arXiv subjects

Derek Long

Publications and source records attributed to Derek Long.

16 recordsLinked to original sources

arXiv2026

Near-Linear Time Generalized Sinkhorn Algorithms for Bounded Genus Graphs

We present GenusSink, a new class of approximate generalized Sinkhorn algorithms with shortest-path-distance costs for bounded genus (e.g. planar) graphs, providing near-linear time: (1) pre-processing, (2) iteration step, (3) final transport plan matrix querying and near-linear memory. Graphs handled by GenusSink include in particular planar graphs and bounded-genus meshes approximating 3D objects. GenusSink addresses total quadratic time complexity of its brute-force counterpart by leveraging separator-based decomposition of graphs, computational geometry techniques, and new results on fast matrix-vector multiplications with generalized distance matrices, using, in particular, Fourier analysis and low displacement rank theory. It is inspired by recent breakthroughs in graph theory on approximating bounded genus metrics with small treewidth metrics \citep{minor-free-paper}. The graph-centric approach enables us to target optimal transport problem with the corresponding distributions defined on the manifolds approximated by weighted graphs and with cost functions given by geodesic distances. We conduct rigorous theoretical analysis of GenusSink, provide practical implementations, leveraging newly introduced in this paper \textit{separation graph field integrators} (S-GFIs) data structures and present empirical verification. GenusSink provides orders of magnitude more accurate computations than other efficient Sinkhorn algorithms, while still guaranteeing significant computational improvements, as compared to the baseline. As a by-product of the developed methods, we show that GenusSink is \textbf{numerically equivalent} to the brute-force geodesic Sinkhorn algorithm on $n$-vertex graphs with treewidth $O(\log \log (n))$ (e.g. on trees).

cs.DS↗

arXiv2026

Manifold Random Features

We present a new paradigm for creating random features to approximate bi-variate functions (in particular, kernels) defined on general manifolds. This new mechanism of Manifold Random Features (MRFs) leverages discretization of the manifold and the recently introduced technique of Graph Random Features (GRFs) to learn continuous fields on manifolds. Those fields are used to find continuous approximation mechanisms that otherwise, in general scenarios, cannot be derived analytically. MRFs provide positive and bounded features, a key property for accurate, low-variance approximation. We show deep asymptotic connection between GRFs, defined on discrete graph objects, and continuous random features used for regular kernels. As a by-product of our method, we re-discover recently introduced mechanism of Gaussian kernel approximation applied in particular to improve linear-attention Transformers, considering simple random walks on graphs and by-passing original complex mathematical computations. We complement our algorithm with a rigorous theoretical analysis and verify in thorough experimental studies.

cs.LG↗

arXiv2025

Shift-Aware Gaussian-Supremum Validation for Wasserstein-DRO CVaR Portfolios

We study portfolio selection with a Conditional Value-at-Risk (CVaR) constraint under distribution shift and serial dependence. While Wasserstein distributionally robust optimization (DRO) offers tractable protection via an ambiguity ball around empirical data, choosing the ball radius is delicate: large radii are conservative, small radii risk violation under regime change. We propose a shift-aware Gaussian-supremum (GS) validation framework for Wasserstein-DRO CVaR portfolios, building on the work by Lam and Qian (2019). Phase I of the framework generates a candidate path by solving the exact reformulation of the robust CVaR constraint over a grid of Wasserstein radii. Phase II of the framework learns a target deployment law $Q$ by density-ratio reweighting of a time-ordered validation fold, computes weighted CVaR estimates, and calibrates a simultaneous upper confidence band via a block multiplier bootstrap to account for dependence. We select the least conservative feasible portfolio (or abstain if the effective sample size collapses). Theoretically, we extend the normalized GS validator to non-i.i.d. financial data: under weak dependence and regularity of the weighted scores, any portfolio passing our validator satisfies the CVaR limit under $Q$ with probability at least $1-\beta$; the Wasserstein term contributes a deterministic margin $(\delta/\alpha)\|x\|_*$. Empirical results indicate improved return-risk trade-offs versus the naive baseline.

