---
title: "Reconciling Rewards with Predictive State Representations"
authors:
  - "Andrea Baisero"
  - "Christopher Amato"
doi: "10.24963/ijcai.2021/299"
url: "https://ijcai.org/proceedings/2021/299"
pdf: "https://ijcai.org/proceedings/2021/0299.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "2170-2176"
track: "Main Track"
keywords:
  - "Machine Learning: Reinforcement Learning"
  - "Uncertainty in AI: Uncertainty Representations"
  - "Planning and Scheduling: POMDPs"
---

# Reconciling Rewards with Predictive State Representations

Andrea Baisero, Christopher Amato

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 2170-2176. DOI: [10.24963/ijcai.2021/299](https://doi.org/10.24963/ijcai.2021/299)

## Abstract

Predictive state representations (PSRs) are models of controlled non-Markov
  observation sequences which exhibit the same generative process governing
  POMDP observations without relying on an underlying latent state.  In that
  respect, a PSR is indistinguishable from the corresponding POMDP.  However,
  PSRs notoriously ignore the notion of rewards, which undermines the general
  utility of PSR models for control, planning, or reinforcement learning.
  Therefore, we describe a sufficient and necessary accuracy condition
  which determines whether a PSR is able to accurately model POMDP rewards, we
  show that rewards can be approximated even when the accuracy condition is not
  satisfied, and we find that a non-trivial number of POMDPs taken from a
  well-known third-party repository do not satisfy the accuracy condition.  
  We propose reward-predictive state representations (R-PSRs), a
  generalization of PSRs which accurately models both observations and rewards,
  and develop value iteration for R-PSRs.  We show that there is a mismatch
  between optimal POMDP policies and the optimal PSR policies derived from
  approximate rewards.  On the other hand, optimal R-PSR policies perfectly
  match optimal POMDP policies, reconfirming R-PSRs as accurate state-less
  generative models of observations and rewards.