arXiv subjects

Peter J. Stuckey

Publications and source records attributed to Peter J. Stuckey.

At least 55 records · Page 3Linked to original sources

arXiv2022

Auditing Ranked Voting Elections with Dirichlet-Tree Models: First Steps

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.

stat.AP↗

arXiv2022

MurTree: Optimal Classification Trees via Dynamic Programming and Search

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.

cs.LG↗

arXiv2022

Assessing the accuracy of the Australian Senate count: Key steps for a rigorous and transparent audit

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.

stat.AP↗

arXiv2021

A First Approach to Risk-Limiting Audits for Single Transferable Vote Elections

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.

cs.CY↗

arXiv2021

Symmetry Breaking for k-Robust Multi-Agent Path Finding

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.

cs.AI↗

arXiv2021

Integrated Task Assignment and Path Planning for Capacitated Multi-Agent Pickup and Delivery

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.

cs.MA↗

arXiv2021

Optimal Decision Trees for Nonlinear Metrics

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.

cs.LG↗

arXiv2021

Assertion-Based Approaches to Auditing Complex Elections, with Application to Party-List Proportional Elections

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.

cs.CY↗

arXiv2021

Transformation-Enabled Precondition Inference

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.

cs.PL↗

arXiv2021

Planning with Learned Binarized Neural Networks Benchmarks for MaxSAT Evaluation 2021

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.

cs.AI↗

arXiv2021

Auditing Hamiltonian Elections

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.

cs.CY↗

arXiv2021

Pairwise Symmetry Reasoning for Multi-Agent Path Finding Search

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.

cs.AI↗

arXiv2021

A Scalable Two Stage Approach to Computing Optimal Decision Sets

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.

cs.AI↗

arXiv2020

Divide and Learn: A Divide and Conquer Approach for Predict+Optimize

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.

cs.LG↗

arXiv2020

Optimal Decision Lists using SAT

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.

cs.AI↗

arXiv2020

Random errors are not necessarily politically neutral

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.

cs.CY↗

arXiv2020

Computing Optimal Decision Sets with SAT

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.

cs.AI↗

arXiv2020

You can do RLAs for IRV

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.

cs.CY↗