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Faster pathfinding in time-dependent transport networks is an important and challenging problem in navigation systems. There are two main types of transport networks: road networks for car driving and public transport route network. The solutions that work well in road networks, such as Time-dependent Contraction Hierarchies and other graph-based approaches, do not usually apply in transport networks. In transport networks, non-graph solutions such as CSA and RAPTOR show the best results compared to graph-based techniques. In our work, we propose a method that advances graph-based approaches by using different optimization techniques from computational geometry to speed up the search process in transport networks. We apply a new pre-computation step, which we call timetable nodes (TTN). Our inspiration comes from an iterative search problem in computational geometry. We implement two versions of the TTN: one uses a Combined Search Tree (TTN-CST), and the second uses Fractional Cascading (TTN-FC). Both of these approaches decrease the asymptotic complexity of reaching new nodes from $O(k\times \log|C|)$ to $O(k + \log(k) + \log(|C|))$, where $k$ is the number of outgoing edges from a node and $|C|$ is the size of the timetable information (total outgoing edges). Our solution suits any other time-dependent networks and can be integrated into other pathfinding algorithms. Our experiments indicate that this pre-computation significantly enhances the performance on high-density graphs. This study showcases how leveraging computational geometry can enhance pathfinding in transport networks, enabling faster pathfinding in scenarios involving large numbers of outgoing edges.

Despite the practical success of Artificial Intelligence (AI), current neural AI algorithms face two significant issues. First, the decisions made by neural architectures are often prone to bias and brittleness. Second, when a chain of reasoning is required, neural systems often perform poorly. Neuro-symbolic artificial intelligence is a promising approach that tackles these (and other) weaknesses by combining the power of neural perception and symbolic reasoning. Meanwhile, the success of AI has made it critical to understand its behaviour, leading to the development of explainable artificial intelligence (XAI). While neuro-symbolic AI systems have important advantages over purely neural AI, we still need to explain their actions, which are obscured by the interactions of the neural and symbolic components. To address the issue, this paper proposes a formal approach to explaining the decisions of neuro-symbolic systems. The approach hinges on the use of formal abductive explanations and on solving the neuro-symbolic explainability problem hierarchically. Namely, it first computes a formal explanation for the symbolic component of the system, which serves to identify a subset of the individual parts of neural information that needs to be explained. This is followed by explaining only those individual neural inputs, independently of each other, which facilitates succinctness of hierarchical formal explanations and helps to increase the overall performance of the approach. Experimental results for a few complex reasoning tasks demonstrate practical efficiency of the proposed approach, in comparison to purely neural systems, from the perspective of explanation size, explanation time, training time, model sizes, and the quality of explanations reported.

Single Transferable Vote (STV) counting, used in several jurisdictions in Australia, is a system for choosing multiple election winners given voters' preferences over candidates. There are a variety of different versions of STV legislated and/or applied across Australia. This paper shows some of the unintuitive properties of some of these systems.

This paper addresses the problem of autonomous UAV search missions, where a UAV must locate specific Entities of Interest (EOIs) within a time limit, based on brief descriptions in large, hazard-prone environments with keep-out zones. The UAV must perceive, reason, and make decisions with limited and uncertain information. We propose NEUSIS, a compositional neuro-symbolic system designed for interpretable UAV search and navigation in realistic scenarios. NEUSIS integrates neuro-symbolic visual perception, reasoning, and grounding (GRiD) to process raw sensory inputs, maintains a probabilistic world model for environment representation, and uses a hierarchical planning component (SNaC) for efficient path planning. Experimental results from simulated urban search missions using AirSim and Unreal Engine show that NEUSIS outperforms a state-of-the-art (SOTA) vision-language model and a SOTA search planning model in success rate, search efficiency, and 3D localization. These results demonstrate the effectiveness of our compositional neuro-symbolic approach in handling complex, real-world scenarios, making it a promising solution for autonomous UAV systems in search missions.

