  We seek the best stroke sequences of a finite-size swimming predator chasing
a non-motile point or finite--size prey at low Reynolds number. We use optimal
control to seek the globally-optimal solutions for the former and RL for
general situations. The predator is represented by a squirmer model that can
translate forward and laterally, rotate and generate a stresslet flow. We
identify the predator's best squirming sequences to achieve the time-optimal
(TO) and efficiency-optimal (EO) predation. For a point prey, the TO squirmer
executing translational motions favours a two-fold L-shaped trajectory that
enables it to exploit the disturbance flow for accelerated predation; using a
stresslet mode significantly expedites the EO predation, allowing the predator
to catch the prey faster yet with lower energy consumption and higher predatory
efficiency; the predator can harness its stresslet disturbance flow to suck the
prey towards itself; compared to a translating predator, its compeer combining
translation and rotation is less time--efficient, and the latter occasionally
achieves the TO predation via retreating in order to advance. We also adopt RL
to reproduce the globally-optimal predatory strategy of chasing a point prey,
qualitatively capturing the crucial two--fold attribute of TO path. Using a
numerically emulated RL environment, we explore the dependence of the optimal
predatory path on the size of prey. Our results might provide useful
information that help design synthetic microswimmers such as \textit{in vivo}
medical micro-robots capable of capturing and approaching objects in viscous
flows.
