DataSP: A Differential All-to-All Shortest Path Algorithm for Learning Costs and Predicting Paths with Context

• URL: http://arxiv.org/abs/2405.04923v2
• Date: Thu, 30 May 2024 12:04:17 GMT
• Title: DataSP: A Differential All-to-All Shortest Path Algorithm for Learning Costs and Predicting Paths with Context
• Authors: Alan A. Lahoud, Erik Schaffernicht, Johannes A. Stork,
• Abstract summary: This paper introduces DataSP, a differentiable all-to-all shortest path algorithm to facilitate learning latent costs from trajectories. Complex latent cost functions from contextual features can be represented in the algorithm through a neural network approximation. We show that DataSP outperforms state-of-the-art machine learning approaches in predicting paths on graphs.
• Score: 4.202961704179733
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning latent costs of transitions on graphs from trajectories demonstrations under various contextual features is challenging but useful for path planning. Yet, existing methods either oversimplify cost assumptions or scale poorly with the number of observed trajectories. This paper introduces DataSP, a differentiable all-to-all shortest path algorithm to facilitate learning latent costs from trajectories. It allows to learn from a large number of trajectories in each learning step without additional computation. Complex latent cost functions from contextual features can be represented in the algorithm through a neural network approximation. We further propose a method to sample paths from DataSP in order to reconstruct/mimic observed paths' distributions. We prove that the inferred distribution follows the maximum entropy principle. We show that DataSP outperforms state-of-the-art differentiable combinatorial solver and classical machine learning approaches in predicting paths on graphs.

Related papers

• SSP-GNN: Learning to Track via Bilevel Optimization [3.1889516673296807]
  We propose a graph-based tracking formulation for multi-object tracking (MOT) Our method applies a successive shortest paths (SSP) algorithm to a tracking graph defined over a batch of frames. The edge costs in this tracking graph are computed via a message-passing network, a graph neural network (GNN) variant.
  arXiv  Detail & Related papers  (2024-07-05T07:23:51Z)
• Generalized Differentiable RANSAC [95.95627475224231]
  $nabla$-RANSAC is a differentiable RANSAC that allows learning the entire randomized robust estimation pipeline. $nabla$-RANSAC is superior to the state-of-the-art in terms of accuracy while running at a similar speed to its less accurate alternatives.
  arXiv  Detail & Related papers  (2022-12-26T15:13:13Z)
• TransPath: Learning Heuristics For Grid-Based Pathfinding via Transformers [64.88759709443819]
  We suggest learning the instance-dependent proxies that are supposed to notably increase the efficiency of the search. The first proxy we suggest to learn is the correction factor, i.e. the ratio between the instance independent cost-to-go estimate and the perfect one. The second proxy is the path probability, which indicates how likely the grid cell is lying on the shortest path.
  arXiv  Detail & Related papers  (2022-12-22T14:26:11Z)
• Learning Graph Search Heuristics [48.83557172525969]
  We present PHIL (Path Heuristic with Imitation Learning), a novel neural architecture and a training algorithm for discovering graph search and navigations from data. Our function learns graph embeddings useful for inferring node distances, runs in constant time independent of graph sizes, and can be easily incorporated in an algorithm such as A* at test time. Experiments show that PHIL reduces the number of explored nodes compared to state-of-the-art methods on benchmark datasets by 58.5% on average.
  arXiv  Detail & Related papers  (2022-12-07T22:28:00Z)
• One-Pass Learning via Bridging Orthogonal Gradient Descent and Recursive Least-Squares [8.443742714362521]
  We develop an algorithm for one-pass learning which seeks to perfectly fit every new datapoint while changing the parameters in a direction that causes the least change to the predictions on previous datapoints. Our algorithm uses the memory efficiently by exploiting the structure of the streaming data via an incremental principal component analysis (IPCA) Our experiments show the effectiveness of the proposed method compared to the baselines.
  arXiv  Detail & Related papers  (2022-07-28T02:01:31Z)
• Condensing Graphs via One-Step Gradient Matching [50.07587238142548]
  We propose a one-step gradient matching scheme, which performs gradient matching for only one single step without training the network weights. Our theoretical analysis shows this strategy can generate synthetic graphs that lead to lower classification loss on real graphs. In particular, we are able to reduce the dataset size by 90% while approximating up to 98% of the original performance.
  arXiv  Detail & Related papers  (2022-06-15T18:20:01Z)
• GraphWalks: Efficient Shape Agnostic Geodesic Shortest Path Estimation [93.60478281489243]
  We propose a learnable network to approximate geodesic paths on 3D surfaces. The proposed method provides efficient approximations of the shortest paths and geodesic distances estimations.
  arXiv  Detail & Related papers  (2022-05-30T16:22:53Z)
• Simple Stochastic and Online Gradient DescentAlgorithms for Pairwise Learning [65.54757265434465]
  Pairwise learning refers to learning tasks where the loss function depends on a pair instances. Online descent (OGD) is a popular approach to handle streaming data in pairwise learning. In this paper, we propose simple and online descent to methods for pairwise learning.
  arXiv  Detail & Related papers  (2021-11-23T18:10:48Z)
• Neural Weighted A*: Learning Graph Costs and Heuristics with Differentiable Anytime A* [12.117737635879037]
  Recent works related to data-driven planning aim at learning either cost functions or planner functions, but not both. We propose Neural Weighted A*, a differentiable anytime planner able to produce improved representations of planar maps as graph costs and planners. We experimentally show the validity of our claims by testing Neural Weighted A* against several baselines, introducing a novel, tile-based navigation dataset.
  arXiv  Detail & Related papers  (2021-05-04T13:17:30Z)
• Learning to Sparsify Travelling Salesman Problem Instances [0.5985204759362747]
  We use a pruning machine learning as a pre-processing step followed by an exact Programming approach to sparsify the travelling salesman problem. Our learning approach requires very little training data and is amenable to mathematical analysis.
  arXiv  Detail & Related papers  (2021-04-19T14:35:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.