### Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions

@article{mehr_maximum-entropy_2022,
title = {Maximum-{Entropy} {Multi}-{Agent} {Dynamic} {Games}: {Forward} and {Inverse} {Solutions}},
abstract = {In  this  paper,  we  study  the  problem  of  multiple stochastic  agents  interacting  in  a  dynamic  game  scenario  with continuous  state  and  action  spaces.  We  define  a  new  notion of  stochastic  Nash  equilibrium  for  boundedly  rational  agents, which  we  call  the  Entropic  Cost  Equilibrium  (ECE).  We  show that ECE is a natural extension to multiple agents of MaximumEntropy optimality for single agents. We solve both the “forward”and  “inverse”  problems  for  the  multi-agent  ECE  game.  For  the forward  problem,  we  provide  a  Riccati  algorithm  to  compute closed-form  ECE  feedback  policies  for  the  agents,  which  are exact in the Linear-Quadratic-Gaussian case. We give an iterative variant  to  find  locally  ECE  feedback  policies  for  the  nonlinear case.  For  the  inverse  problem,  we  present  an  algorithm  to  infer the cost functions of the multiple interacting agents given noisy,
boundedly  rational  input  and  state  trajectory  examples  from agents  acting  in  an  ECE.  The  effectiveness  of  our  algorithms is  demonstrated  in  a  simulated  multi-agent  collision  avoidance scenario, and with data from the INTERACTION traffic dataset.In  both  cases,  we  show  that,  by  taking  into  account  the  agents’ game theoretic interactions using our algorithm, a more accurate model  of  agents’  costs  can  be  learned,  compared  with  standard inverse  optimal  control  methods.},
language = {en},
journal = {IEEE Transactions on Robotics},
author = {Mehr, Negar and Wang, Mingyu and Schwager, Mac},
year = {2022},
note = {Under Review}
}