  A common setting in multitask reinforcement learning (RL) demands that an
agent rapidly adapt to various stationary reward functions randomly sampled
from a fixed distribution. In such situations, the successor representation
(SR) is a popular framework which supports rapid policy evaluation by
decoupling a policy's expected discounted, cumulative state occupancies from a
specific reward function. However, in the natural world, sequential tasks are
rarely independent, and instead reflect shifting priorities based on the
availability and subjective perception of rewarding stimuli. Reflecting this
disjunction, in this paper we study the phenomenon of diminishing marginal
utility and introduce a novel state representation, the $\lambda$
representation ($\lambda$R) which, surprisingly, is required for policy
evaluation in this setting and which generalizes the SR as well as several
other state representations from the literature. We establish the $\lambda$R's
formal properties and examine its normative advantages in the context of
machine learning, as well as its usefulness for studying natural behaviors,
particularly foraging.
