- Generally, algorithms assume the Lipshitz constant is known. This paper does not assume this.
- Shows it is possible to develop an algorithm that has regret that is minimax optimal in the globally Lipshitz setting without knowing the Lipshitz constants
- Functions in noisy domains
- Mention DIRECT, which doesn’t assume a Lipshitz constant, which is said to work well in practice, but only asymptotic convergence is guaranteed
- Says the discretization method used is similar to Kleinberg’s. Then has 2 phases:
- Starts with uniform exploration to make some estimate of the Lipshitz constant (which is good enough to get the bounds)
- Find the optimal interval using a “standard” exploration-exploitation strategy

- Mentions this 2-step method may be useful for domains aside from bandits
- Basically assumptions are that
*f(x)*and its derivative are Lipshitz in the hypercube