AWAIRE is one of two extant methods for conducting risk-limiting audits of instant-runoff voting (IRV) elections. In principle AWAIRE can audit IRV contests with any number of candidates, but the original implementation incurred memory and computation costs that grew superexponentially with the number of candidates. This paper improves the algorithmic implementation of AWAIRE in three ways that make it practical to audit IRV contests with 55 candidates, compared to the previous 6 candidates. First, rather than trying from the start to rule out all candidate elimination orders that produce a different winner, the algorithm starts by considering only the final round, testing statistically whether each candidate could have won that round. For those candidates who cannot be ruled out at that stage, it expands to consider earlier and earlier rounds until either it provides strong evidence that the reported winner really won or a full hand count is conducted, revealing who really won. Second, it tests a richer collection of conditions, some of which can rule out many elimination orders at once. Third, it exploits relationships among those conditions, allowing it to abandon testing those that are unlikely to help. We provide real-world examples with up to 36 candidates and synthetic examples with up to 55 candidates, showing how audit sample size depends on the margins and on the tuning parameters. An open-source Python implementation is publicly available., Comment: 16 pages, 4 figures, accepted for E-Vote-ID 2024

Statically typed languages offer significant advantages, such as bug prevention, enhanced code quality, and reduced maintenance costs. However, these benefits often come at the expense of a steep learning curve and a slower development pace. Haskell, known for its expressive and strict type system, poses challenges for inexperienced programmers in learning and using its type system, especially in debugging type errors. We introduce Goanna, a novel tool that serves as a type checker and an interactive type error debugging tool for Haskell. When encountering type errors, Goanna identifies a comprehensive list of potential causes and resolutions based on the minimum correction subsets (MCS) enumeration. We evaluated Goanna's effectiveness using 86 diverse Haskell programs from online discourse, demonstrating its ability to accurately identify and resolve type errors. Additionally, we present a collection of techniques and heuristics to enhance Goanna's suggestion-based error diagnosis and show their effectiveness from our evaluation.

Polymorphic types are an important feature in most strongly typed programming languages. They allow functions to be written in a way that can be used with different data types, while still enforcing the relationship and constraints between the values. However, programmers often find polymorphic types difficult to use and understand and tend to reason using concrete types. We propose GeckoGraph, a graphical notation for types. GeckoGraph aims to accompany traditional text-based type notation and to make reading, understanding, and comparing types easier. We conducted a large-scale human study using GeckoGraph compared to text-based type notation. To our knowledge, this is the largest controlled user study on functional programming ever conducted. The results of the study show that GeckoGraph helps improve programmers' ability to succeed in the programming tasks we designed, especially for novice programmers.

Various risk-limiting audit (RLA) methods have been developed for instant-runoff voting (IRV) elections. A recent method, AWAIRE, is the first efficient approach that can take advantage of but does not require cast vote records (CVRs). AWAIRE involves adaptively weighted averages of test statistics, essentially "learning" an effective set of hypotheses to test. However, the initial paper on AWAIRE only examined a few weighting schemes and parameter settings. We explore schemes and settings more extensively, to identify and recommend efficient choices for practice. We focus on the case where CVRs are not available, assessing performance using simulations based on real election data. The most effective schemes are often those that place most or all of the weight on the apparent "best" hypotheses based on already seen data. Conversely, the optimal tuning parameters tended to vary based on the election margin. Nonetheless, we quantify the performance trade-offs for different choices across varying election margins, aiding in selecting the most desirable trade-off if a default option is needed. A limitation of the current AWAIRE implementation is its restriction to a small number of candidates -- up to six in previous implementations. One path to a more computationally efficient implementation would be to use lazy evaluation and avoid considering all possible hypotheses. Our findings suggest that such an approach could be done without substantially compromising statistical performance., Comment: 15 pages, 4, figures, presented at Voting'24. The current version includes some improved wording and fixes a few errors

Single Transferable Vote (STV) elections are a principled approach to electing multiple candidates in a single election. Each ballot has a starting value of 1, and a candidate is elected if they gather a total vote value more than a defined quota. Votes over the quota have their value reduced by a transfer value so as to remove the quota, and are passed to the next candidate on the ballot. Risk-limiting audits (RLAs) are a statistically sound approach to election auditing which guarantees that failure to detect an error in the result is bounded by a limit. A first approach to RLAs for 2-seat STV elections has been defined. In this paper we show how we can improve this approach by reasoning about lower bounds on transfer values, and how we can extend the approach to partially audit an election, if the method does not support a full audit.

