  Policy evaluation with linear function approximation is an important problem
in reinforcement learning. When facing high-dimensional feature spaces, such a
problem becomes extremely hard considering the computation efficiency and
quality of approximations. We propose a new algorithm, LSTD($\lambda$)-RP,
which leverages random projection techniques and takes eligibility traces into
consideration to tackle the above two challenges. We carry out theoretical
analysis of LSTD($\lambda$)-RP, and provide meaningful upper bounds of the
estimation error, approximation error and total generalization error. These
results demonstrate that LSTD($\lambda$)-RP can benefit from random projection
and eligibility traces strategies, and LSTD($\lambda$)-RP can achieve better
performances than prior LSTD-RP and LSTD($\lambda$) algorithms.
