Many modern probabilistic models rely on SDEs, but their adoption is hampered by instability, poor inductive bias outside bounded domains, and reliance on restrictive dynamics or training tricks. While recent work constrains SDEs to compact spaces using reflected dynamics, these approaches lack continuous dynamics and efficient high-order solvers, limiting interpretability and applicability. We propose a novel class of neural SDEs on compact polyhedral spaces with continuous dynamics, amenable to higher-order solvers, and with favorable inductive bias.

In many real-world scenarios, agents are involved in optimization problems. Since most of these scenarios are over-constrained, optimal solutions do not always satisfy all agents. Some agents might be unhappy and ask questions of the form ``Why does solution $S$ not satisfy property $P$?''. In this paper, we propose MAoE, a domain-independent approach to obtain contrastive explanations by (i) generating a new solution $S^\prime$ where the property $P$ is enforced, while also minimizing the differences between $S$ and $S^\prime$; and (ii) highlighting the differences between the two solutions. Such explanations aim to help agents understanding why the initial solution is better than what they expected. We have carried out a computational evaluation that shows that MAoE can generate contrastive explanations for large multi-agent optimization problems. We have also performed an extensive user study in four different domains that shows that, after being presented with these explanations, humans' satisfaction with the original solution increases.

Building query graphs from natural language questions is an important step in complex question answering over knowledge graph (Complex KGQA). In general, a question can be correctly answered if its query graph is built correctly and the right answer is then retrieved by issuing the query graph against the KG. Therefore, this paper focuses on query graph generation from natural language questions. Existing approaches for query graph generation ignore the semantic structure of a question, resulting in a large number of noisy query graph candidates that undermine prediction accuracies. In this paper, we define six semantic structures from common questions in KGQA and develop a novel Structure-BERT to predict the semantic structure of a question. By doing so, we can first filter out noisy candidate query graphs, and then rank the remaining candidates with a BERT-based ranking model. Extensive experiments on two popular benchmarks MetaQA and WebQuestionsSP (WSP) demonstrate the effectiveness of our method as compared to state-of-the-arts.

The workflow satisfiability problem (WSP) is a well-studied problem in access control seeking allocation of authorised users to every step of the workflow, subject to workflow specification constraints. It was noticed that the number $k$ of steps is typically small compared to the number of users in the real-world instances of WSP; therefore $k$ is considered as the parameter in WSP parametrised complexity research. While WSP in general was shown to be W[1]-hard, WSP restricted to a special case of user-independent (UI) constraints is fixed-parameter tractable (FPT). However, restriction to the UI constraints might be impractical. To efficiently handle non-UI constraints, we introduce the notion of branching factor of a constraint. As long as the branching factors of the constraints are relatively small and the number of non-UI constraints is reasonable, WSP can be solved in FPT time. Extending the results from Karapetyan et al. (2019), we demonstrate that general-purpose solvers are capable of achieving FPT-like performance on WSP with arbitrary constraints when used with appropriate formulations. This enables one to tackle most of practical WSP instances. While important on its own, we hope that this result will also motivate researchers to look for FPT-aware formulations of other FPT problems.

The fixed parameter tractable (FPT) approach is a powerful tool in tackling computationally hard problems.  In this paper, we link FPT results to classic artificial intelligence (AI) techniques to show how they complement each other.  Specifically, we consider the workflow satisfiability problem (WSP) which asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment.  It was shown by Cohen et al. (JAIR 2014) that WSP restricted to the class of user-independent constraints (UI), covering many practical cases, admits FPT algorithms, i.e. can be solved in time exponential only in the number of steps k and polynomial in the number of users n.  Since usually k << n in WSP, such FPT algorithms are of great practical interest.We present a new interpretation of the FPT nature of the WSP with UI constraints giving a decomposition of the problem into two levels.  Exploiting this two-level split, we develop a new FPT algorithm that is by many orders of magnitude faster than the previous state-of-the-art WSP algorithm and also has only polynomial-space complexity.  We also introduce new pseudo-Boolean (PB) and Constraint Satisfaction (CSP) formulations of the WSP with UI constraints which efficiently exploit this new decomposition of the problem and raise the novel issue of how to use general-purpose solvers to tackle FPT problems in a fashion that meets FPT efficiency expectations.  In our computational study, we investigate, for the first time, the phase transition (PT) properties of the WSP, under a model for generation of random instances.  We show how PT studies can be extended, in a novel fashion, to support empirical evaluation of scaling of FPT algorithms.

The fixed parameter tractable (FPT) approach is a powerful tool in tackling computationally hard problems. In this paper, we link FPT results to classic artificial intelligence (AI) techniques to show how they complement each other. Specifically, we consider the workflow satisfiability problem (WSP) which asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment. It was shown by Cohen et al. (JAIR 2014) that WSP restricted to the class of user-independent constraints (UI), covering many practical cases, admits FPT algorithms, i.e. can be solved in time exponential only in the number of steps $k$ and polynomial in the number of users $n$. Since usually $k \ll n$ in WSP, such FPT algorithms are of great practical interest as they significantly extend the size of the problem that can be routinely solved. We give a new view of the FPT nature of the WSP with UI constraints, showing that it decomposes the problem into two levels. Exploiting this two-level split, we develop a new FPT algorithm that is by many orders of magnitude faster than the previous state-of-the-art WSP algorithm; and it also has only polynomial space complexity whereas the old algorithm takes memory exponential in $k$, which limits its application. We also provide a new pseudo-boolean (PB) formulation of the WSP with UI constraints which exploits this new decomposition of the problem into two levels. Our experiments show that efficiency of solving this new PB formulation of the problem by a general purpose PB solver can be close to the bespoke FPT algorithm, which raises the potential of using general purpose solvers to tackle FPT problems efficiently. We also study the computational performance of various algorithms to complement the overly-pessimistic worst-case analysis that is usually done in FPT studies.

The Workflow Satisfiability Problem (WSP) is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether there exists a plan - an assignment of tasks to authorized users - such that all constraints are satisfied. It is natural to see the WSP as a subclass of the Constraint Satisfaction Problem (CSP) in which the variables are tasks and the domain is the set of users. What makes the WSP distinctive is that the number of tasks is usually very small compared to the number of users, so it is appropriate to ask for which constraint languages the WSP is fixed-parameter tractable (FPT), parameterized by the number of tasks. This novel approach to the WSP, using techniques from CSP, has enabled us to design a generic algorithm which is FPT for several families of workflow constraints considered in the literature. Furthermore, we prove that the union of FPT languages remains FPT if they satisfy a simple compatibility condition. Lastly, we identify a new FPT constraint language, user-independent constraints, that includes many of the constraints of interest in business processing systems. We demonstrate that our generic algorithm has provably optimal running time O*(2^(klog k)), for this language, where k is the number of tasks.