stat.ME↗

arXiv2022

Autonomous Passage Planning for a Polar Vessel

We introduce a method for long-distance maritime route planning in polar regions, taking into account complex changing environmental conditions. The method allows the construction of optimised routes, describing the three main stages of the process: discrete modelling of the environmental conditions using a non-uniform mesh, the construction of mesh-optimal paths, and path smoothing. In order to account for different vehicle properties we construct a series of data driven functions that can be applied to the environmental mesh to determine the speed limitations and fuel requirements for a given vessel and mesh cell, representing these quantities graphically and geospatially. In describing our results, we demonstrate an example use case for route planning for the polar research ship the RRS Sir David Attenborough (SDA), accounting for ice-performance characteristics and validating the spatial-temporal route construction in the region of the Weddell Sea, Antarctica. We demonstrate the versatility of this route construction method by demonstrating that routes change depending on the seasonal sea ice variability, differences in the route-planning objective functions used, and the presence of other environmental conditions such as currents. To demonstrate the generality of our approach, we present examples in the Arctic Ocean and the Baltic Sea. The techniques outlined in this manuscript are generic and can therefore be applied to vessels with different characteristics. Our approach can have considerable utility beyond just a single vessel planning procedure, and we outline how this workflow is applicable to a wider community, e.g. commercial and passenger shipping.

cs.RO↗

arXiv2022

Understanding a Robot's Guiding Ethical Principles via Automatically Generated Explanations

The continued development of robots has enabled their wider usage in human surroundings. Robots are more trusted to make increasingly important decisions with potentially critical outcomes. Therefore, it is essential to consider the ethical principles under which robots operate. In this paper we examine how contrastive and non-contrastive explanations can be used in understanding the ethics of robot action plans. We build upon an existing ethical framework to allow users to make suggestions about plans and receive automatically generated contrastive explanations. Results of a user study indicate that the generated explanations help humans to understand the ethical principles that underlie a robot's plan.

cs.AI↗

arXiv2021

Non-invasive hemodynamic analysis for aortic regurgitation using computational fluid dynamics and deep learning

Changes in cardiovascular hemodynamics are closely related to the development of aortic regurgitation, a type of valvular heart disease. Metrics derived from blood flows are used to indicate aortic regurgitation onset and evaluate its severity. These metrics can be non-invasively obtained using four-dimensional (4D) flow magnetic resonance imaging (MRI), where accuracy is primarily dependent on spatial resolution. However, insufficient resolution often results from limitations in 4D flow MRI and complex aortic regurgitation hemodynamics. To address this, computational fluid dynamics simulations were transformed into synthetic 4D flow MRI data and used to train a variety of neural networks. These networks generated super resolution, full-field phase images with an upsample factor of 4. Results showed decreased velocity error, high structural similarity scores, and improved learning capabilities from previous work. Further validation was performed on two sets of in-vivo 4D flow MRI data and demonstrated success in de-noising flow images. This approach presents an opportunity to comprehensively analyse aortic regurgitation hemodynamics in a non-invasive manner.

cs.CV↗

arXiv2021

Long-Range Route-planning for Autonomous Vehicles in the Polar Oceans

There is an increasing demand for piloted autonomous underwater vehicles (AUVs) to operate in polar ice conditions. At present, AUVs are deployed from ships and directly human-piloted in these regions, entailing a high carbon cost and limiting the scope of operations. A key requirement for long-term autonomous missions is a long-range route planning capability that is aware of the changing ice conditions. In this paper we address the problem of automating long-range route-planning for AUVs operating in the Southern Ocean. We present the route-planning method and results showing that efficient, ice-avoiding, long-distance traverses can be planned.

cs.RO↗

arXiv2021

Improving Search by Utilizing State Information in OPTIC Planners Compilation to LP

Automated planners are computer tools that allow autonomous agents to make strategies and decisions by determining a set of actions for the agent that to take, which will carry a system from a given initial state to the desired goal state. Many planners are domain-independent, allowing their deployment in a variety of domains. Such is the broad family of OPTIC planners. These planners perform Forward Search and call a Linear Programming (LP) solver multiple times at every state to check for consistency and to set bounds on the numeric variables. These checks can be computationally costly, especially in real-life applications. This paper suggests a method for identifying information about the specific state being evaluated, allowing the formulation of the equations to facilitate better solver selection and faster LP solving. The usefulness of the method is demonstrated in six domains and is shown to enhance performance significantly.

