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Subdimensional Expansion for Multi-objective Multi-agent Path Finding

arXiv.org Artificial Intelligence

Conventional multi-agent path planners typically determine a path that optimizes a single objective, such as path length. Many applications, however, may require multiple objectives, say time-to-completion and fuel use, to be simultaneously optimized in the planning process. Often, these criteria may not be readily compared and sometimes lie in competition with each other. Simply applying standard multi-objective search algorithms to multi-agent path finding may prove to be inefficient because the size of the space of possible solutions, i.e., the Pareto-optimal set, can grow exponentially with the number of agents (the dimension of the search space). This paper presents an approach that bypasses this so-called curse of dimensionality by leveraging our prior multi-agent work with a framework called subdimensional expansion. One example of subdimensional expansion, when applied to A*, is called M* and M* was limited to a single objective function. We combine principles of dominance and subdimensional expansion to create a new algorithm named multi-objective M* (MOM*), which dynamically couples agents for planning only when those agents have to "interact" with each other. MOM* computes the complete Pareto-optimal set for multiple agents efficiently and naturally trades off sub-optimal approximations of the Pareto-optimal set and computational efficiency. Our approach is able to find the complete Pareto-optimal set for problem instances with hundreds of solutions which the standard multi-objective A* algorithms could not find within a bounded time.


Synthesizing Pareto-Optimal Interpretations for Black-Box Models

arXiv.org Artificial Intelligence

We present a new multi-objective optimization approach for synthesizing interpretations that "explain" the behavior of black-box machine learning models. Constructing human-understandable interpretations for black-box models often requires balancing conflicting objectives. A simple interpretation may be easier to understand for humans while being less precise in its predictions vis-a-vis a complex interpretation. Existing methods for synthesizing interpretations use a single objective function and are often optimized for a single class of interpretations. In contrast, we provide a more general and multi-objective synthesis framework that allows users to choose (1) the class of syntactic templates from which an interpretation should be synthesized, and (2) quantitative measures on both the correctness and explainability of an interpretation. For a given black-box, our approach yields a set of Pareto-optimal interpretations with respect to the correctness and explainability measures. We show that the underlying multi-objective optimization problem can be solved via a reduction to quantitative constraint solving, such as weighted maximum satisfiability. To demonstrate the benefits of our approach, we have applied it to synthesize interpretations for black-box neural-network classifiers. Our experiments show that there often exists a rich and varied set of choices for interpretations that are missed by existing approaches.


Multi-objective Conflict-based Search for Multi-agent Path Finding

arXiv.org Artificial Intelligence

Conventional multi-agent path planners typically compute an ensemble of paths while optimizing a single objective, such as path length. However, many applications may require multiple objectives, say fuel consumption and completion time, to be simultaneously optimized during planning and these criteria may not be readily compared and sometimes lie in competition with each other. Naively applying existing multi-objective search algorithms to multi-agent path finding may prove to be inefficient as the size of the space of possible solutions, i.e., the Pareto-optimal set, can grow exponentially with the number of agents (the dimension of the search space). This article presents an approach named Multi-objective Conflict-based Search (MO-CBS) that bypasses this so-called curse of dimensionality by leveraging prior Conflict-based Search (CBS), a well-known algorithm for single-objective multi-agent path finding, and principles of dominance from multi-objective optimization literature. We prove that MO-CBS is able to compute the entire Pareto-optimal set. Our results show that MO-CBS can solve problem instances with hundreds of Pareto-optimal solutions which the standard multi-objective A* algorithms could not find within a bounded time.


Multi-criteria Anomaly Detection using Pareto Depth Analysis

Neural Information Processing Systems

We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single criterion, such as Euclidean distance. However, in many cases there may not exist a single dissimilarity measure that captures all possible anomalous patterns. In such a case, multiple criteria can be defined, and one can test for anomalies by scalarizing the multiple criteria by taking some linear combination of them. If the importance of the different criteria are not known in advance, the algorithm may need to be executed multiple times with different choices of weights in the linear combination. In this paper, we introduce a novel non-parametric multi-criteria anomaly detection method using Pareto depth analysis (PDA). PDA uses the concept of Pareto optimality to detect anomalies under multiple criteria without having to run an algorithm multiple times with different choices of weights. The proposed PDA approach scales linearly in the number of criteria and is provably better than linear combinations of the criteria.


Learning Interpretable Models Through Multi-Objective Neural Architecture Search

arXiv.org Artificial Intelligence

Monumental advances in deep learning have led to unprecedented achievements across a multitude of domains. While the performance of deep neural networks is indubitable, the architectural design and interpretability of such models are nontrivial. Research has been introduced to automate the design of neural network architectures through neural architecture search (NAS). Recent progress has made these methods more pragmatic by exploiting distributed computation and novel optimization algorithms. However, there is little work in optimizing architectures for interpretability. To this end, we propose a multi-objective distributed NAS framework that optimizes for both task performance and introspection. We leverage the non-dominated sorting genetic algorithm (NSGA-II) and explainable AI (XAI) techniques to reward architectures that can be better comprehended by humans. The framework is evaluated on several image classification datasets. We demonstrate that jointly optimizing for introspection ability and task error leads to more disentangled architectures that perform within tolerable error.