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RoSSO: A High-Performance Python Package for Robotic Surveillance Strategy Optimization Using JAX

Yohan John, Connor Hughes, Gilberto Diaz-Garcia, Jason R. Marden, Francesco Bullo

TL;DR

RoSSO addresses the challenge of designing effective randomized patrol routes on graphs by enabling tractable Markov-chain optimization with diverse metrics. The authors implement a JAX-enabled Python package that supports MHT, RTE, and Stackelberg-formulated patrol strategies, along with a greedy co-optimization for defense placement and a multi-robot SG extension. Key contributions include a gradient-based MC optimizer, a novel greedy defense-allocation method, and scalable multi-robot formulations validated on a San Francisco district graph, all within a modular framework. The work demonstrates improved computational efficiency and practical patrol designs that balance movement speed, unpredictability, and defense constraints, with potential for GPU/TPU deployment and RL integration.

Abstract

To enable the computation of effective randomized patrol routes for single- or multi-robot teams, we present RoSSO, a Python package designed for solving Markov chain optimization problems. We exploit machine-learning techniques such as reverse-mode automatic differentiation and constraint parametrization to achieve superior efficiency compared to general-purpose nonlinear programming solvers. Additionally, we supplement a game-theoretic stochastic surveillance formulation in the literature with a novel greedy algorithm and multi-robot extension. We close with numerical results for a police district in downtown San Francisco that demonstrate RoSSO's capabilities on our new formulations and the prior work.

RoSSO: A High-Performance Python Package for Robotic Surveillance Strategy Optimization Using JAX

TL;DR

RoSSO addresses the challenge of designing effective randomized patrol routes on graphs by enabling tractable Markov-chain optimization with diverse metrics. The authors implement a JAX-enabled Python package that supports MHT, RTE, and Stackelberg-formulated patrol strategies, along with a greedy co-optimization for defense placement and a multi-robot SG extension. Key contributions include a gradient-based MC optimizer, a novel greedy defense-allocation method, and scalable multi-robot formulations validated on a San Francisco district graph, all within a modular framework. The work demonstrates improved computational efficiency and practical patrol designs that balance movement speed, unpredictability, and defense constraints, with potential for GPU/TPU deployment and RL integration.

Abstract

To enable the computation of effective randomized patrol routes for single- or multi-robot teams, we present RoSSO, a Python package designed for solving Markov chain optimization problems. We exploit machine-learning techniques such as reverse-mode automatic differentiation and constraint parametrization to achieve superior efficiency compared to general-purpose nonlinear programming solvers. Additionally, we supplement a game-theoretic stochastic surveillance formulation in the literature with a novel greedy algorithm and multi-robot extension. We close with numerical results for a police district in downtown San Francisco that demonstrate RoSSO's capabilities on our new formulations and the prior work.
Paper Structure (18 sections, 11 equations, 4 figures, 3 tables, 2 algorithms)

This paper contains 18 sections, 11 equations, 4 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. Problem Formulation
  5. Notation
  6. Graphs & Markov Chains
  7. Mean Hitting Time (MHT) Formulation
  8. Return-Time Entropy (RTE) Formulation
  9. Stackelberg Game (SG) Formulation
  10. RoSSO
  11. JAX
  12. Handling Constraints
  13. Stackelberg Game Co-Optimization Formulation
  14. Multi-Robot Stackelberg Game Formulation
  15. Results
  16. ...and 3 more sections

Figures (4)

  • Figure 1: Twelve intersections in the central district of the San Francisco police department.
  • Figure 2: Heatmaps of optimized single-robot patrol strategies for San Francisco graph from RoSSO.
  • Figure 3: Heatmaps of SG-optimized robot team patrol strategies for San Francisco graph from RoSSO, Section \ref{['sect:multi']}.
  • Figure 4: Heatmaps of SG-optimized robot team patrol strategies for partitioned San Francisco graph from RoSSO.