  We present a model of optimal training of a rational, sluggish agent. A
trainer commits to a discrete-time, finite-state Markov process that governs
the evolution of training intensity. Subsequently, the agent monitors the state
and adjusts his capacity at every period. Adjustments are incremental: the
agent's capacity can only change by one unit at a time. The trainer's objective
is to maximize the agent's capacity - evaluated according to its lowest value
under the invariant distribution - subject to an upper bound on average
training intensity. We characterize the trainer's optimal policy, and show how
stochastic, time-varying training intensity can dramatically increase the
long-run capacity of a rational, sluggish agent. We relate our theoretical
findings to "periodization" training techniques in exercise physiology.