Widespread use of artificial intelligence (AI) algorithms and machine learning (ML) models on the one hand and a number of crucial issues pertaining to them warrant the need for explainable artificial intelligence (XAI). A key explainability question is: given this decision was made, what are the input features which contributed to the decision? Although a range of XAI approaches exist to tackle this problem, most of them have significant limitations. Heuristic XAI approaches suffer from the lack of quality guarantees, and often try to approximate Shapley values, which is not the same as explaining which features contribute to a decision. A recent alternative is so-called formal feature attribution (FFA), which defines feature importance as the fraction of formal abductive explanations (AXp's) containing the given feature. This measures feature importance from the view of formally reasoning about the model's behavior. It is challenging to compute FFA using its definition because that involves counting AXp's, although one can approximate it. Based on these results, this paper makes several contributions. First, it gives compelling evidence that computing FFA is intractable, even if the set of contrastive formal explanations (CXp's) is provided, by proving that the problem is #P-hard. Second, by using the duality between AXp's and CXp's, it proposes an efficient heuristic to switch from CXp enumeration to AXp enumeration on-the-fly resulting in an adaptive explanation enumeration algorithm effectively approximating FFA in an anytime fashion. Finally, experimental results obtained on a range of widely used datasets demonstrate the effectiveness of the proposed FFA approximation approach in terms of the error of FFA approximation as well as the number of explanations computed and their diversity given a fixed time limit.

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics that asks us to compute collision-free paths for a team of agents, all moving across a shared map. Although many works appear on this topic, all current algorithms struggle as the number of agents grows. The principal reason is that existing approaches typically plan free-flow optimal paths, which creates congestion. To tackle this issue, we propose a new approach for MAPF where agents are guided to their destination by following congestion-avoiding paths. We evaluate the idea in two large-scale settings: one-shot MAPF, where each agent has a single destination, and lifelong MAPF, where agents are continuously assigned new destinations. Empirically, we report large improvements in solution quality for one-short MAPF and in overall throughput for lifelong MAPF., Comment: The paper was accepted for publication at AAAI 2024

A complete time-parameterized statistical model quantifying the divergent evolution of protein structures in terms of the patterns of conservation of their secondary structures is inferred from a large collection of protein 3D structure alignments. This provides a better alternative to time-parameterized sequence-based models of protein relatedness, that have clear limitations dealing with twilight and midnight zones of sequence relationships. Since protein structures are far more conserved due to the selection pressure directly placed on their function, divergence time estimates can be more accurate when inferred from structures. We use the Bayesian and information-theoretic framework of Minimum Message Length to infer a time-parameterized stochastic matrix (accounting for perturbed structural states of related residues) and associated Dirichlet models (accounting for insertions and deletions during the evolution of protein domains). These are used in concert to estimate the Markov time of divergence of tertiary structures, a task previously only possible using proxies (like RMSD). By analyzing one million pairs of homologous structures, we yield a relationship between the Markov divergence time of structures and of sequences. Using these inferred models and the relationship between the divergence of sequences and structures, we demonstrate a competitive performance in secondary structure prediction against neural network architectures commonly employed for this task. The source code and supplementary information are downloadable from \url{http://lcb.infotech.monash.edu.au/sstsum}., Comment: 12 pages, 6 figures

An election audit is risk-limiting if the audit limits (to a pre-specified threshold) the chance that an erroneous electoral outcome will be certified. Extant methods for auditing instant-runoff voting (IRV) elections are either not risk-limiting or require cast vote records (CVRs), the voting system's electronic record of the votes on each ballot. CVRs are not always available, for instance, in jurisdictions that tabulate IRV contests manually. We develop an RLA method (AWAIRE) that uses adaptively weighted averages of test supermartingales to efficiently audit IRV elections when CVRs are not available. The adaptive weighting 'learns' an efficient set of hypotheses to test to confirm the election outcome. When accurate CVRs are available, AWAIRE can use them to increase the efficiency to match the performance of existing methods that require CVRs. We provide an open-source prototype implementation that can handle elections with up to six candidates. Simulations using data from real elections show that AWAIRE is likely to be efficient in practice. We discuss how to extend the computational approach to handle elections with more candidates. Adaptively weighted averages of test supermartingales are a general tool, useful beyond election audits to test collections of hypotheses sequentially while rigorously controlling the familywise error rate., Comment: 16 pages, 3 figures. Presented at E-Vote-ID 2023. This version contains minor corrections to match the final published version

