If you take the path of aggressive incentives, you need to provide training and let it be up to the user to partake of it. But you also need to offer very enticing rewards for getting trained.
For example, consider offering training that provides credits toward a day off. Maybe you give extra credits for courses they take on their own time, such as during evenings and weekends. You might also create contests with prizes for individuals or departments that take the most training in a set period.
One company I know of recently offered $1,000 bonuses for people who passed Microsoft certifications. Some people didn't pass the tests, but everyone who tried got more knowledgeable, making them better employees in the process.
Today's organic training method lets the majority of users choose a lazy path. Yes, the A-type personalities continue to push themselves to do better regardless of the company's mindset. But the rest don't improve without some form of reward. And some need rules to make them act. And for those employees, following those rules needs to be mandatory.
Whether you go the mandatory route or the incentive route or a combination, the result is the same: smarter, more appreciative workers.