cs.AI↗

arXiv2021

Efficient Temporal Piecewise-Linear Numeric Planning with Lazy Consistency Checking

Temporal planning often involves numeric effects that are directly proportional to their action's duration. These include continuous effects, where a numeric variable is subjected to a rate of change while the action is being executed, and discrete duration-dependent effects, where the variable is updated instantaneously but the magnitude of such change is computed from the action's duration. When these effects are linear, state--of--the--art temporal planners often make use of Linear Programming to ensure that these numeric updates are consistent with the chosen start times and durations of the plan's actions. This is typically done for each evaluated state as part of the search process. This exhaustive approach is not scalable to solve real-world problems that require long plans, because the linear program's size becomes larger and slower to solve. In this work we propose techniques that minimise this overhead by computing these checks more selectively and formulating linear programs that have a smaller footprint. The effectiveness of these techniques is demonstrated on domains that use a mix of discrete and continuous effects, which is typical of real-world planning problems. The resultant planner also outperforms most state-of-the-art temporal-numeric and hybrid planners, in terms of both coverage and scalability.

cs.AI↗

arXiv2021

D-VAL: An automatic functional equivalence validation tool for planning domain models

This paper introduces an approach to validate the functional equivalence of planning domain models. Validating the functional equivalence of planning domain models is the problem of formally confirming that two planning domain models can be used to solve the same set of problems for any set of objects. The need for techniques to validate the functional equivalence of planning domain models has been highlighted in previous research and has applications in model learning, development and extension. We prove the soundness and completeness of our method. We also develop D-VAL, an automatic functional equivalence validation tool for planning domain models. Empirical evaluation shows that D-VAL validates the functional equivalence of all examined domains in less than 43 seconds. Additionally, we provide a benchmark to evaluate the feasibility and performance of this and future related work.

cs.AI↗

arXiv2021

Contrastive Explanations of Plans Through Model Restrictions

In automated planning, the need for explanations arises when there is a mismatch between a proposed plan and the user's expectation. We frame Explainable AI Planning in the context of the plan negotiation problem, in which a succession of hypothetical planning problems are generated and solved. The object of the negotiation is for the user to understand and ultimately arrive at a satisfactory plan. We present the results of a user study that demonstrates that when users ask questions about plans, those questions are contrastive, i.e. "why A rather than B?". We use the data from this study to construct a taxonomy of user questions that often arise during plan negotiation. We formally define our approach to plan negotiation through model restriction as an iterative process. This approach generates hypothetical problems and contrastive plans by restricting the model through constraints implied by user questions. We formally define model-based compilations in PDDL2.1 of each constraint derived from a user question in the taxonomy, and empirically evaluate the compilations in terms of computational complexity. The compilations were implemented as part of an explanation framework that employs iterative model restriction. We demonstrate its benefits in a second user study.

cs.AI↗

arXiv2020

Towards Contrastive Explanations for Comparing the Ethics of Plans

The development of robotics and AI agents has enabled their wider usage in human surroundings. AI agents are more trusted to make increasingly important decisions with potentially critical outcomes. It is essential to consider the ethical consequences of the decisions made by these systems. In this paper, we present how contrastive explanations can be used for comparing the ethics of plans. We build upon an existing ethical framework to allow users to make suggestions to plans and receive contrastive explanations.

cs.AI↗

arXiv2017

Explainable Planning

As AI is increasingly being adopted into application solutions, the challenge of supporting interaction with humans is becoming more apparent. Partly this is to support integrated working styles, in which humans and intelligent systems cooperate in problem-solving, but also it is a necessary step in the process of building trust as humans migrate greater responsibility to such systems. The challenge is to find effective ways to communicate the foundations of AI-driven behaviour, when the algorithms that drive it are far from transparent to humans. In this paper we consider the opportunities that arise in AI planning, exploiting the model-based representations that form a familiar and common basis for communication with users, while acknowledging the gap between planning algorithms and human problem-solving.

