Before the pax Romona, the Roman Republic had been at war for nearly 200 years, allowing for continuous lines of officers and soldiers to gain experience and knowledge and pass it on to their replacements.
But the Pax Romana, particularly the Nerva–Antonine dynasty, was notable for its absence of conflict. During the reigns of Hadrian, Antoninus Pius, and up through the beginning of the reign of Marcus Aurelius, roughly 44 years passed with virtually no major conflicts.
How, then did officer tactical knowledge and skill not degrade? Today we have West Point, but the Romans didn't have that sort of military academy. Their officers gained skill in the field, and for 44 years the legions were usually just building roads and fortifications. Sure, they probably read a few tactical manuals, but was that enough?
But it seems like the Romans didn't lose a step. When the Persians invaded at the beginning of Marcus Aurelius's reign, his generals threw them back without much trouble.
How could this be?
It's important to remember that Pax Romana was, to a certain extent, a trope - part of the image of peace and prosperity ushered in by Augustus and his successors. Even during periods that might be presented as peaceful, there's no reason to think that there was a total absence of armed conflict at that time. There may have been minor skirmishes or battles that went unrecorded by the historical sources we have, and particularly the troops stationed in the German, British, Danubian and Parthian frontier zones will have been in pretty constant readiness to react to raiding or assaults on the limes. On top of that, there is every reason to think that the army drilled regularly, keeping up training, skill and knowledge among all ranks. Josephus certainly mentions this - I'm on my phone so can't give references right now. Add to this the occasional civil war or armed usurpation, and the army begins to look much more active than the image of pax romana might suggest.
In terms of the officer class, the Roman army operated differently to modern forces. The highest officers were appointed by the emperor for short terms - perhaps a year or two - as part of the career path of aristocratic men destined for (or already holding) political positions in the city of Rome. These men wouldn't have necessarily had specific training in military leadership - there was no Roman Sandhurst or West Point as you say - so they would rely on their more experienced lower officers for their expertise. It seems that the centurions in particular held a wealth of practical knowledge on the business of fighting, and could both command their own units and advise their superiors as necessary. There were some guidebooks to military strategy and tactics which have survived, again I can post references later if you're interested.