It turns out that the relationship between risk and creativity is complex. While moderate levels of risk can stifle creative output - and acceptance of creative ideas - high levels of creativity are often associated with high levels of risk. Albert Einstein, noted for his creative thinking in the discipline of physics, was also quite the risk-taker. When risk is great the brain needs to go to greater lengths for a solution. And it often comes back with something unexpected.
This doesn't mean that you need to conduct brainstorming sessions while base-jumping. Two easy ways to elevate risk are to shorten deadlines or lower budgets. Hackathons - ridiculously time-boxed development sessions - are well known for producing an amazing amount of creative work in a short span of time.
Of course you might not want to turn the risk dial up to 11. The other way to foster innovation is to create a culture of innovation by distributing the benefits and risks across the organization. Burkus suggests that instead of top-down innovation (you come up with the idea and I, the leader, will reject it), a better model might be to hand over the decision-making across the organization. Giving peers the ability to vote on new ideas can minimize the risk that any single individual will make the wrong choice, freeing people to select ideas that they think are the most creative.