Reconciling Rewards with Predictive State Representations

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.