This paper studies the possibilities made open by the use of Lazy Clause Generation (LCG) based approaches to Constraint Programming (CP) for tackling sequential classical planning. We propose a novel CP model based on seminal ideas on so-called lifted causal encodings for planning as satisfiability, that does not require grounding, as choosing groundings for functions and action schemas becomes an integral part of the problem of designing valid plans. This encoding does not require encoding frame axioms, and does not explicitly represent states as decision variables for every plan step. We also present a propagator procedure that illustrates the possibilities of LCG to widen the kind of inference methods considered to be feasible in planning as (iterated) CSP solving. We test encodings and propagators over classic IPC and recently proposed benchmarks for lifted planning, and report that for planning problem instances requiring fewer plan steps our methods compare very well with the state-of-the-art in optimal sequential planning.

Recent years have witnessed the widespread use of artificial intelligence (AI) algorithms and machine learning (ML) models. Despite their tremendous success, a number of vital problems like ML model brittleness, their fairness, and the lack of interpretability warrant the need for the active developments in explainable artificial intelligence (XAI) and formal ML model verification. The two major lines of work in XAI include feature selection methods, e.g. Anchors, and feature attribution techniques, e.g. LIME and SHAP. Despite their promise, most of the existing feature selection and attribution approaches are susceptible to a range of critical issues, including explanation unsoundness and out-of-distribution sampling. A recent formal approach to XAI (FXAI) although serving as an alternative to the above and free of these issues suffers from a few other limitations. For instance and besides the scalability limitation, the formal approach is unable to tackle the feature attribution problem. Additionally, a formal explanation despite being formally sound is typically quite large, which hampers its applicability in practical settings. Motivated by the above, this paper proposes a way to apply the apparatus of formal XAI to the case of feature attribution based on formal explanation enumeration. Formal feature attribution (FFA) is argued to be advantageous over the existing methods, both formal and non-formal. Given the practical complexity of the problem, the paper then proposes an efficient technique for approximating exact FFA. Finally, it offers experimental evidence of the effectiveness of the proposed approximate FFA in comparison to the existing feature attribution algorithms not only in terms of feature importance and but also in terms of their relative order.

JPS (Jump Point Search) is a state-of-the-art optimal algorithm for online grid-based pathfinding. Widely used in games and other navigation scenarios, JPS nevertheless can exhibit pathological behaviours which are not well studied: (i) it may repeatedly scan the same area of the map to find successors; (ii) it may generate and expand suboptimal search nodes. In this work, we examine the source of these pathological behaviours, show how they can occur in practice, and propose a purely online approach, called Constrained JPS (CJPS), to tackle them efficiently. Experimental results show that CJPS has low overheads and is often faster than JPS in dynamically changing grid environments: by up to 7x in large game maps and up to 14x in pathological scenarios.

The Flatland Challenge, which was first held in 2019 and reported in NeurIPS 2020, is designed to answer the question: How to efficiently manage dense traffic on complex rail networks? Considering the significance of punctuality in real-world railway network operation and the fact that fast passenger trains share the network with slow freight trains, Flatland version 3 introduces trains with different speeds and scheduling time windows. This paper introduces the Flatland 3 problem definitions and extends an award-winning MAPF-based software, which won the NeurIPS 2020 competition, to efficiently solve Flatland 3 problems. The resulting system won the Flatland 3 competition. We designed a new priority ordering for initial planning, a new neighbourhood selection strategy for efficient solution quality improvement with Multi-Agent Path Finding via Large Neighborhood Search(MAPF-LNS), and use MAPF-LNS for partially replanning the trains influenced by malfunction.

Multi-Agent Path Finding (MAPF) is an important core problem for many new and emerging industrial applications. Many works appear on this topic each year, and a large number of substantial advancements and performance improvements have been reported. Yet measuring overall progress in MAPF is difficult: there are many potential competitors, and the computational burden for comprehensive experimentation is prohibitively large. Moreover, detailed data from past experimentation is usually unavailable. In this work, we introduce a set of methodological and visualisation tools which can help the community establish clear indicators for state-of-the-art MAPF performance and which can facilitate large-scale comparisons between MAPF solvers. Our objectives are to lower the barrier of entry for new researchers and to further promote the study of MAPF, since progress in the area and the main challenges are made much clearer.

