## Lower Bounds for Stochastic Linear Bandits

Lower bounds for linear bandits turn out to be more nuanced than the finite-armed case. The big difference is that for linear bandits the shape of the action-set plays a role in the form of the regret, not just the Continue Reading

## Stochastic Linear Bandits and UCB

Recall that in the adversarial contextual $K$-action bandit problem, at the beginning of each round $t$ a context $c_t\in \Ctx$ is observed. The idea is that the context $c_t$ may help the learner to choose a better action. This led Continue Reading

## Contextual Bandits and the Exp4 Algorithm

In most bandit problems there is likely to be some additional information available at the beginning of rounds and often this information can potentially help with the action choices. For example, in a web article recommendation system, where the goal Continue Reading

## High probability lower bounds

In the post on adversarial bandits we proved two high probability upper bounds on the regret of Exp-IX. Specifically, we showed: Theorem: There exists a policy $\pi$ such that for all $\delta \in (0,1)$ for any adversarial environment $\nu\in [0,1]^{nK}$, Continue Reading

A stochastic bandit with $K$ actions is completely determined by the distributions of rewards, $P_1,\dots,P_K$, of the respective actions. In particular, in round $t$, the distribution of the reward $X_t$ received by a learner choosing action $A_t\in [K]$ is $P_{A_t}$, Continue Reading