptability degrees. First, we re-examine the inverse problem, seeking to identify each argument's initial weights within the argumentation framework which lead to a specific final acceptability degree. Second, we ask whether the function mapping between argument weights and acceptability degrees is one-to-one. Third, we ask if this mapping is a homeomorphism so that small perturbations in weights lead to small perturbation in acceptability degrees and vice versa. Fourth, we ask whether argument weights can be found when preferences, rather than acceptability degrees for arguments are considered. Last, we consider the geometry of the space of valid acceptability degrees, asking whether ``"gaps" exist in this space. While different gradual semantics have been proposed in the literature, in this paper, and building on the geometry of the acceptability degree space, we identify a large family of weighted gradual semantics which contains many of the existing well-known semantics while maintaining desirable properties such as convergence to a unique fixed point and solving all five aforementioned problems.
We investigate the problem of fairly dividing a divisible heterogeneous resource, also known as a cake, among a set of n agents who may have different entitlements. We characterize the existence of a connected super-proportional (also called strongly-proportional) allocation-one in which every agent receives a contiguous piece worth strictly more than their proportional share. The characterization is supplemented with an algorithm that determines its existence using O(n & centerdot; 2n) queries. We devise a simpler characterization for agents with strictly positive valuations and with equal entitlements, and present an algorithm to determine the existence of such an allocation using O(n2) queries. We provide matching lower bounds in the number of queries for both algorithms. When a connected super-proportional allocation exists, we show that it can also be computed using a similar number of queries. We also consider the problem of deciding the existence of a connected allocation of a cake in which each agent receives a piece worth a small fixed value more than their proportional share, and the problem of deciding the existence of a connected super-proportional allocation of a pie (a 1-dimensional circular cake).
Background: Constraint Programming (CP) has been successfully used to model and solve complex combinatorial problems. However, modeling is often not trivial and requires expertise, which is a bottleneck to wider adoption of CP. As a result, the field of Constraint Acquisition (CA) has emerged with the aim to (semi-)automate the modeling process. In CA, the goal is to assist the user by automatically learning the model. In (inter)active CA, this is done by interactively posting queries to the user, e.g., asking whether a partial solution satisfies their (unspecified) constraints or not. Objectives: However, a large number of queries is required to learn the model, which is a major limitation of state-of-the-art CA, especially for human users. We believe this is due to the search-based learning of interactive CA, which is based on symbolic concept learning, being mostly uninformed. During learning, the system is not aware of any patterns that may appear in the constraints acquired so far, which could be used to guide the rest of the process. Methods: In this paper, we aim to alleviate this limitation by, for the first time, utilizing statistical Machine Learning (ML) in the context of interactive CA. We propose to use probabilistic classification models to guide interactive CA to generate more informative queries. Specifically, we propose a probability-based objective function to use in the query generation process across all components of interactive CA: the top-level query generation, the scope finding, and the lowest-level constraint finding. To ease the guiding of the scope-finding process, we also propose a novel FindScope function, which includes an explicit query generation step. Effective guidance, however, relies on (probabilistic) estimates of whether candidate expressions belong to the problem or not. To this end, we propose a framework for the training of ML classifiers within the interactive CA process, as well as an expressive feature representation of constraints. Results: We experimentally evaluate our proposed methods on 7 different problem classes, using different classifiers and feature representations, and show that our methods greatly outperform the state of the art, decreasing the number of queries needed to converge by up to 75%. Conclusions: Our findings confirm that statistical ML methods can detect patterns in constraint models, while they are being learned, and can be successfully used within the search-based interactive CA for reducing the number of queries needed.
Background: With AI systems increasingly being applied to assist humans in decision-making processes such as talent hiring, school admissions, and loan approvals, there is a growing need to ensure that the resulting decisions are fair. A major challenge in analyzing fairness is that standards are highly subjective and context-dependent -- there is no consensus on what absolute fairness means in every scenario. Moreover, different standards of fairness often conflict with each other. Objectives: To address this issue, this work aims to evaluate the relative fairness between decisions. Methods: Instead of defining what constitutes "absolutely" fair decisions, we propose assessing the relative fairness of one decision set against another using differential parity -- two sets of decisions are considered relatively fair with respect to each other if and only if the difference between them is independent of a given sensitive attribute. The proposed notion of differential parity fairness offers three key benefits: (1) it avoids the ambiguity and contradictions inherent in defining "absolutely" fair decisions; (2) it reveals relative preferences and biases between two decision sets; and (3) it can serve as a new notion of group fairness when a reference set of decisions (e.g., ground truth) is available. One limitation of differential parity is that the two sets of decisions being compared must be made on the same data subjects. To overcome this limitation, we propose to utilize a machine learning model to bridge the gap between the two sets of decisions made on different data and approximate the differential parity metrics. In addition to differential parity and inspired by the statistical parity fairness notion, we also define relative statistical parity-the difference between the means of two sets of decisions is required to be independent of the sensitive attribute-as a weaker notion of relative fairness compared to differential parity. Results: Theoretically, we show how the proposed metrics statistically evaluate differential parity and relative statistical parity. We also proved the feasibility of using the proposed biased bridge algorithm to approximate differential parity metrics between decisions made on different data. Empirically, we evaluated the Type I and Type II error rates of differential parity and relative statistical parity both between decisions made on the same data and on different data. Experimental results suggest that differential parity outperforms relative statistical parity by having a much lower Type II error rate in both scenarios. Conclusions: With lower than 0.1 Type Iand Type II error rates in both scenarios, the effectiveness of differential parity demonstrated in this article suggests that it is feasible and beneficial to evaluate relative bias between decisions made by different entities. We expect this to pave the way for the analysis of relative fairness in AI and beyond.
