From open-loop representations to closed-loop feedback implementations in differential games: A numerical case study

TL;DR

This paper introduces a neural network-based numerical scheme to derive feedback strategies in differential games, specifically for pursuit-evasion scenarios, highlighting the effectiveness of learned strategies and analyzing their discontinuities.

Contribution

It presents a novel neural network approach to approximate feedback strategies from open-loop solutions in differential games, addressing discontinuities and performance.

Findings

Neural networks effectively approximate feedback strategies in pursuit-evasion games.

Training with an appropriate loss function improves strategy accuracy.

Discontinuities in optimal feedback strategies impact players' potential gains.

Abstract

Solutions to pursuit-evasion and surveillance-evasion differential games are typically computed and expressed using open-loop representations, with the synthesis of feedback strategies significantly less common. We propose a numerical scheme for obtaining feedback strategies for the recently introduced prying-pedestrian surveillance-evasion differential game. The scheme involves computing feedback strategies as input-output maps approximated via neural networks trained using data obtained from open-loop representations of solutions. Simulations show the effectiveness of neural networks trained with an appropriate learning-loss function. Since optimal feedback strategies are discontinuous, as a second contribution, the potential loss/gain of individual players is subsequently studied for players using sample-and-hold feedback compared to continuous-time feedback.