cs.AI↗

arXiv2014

A Hybrid LP-RPG Heuristic for Modelling Numeric Resource Flows in Planning

Although the use of metric fluents is fundamental to many practical planning problems, the study of heuristics to support fully automated planners working with these fluents remains relatively unexplored. The most widely used heuristic is the relaxation of metric fluents into interval-valued variables --- an idea first proposed a decade ago. Other heuristics depend on domain encodings that supply additional information about fluents, such as capacity constraints or other resource-related annotations. A particular challenge to these approaches is in handling interactions between metric fluents that represent exchange, such as the transformation of quantities of raw materials into quantities of processed goods, or trading of money for materials. The usual relaxation of metric fluents is often very poor in these situations, since it does not recognise that resources, once spent, are no longer available to be spent again. We present a heuristic for numeric planning problems building on the propositional relaxed planning graph, but using a mathematical program for numeric reasoning. We define a class of producer--consumer planning problems and demonstrate how the numeric constraints in these can be modelled in a mixed integer program (MIP). This MIP is then combined with a metric Relaxed Planning Graph (RPG) heuristic to produce an integrated hybrid heuristic. The MIP tracks resource use more accurately than the usual relaxation, but relaxes the ordering of actions, while the RPG captures the causal propositional aspects of the problem. We discuss how these two components interact to produce a single unified heuristic and go on to explore how further numeric features of planning problems can be integrated into the MIP. We show that encoding a limited subset of the propositional problem to augment the MIP can yield more accurate guidance, partly by exploiting structure such as propositional landmarks and propositional resources. Our results show that the use of this heuristic enhances scalability on problems where numeric resource interaction is key in finding a solution.

cs.AI↗

arXiv2014

COLIN: Planning with Continuous Linear Numeric Change

In this paper we describe COLIN, a forward-chaining heuristic search planner, capable of reasoning with COntinuous LINear numeric change, in addition to the full temporal semantics of PDDL. Through this work we make two advances to the state-of-the-art in terms of expressive reasoning capabilities of planners: the handling of continuous linear change, and the handling of duration-dependent effects in combination with duration inequalities, both of which require tightly coupled temporal and numeric reasoning during planning. COLIN combines FF-style forward chaining search, with the use of a Linear Program (LP) to check the consistency of the interacting temporal and numeric constraints at each state. The LP is used to compute bounds on the values of variables in each state, reducing the range of actions that need to be considered for application. In addition, we develop an extension of the Temporal Relaxed Planning Graph heuristic of CRIKEY3, to support reasoning directly with continuous change. We extend the range of task variables considered to be suitable candidates for specifying the gradient of the continuous numeric change effected by an action. Finally, we explore the potential for employing mixed integer programming as a tool for optimising the timestamps of the actions in the plan, once a solution has been found. To support this, we further contribute a selection of extended benchmark domains that include continuous numeric effects. We present results for COLIN that demonstrate its scalability on a range of benchmarks, and compare to existing state-of-the-art planners.

cs.AI↗

arXiv2014

Plan-based Policies for Efficient Multiple Battery Load Management

Efficient use of multiple batteries is a practical problem with wide and growing application. The problem can be cast as a planning problem under uncertainty. We describe the approach we have adopted to modelling and solving this problem, seen as a Markov Decision Problem, building effective policies for battery switching in the face of stochastic load profiles. Our solution exploits and adapts several existing techniques: planning for deterministic mixed discrete-continuous problems and Monte Carlo sampling for policy learning. The paper describes the development of planning techniques to allow solution of the non-linear continuous dynamic models capturing the battery behaviours. This approach depends on carefully handled discretisation of the temporal dimension. The construction of policies is performed using a classification approach and this idea offers opportunities for wider exploitation in other problems. The approach and its generality are described in the paper. Application of the approach leads to construction of policies that, in simulation, significantly outperform those that are currently in use and the best published solutions to the battery management problem. We achieve solutions that achieve more than 99% efficiency in simulation compared with the theoretical limit and do so with far fewer battery switches than existing policies. Behaviour of physical batteries does not exactly match the simulated models for many reasons, so to confirm that our theoretical results can lead to real measured improvements in performance we also conduct and report experiments using a physical test system. These results demonstrate that we can obtain 5%-15% improvement in lifetimes in the case of a two battery system.

cs.AI↗