Minimax Lower Bounds for the Two-Armed Bandit Problem

Minimax Lower Bounds for the Two-Armed Bandit Problem

We obtain minimax lower bounds on the regret for the classical two-armed bandit problem. We provide a nite-sample minimax version of the well-known log n asymptotic lower bound of Lai and Robbins. Also, in contrast to the logn asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable con gurations o...

Finite-time lower bounds for the two-armed bandit problem

We obtain minimax lower bounds on the regret for the classical two-armed bandit problem. We provide a finite-sample minimax version of the well-known log asymptotic lower bound of Lai and Robbins. The finite-time lower bound allows us to derive conditions for the amount of time necessary to make any significant gain over a random guessing strategy. These bounds depend on the class of possible d...

Minimax R-stage strategy for the multi-armed bandit problem

Contributions to the Asymptotic Minimax Theorem for the Two-Armed Bandit Problem

The asymptotic minimax theorem for Bernoully twoarmed bandit problem states that the minimax risk has the order N as N → ∞, where N is the control horizon, and provides lower and upper estimates. It can be easily extended to normal two-armed bandit. For normal two-armed bandit, we generalize the asymptotic minimax theorem as follows: the minimax risk is approximately equal to 0.637N as N →∞. Ke...

Nearly Tight Bounds for the Continuum-Armed Bandit Problem

In the multi-armed bandit problem, an online algorithm must choose from a set of strategies in a sequence of n trials so as to minimize the total cost of the chosen strategies. While nearly tight upper and lower bounds are known in the case when the strategy set is finite, much less is known when there is an infinite strategy set. Here we consider the case when the set of strategies is a subset...