Elections where electors rank the candidates (or a subset of the candidates) in order of preference allow the collection of more information about the electors' intent. The most widely used election of this type is Instant-Runoff Voting (IRV), where candidates are eliminated one by one, until a single candidate holds the majority of the remaining ballots. Condorcet elections treat the election as a set of simultaneous decisions about each pair of candidates. The Condorcet winner is the candidate who beats all others in these pairwise contests. There are various proposals to determine a winner if no Condorcet winner exists. In this paper we show how we can efficiently audit Condorcet elections for a number of variations. We also compare the audit efficiency (how many ballots we expect to sample) of IRV and Condorcet elections., Comment: 15 pages, accepted for Voting'23. This version fixes some errors in one of the examples

Dynamically typed programming languages are popular in education and the software industry. While presenting a low barrier to entry, they suffer from run-time type errors and longer-term problems in code quality and maintainability. Statically typed languages, while showing strength in these aspects, lack in learnability and ease of use. In particular, fixing type errors poses challenges to both novice users and experts. Further, compiler-type error messages are presented in a static way that is biased toward the first occurrence of the error in the program code. To help users resolve such type errors, we introduce ChameleonIDE, a type debugging tool that presents type errors to the user in an unbiased way, allowing them to explore the full context of where the errors could occur. Programmers can interactively verify the steps of reasoning against their intention. Through three studies involving real programmers, we showed that ChameleonIDE is more effective in fixing type errors than traditional text-based error messages. This difference is more significant in harder tasks. Further, programmers actively using ChameleonIDE's interactive features are shown to be more efficient in fixing type errors than passively reading the type error output.

Instant-runoff voting (IRV) is used in several countries around the world. It requires voters to rank candidates in order of preference, and uses a counting algorithm that is more complex than systems such as first-past-the-post or scoring rules. An even more complex system, the single transferable vote (STV), is used when multiple candidates need to be elected. The complexity of these systems has made it difficult to audit the election outcomes. There is currently no known risk-limiting audit (RLA) method for STV, other than a full manual count of the ballots. A new approach to auditing these systems was recently proposed, based on a Dirichlet-tree model. We present a detailed analysis of this approach for ballot-polling Bayesian audits of IRV elections. We compared several choices for the prior distribution, including some approaches using a Bayesian bootstrap (equivalent to an improper prior). Our findings include that the bootstrap-based approaches can be adapted to perform similarly to a full Bayesian model in practice, and that an overly informative prior can give counter-intuitive results. Via carefully chosen examples, we show why creating an RLA with this model is challenging, but we also suggest ways to overcome this. As well as providing a practical and computationally feasible implementation of a Bayesian IRV audit, our work is important in laying the foundation for an RLA for STV elections., Comment: 17 pages, 6 figures. Presented at EIS 2022. This version contains minor corrections to match the final published version

The Euclidean shortest path problem (ESPP) is a well studied problem with many practical applications. Recently a new efficient online approach to this problem, RayScan, has been developed, based on ray shooting and polygon scanning. In this paper we show how we can improve RayScan by carefully reasoning about polygon scans. We also look into how RayScan could be applied in the single-source multi-target scenario, where logic during scanning is used to reduce the number of rays shots required. This improvement also helps in the single target case. We compare the improved RayScan+ against the state-of-the-art ESPP algorithm, illustrating the situations where it is better., Comment: submitted on SoCS 2021 (as extended abstract)

Ranked voting systems, such as instant-runoff voting (IRV) and single transferable vote (STV), are used in many places around the world. They are more complex than plurality and scoring rules, presenting a challenge for auditing their outcomes: there is no known risk-limiting audit (RLA) method for STV other than a full hand count. We present a new approach to auditing ranked systems that uses a statistical model, a Dirichlet-tree, that can cope with high-dimensional parameters in a computationally efficient manner. We demonstrate this approach with a ballot-polling Bayesian audit for IRV elections. Although the technique is not known to be risk-limiting, we suggest some strategies that might allow it to be calibrated to limit risk., Comment: 5 pages, 2 figures, accepted for E-Vote-ID 2022. This version has an updated URL for the software package

