IO-LVM: Inverse optimization latent variable models with applications to inferring and explaining paths

Alan Lahoud, Erik Schaffernicht, Johannes A. Stork

Keywords: deep learning, path planning, latent space

TL;DR: A framework to learn representation of transition costs in path planning

Abstract: Learning representations from solutions of constrained optimization problems (COPs) with unknown cost functions is challenging, as models like (Variational) Autoencoders struggle to capture constraints to decode structured outputs. We propose an inverse optimization latent variable model (IO-LVM) that constructs a latent space of COP costs based on observed decisions, enabling the inference of feasible and meaningful solutions by reconstructing them with a COP solver. To achieve this, we leverage estimated gradients of a Fenchel-Young loss through a non-differentiable deterministic solver while shaping the embedding space. In contrast to established Inverse Optimization or Inverse Reinforcement Learning methods, which typically identify a single or context-conditioned cost function, we exploit the learned representation to capture underlying COP cost structures and identify solutions likely originating from different agents, each using distinct or slightly different cost functions when making decisions. Using both synthetic and actual ship routing data, we validate our approach through experiments on path planning problems using the Dijkstra algorithm, demonstrating the interpretability of the latent space and its effectiveness in path inference and path distribution reconstruction.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 11622