  A basic assumption of traditional reinforcement learning is that the value of
a reward does not change once it is received by an agent. The present work
forgoes this assumption and considers the situation where the value of a reward
decays proportionally to the time elapsed since it was obtained. Emphasizing
the inflection point occurring at the time of payment, we use the term asset to
refer to a reward that is currently in the possession of an agent. Adopting
this language, we initiate the study of depreciating assets within the
framework of infinite-horizon quantitative optimization. In particular, we
propose a notion of asset depreciation, inspired by classical exponential
discounting, where the value of an asset is scaled by a fixed discount factor
at each time step after it is obtained by the agent. We formulate a
Bellman-style equational characterization of optimality in this context and
develop a model-free reinforcement learning approach to obtain optimal
policies.