The rise of AI methods to make predictions and decisions has led to a pressing need for more explainable artificial intelligence (XAI) methods. One common approach for XAI is to produce a post-hoc explanation, explaining why a black box ML model made a certain prediction. Formal approaches to post-hoc explanations provide succinct reasons for why a prediction was made, as well as why not another prediction was made. But these approaches assume that features are independent and uniformly distributed. While this means that "why" explanations are correct, they may be longer than required. It also means the "why not" explanations may be suspect as the counterexamples they rely on may not be meaningful. In this paper, we show how one can apply background knowledge to give more succinct "why" formal explanations, that are presumably easier to interpret by humans, and give more accurate "why not" explanations. In addition, we show how to use existing rule induction techniques to efficiently extract background information from a dataset, and also how to report which background information was used to make an explanation, allowing a human to examine it if they doubt the correctness of the explanation.

This paper explains the main principles and some of the technical details for auditing the scanning and digitisation of the Australian Senate ballot papers. We give a short summary of the motivation for auditing paper ballots, explain the necessary supporting steps for a rigorous and transparent audit, and suggest some statistical methods that would be appropriate for the Australian Senate. 22 June 2022 Update: The update includes analysis of Senate preference data from the 2022 Australian election.

Risk-limiting audits (RLAs) are an increasingly important method for checking that the reported outcome of an election is, in fact, correct. Indeed, their use is increasingly being legislated. While effective methods for RLAs have been developed for many forms of election -- for example: first-past-the-post, instant-runoff voting, and D'Hondt elections -- auditing methods for single transferable vote (STV) elections have yet to be developed. STV elections are notoriously hard to reason about since there is a complex interaction of votes that change their value throughout the process. In this paper we present the first approach to risk-limiting audits for STV elections, restricted to the case of 2-seat STV elections., Comment: 16 pages

Multi-agent Pickup and Delivery (MAPD) is a challenging industrial problem where a team of robots is tasked with transporting a set of tasks, each from an initial location and each to a specified target location. Appearing in the context of automated warehouse logistics and automated mail sortation, MAPD requires first deciding which robot is assigned what task (i.e., Task Assignment or TA) followed by a subsequent coordination problem where each robot must be assigned collision-free paths so as to successfully complete its assignment (i.e., Multi-Agent Path Finding or MAPF). Leading methods in this area solve MAPD sequentially: first assigning tasks, then assigning paths. In this work we propose a new coupled method where task assignment choices are informed by actual delivery costs instead of by lower-bound estimates. The main ingredients of our approach are a marginal-cost assignment heuristic and a meta-heuristic improvement strategy based on Large Neighbourhood Search. As a further contribution, we also consider a variant of the MAPD problem where each robot can carry multiple tasks instead of just one. Numerical simulations show that our approach yields efficient and timely solutions and we report significant improvement compared with other recent methods from the literature.

Precondition inference is a non-trivial problem with important applications in program analysis and verification. We present a novel iterative method for automatically deriving preconditions for the safety and unsafety of programs. Each iteration maintains over-approximations of the set of safe and unsafe initial states; which are used to partition the program's initial states into those known to be safe, known to be unsafe and unknown. We then construct revised programs with those unknown initial states and iterate the procedure until the approximations are disjoint or some termination criteria are met. An experimental evaluation of the method on a set of software verification benchmarks shows that it can infer precise preconditions (sometimes optimal) that are not possible using previous methods., Comment: Paper presented at the 37th InternationalConference on Logic Programming (ICLP 2021), 16 pages. arXiv admin note: substantial text overlap with arXiv:1811.06771

This document provides a brief introduction to learned automated planning problem where the state transition function is in the form of a binarized neural network (BNN), presents a general MaxSAT encoding for this problem, and describes the four domains, namely: Navigation, Inventory Control, System Administrator and Cellda, that are submitted as benchmarks for MaxSAT Evaluation 2021.

Risk-limiting audits (RLAs), an ingredient in evidence-based elections, are increasingly common. They are a rigorous statistical means of ensuring that electoral results are correct, usually without having to perform an expensive full recount -- at the cost of some controlled probability of error. A recently developed approach for conducting RLAs, SHANGRLA, provides a flexible framework that can encompass a wide variety of social choice functions and audit strategies. Its flexibility comes from reducing sufficient conditions for outcomes to be correct to canonical `assertions' that have a simple mathematical form. Assertions have been developed for auditing various social choice functions including plurality, multi-winner plurality, super-majority, Hamiltonian methods, and instant runoff voting. However, there is no systematic approach to building assertions. Here, we show that assertions with linear dependence on transformations of the votes can easily be transformed to canonical form for SHANGRLA. We illustrate the approach by constructing assertions for party-list elections such as Hamiltonian free list elections and elections using the D'Hondt method, expanding the set of social choice functions to which SHANGRLA applies directly., Comment: 16 pages

Multi-Agent Path Finding (MAPF) is a challenging combinatorial problem that asks us to plan collision-free paths for a team of cooperative agents. In this work, we show that one of the reasons why MAPF is so hard to solve is due to a phenomenon called pairwise symmetry, which occurs when two agents have many different paths to their target locations, all of which appear promising, but every combination of them results in a collision. We identify several classes of pairwise symmetries and show that each one arises commonly in practice and can produce an exponential explosion in the space of possible collision resolutions, leading to unacceptable runtimes for current state-of-the-art (bounded-sub)optimal MAPF algorithms. We propose a variety of reasoning techniques that detect the symmetries efficiently as they arise and resolve them by using specialized constraints to eliminate all permutations of pairwise colliding paths in a single branching step. We implement these ideas in the context of the leading optimal MAPF algorithm CBS and show that the addition of the symmetry reasoning techniques can have a dramatic positive effect on its performance - we report a reduction in the number of node expansions by up to four orders of magnitude and an increase in scalability by up to thirty times. These gains allow us to solve to optimality a variety of challenging MAPF instances previously considered out of reach for CBS.

During Multi-Agent Path Finding (MAPF) problems, agents can be delayed by unexpected events. To address such situations recent work describes k-Robust Conflict-BasedSearch (k-CBS): an algorithm that produces coordinated and collision-free plan that is robust for up to k delays. In this work we introducing a variety of pairwise symmetry breaking constraints, specific to k-robust planning, that can efficiently find compatible and optimal paths for pairs of conflicting agents. We give a thorough description of the new constraints and report large improvements to success rate ina range of domains including: (i) classic MAPF benchmarks;(ii) automated warehouse domains and; (iii) on maps from the 2019 Flatland Challenge, a recently introduced railway domain where k-robust planning can be fruitfully applied to schedule trains., Comment: 8 pages. Accepted by Thirty-Fifth AAAI Conference on Artificial Intelligence

Presidential primaries are a critical part of the United States Presidential electoral process, since they are used to select the candidates in the Presidential election. While methods differ by state and party, many primaries involve proportional delegate allocation using the so-called Hamilton method. In this paper we show how to conduct risk-limiting audits for delegate allocation elections using variants of the Hamilton method where the viability of candidates is determined either by a plurality vote or using instant runoff voting. Experiments on real-world elections show that we can audit primary elections to high confidence (small risk limits) usually at low cost., Comment: 16 pages

Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI. Rule-based models, such as decision trees, decision lists, and decision sets, are conventionally deemed to be the most interpretable. Recent work uses propositional satisfiability (SAT) solving (and its optimization variants) to generate minimum-size decision sets. Motivated by limited practical scalability of these earlier methods, this paper proposes a novel approach to learn minimum-size decision sets by enumerating individual rules of the target decision set independently of each other, and then solving a set cover problem to select a subset of rules. The approach makes use of modern maximum satisfiability and integer linear programming technologies. Experiments on a wide range of publicly available datasets demonstrate the advantage of the new approach over the state of the art in SAT-based decision set learning.

The predict+optimize problem combines machine learning ofproblem coefficients with a combinatorial optimization prob-lem that uses the predicted coefficients. While this problemcan be solved in two separate stages, it is better to directlyminimize the optimization loss. However, this requires dif-ferentiating through a discrete, non-differentiable combina-torial function. Most existing approaches use some form ofsurrogate gradient. Demirovicet alshowed how to directlyexpress the loss of the optimization problem in terms of thepredicted coefficients as a piece-wise linear function. How-ever, their approach is restricted to optimization problemswith a dynamic programming formulation. In this work wepropose a novel divide and conquer algorithm to tackle op-timization problems without this restriction and predict itscoefficients using the optimization loss. We also introduce agreedy version of this approach, which achieves similar re-sults with less computation. We compare our approach withother approaches to the predict+optimize problem and showwe can successfully tackle some hard combinatorial problemsbetter than other predict+optimize methods.

Decision lists are one of the most easily explainable machine learning models. Given the renewed emphasis on explainable machine learning decisions, this machine learning model is increasingly attractive, combining small size and clear explainability. In this paper, we show for the first time how to construct optimal "perfect" decision lists which are perfectly accurate on the training data, and minimal in size, making use of modern SAT solving technology. We also give a new method for determining optimal sparse decision lists, which trade off size and accuracy. We contrast the size and test accuracy of optimal decisions lists versus optimal decision sets, as well as other state-of-the-art methods for determining optimal decision lists. We also examine the size of average explanations generated by decision sets and decision lists.

Nonlinear metrics, such as the F1-score, Matthews correlation coefficient, and Fowlkes-Mallows index, are often used to evaluate the performance of machine learning models, in particular, when facing imbalanced datasets that contain more samples of one class than the other. Recent optimal decision tree algorithms have shown remarkable progress in producing trees that are optimal with respect to linear criteria, such as accuracy, but unfortunately nonlinear metrics remain a challenge. To address this gap, we propose a novel algorithm based on bi-objective optimisation, which treats misclassifications of each binary class as a separate objective. We show that, for a large class of metrics, the optimal tree lies on the Pareto frontier. Consequently, we obtain the optimal tree by using our method to generate the set of all nondominated trees. To the best of our knowledge, this is the first method to compute provably optimal decision trees for nonlinear metrics. Our approach leads to a trade-off when compared to optimising linear metrics: the resulting trees may be more desirable according to the given nonlinear metric at the expense of higher runtimes. Nevertheless, the experiments illustrate that runtimes are reasonable for majority of the tested datasets.

As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type of model with unordered rules, which explains each prediction with a single rule. In order to be easy for humans to understand, these rules must be concise. Earlier work on generating optimal decision sets first minimizes the number of rules, and then minimizes the number of literals, but the resulting rules can often be very large. Here we consider a better measure, namely the total size of the decision set in terms of literals. So we are not driven to a small set of rules which require a large number of literals. We provide the first approach to determine minimum-size decision sets that achieve minimum empirical risk and then investigate sparse alternatives where we trade accuracy for size. By finding optimal solutions we show we can build decision set classifiers that are almost as accurate as the best heuristic methods, but far more concise, and hence more explainable.

Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy. A commonly criticised point, however, is that the resulting trees may not necessarily be the best representation of the data in terms of accuracy and size. In recent years, this motivated the development of optimal classification tree algorithms that globally optimise the decision tree in contrast to heuristic methods that perform a sequence of locally optimal decisions. We follow this line of work and provide a novel algorithm for learning optimal classification trees based on dynamic programming and search. Our algorithm supports constraints on the depth of the tree and number of nodes. The success of our approach is attributed to a series of specialised techniques that exploit properties unique to classification trees. Whereas algorithms for optimal classification trees have traditionally been plagued by high runtimes and limited scalability, we show in a detailed experimental study that our approach uses only a fraction of the time required by the state-of-the-art and can handle datasets with tens of thousands of instances, providing several orders of magnitude improvements and notably contributing towards the practical realisation of optimal decision trees.

Errors are inevitable in the implementation of any complex process. Here we examine the effect of random errors on Single Transferable Vote (STV) elections, a common approach to deciding multi-seat elections. It is usually expected that random errors should have nearly equal effects on all candidates, and thus be fair. We find to the contrary that random errors can introduce systematic bias into election results. This is because, even if the errors are random, votes for different candidates occur in different patterns that are affected differently by random errors. In the STV context, the most important effect of random errors is to invalidate the ballot. This removes far more votes for those candidates whose supporters tend to list a lot of preferences, because their ballots are much more likely to be invalidated by random error. Different validity rules for different voting styles mean that errors are much more likely to penalise some types of votes than others. For close elections this systematic bias can change the result of the election.

The City and County of San Francisco, CA, has used Instant Runoff Voting (IRV) for some elections since 2004. This report describes the first ever process pilot of Risk Limiting Audits for IRV, for the San Francisco District Attorney's race in November, 2019. We found that the vote-by-mail outcome could be efficiently audited to well under the 0.05 risk limit given a sample of only 200 ballots. All the software we developed for the pilot is open source.