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Category: Adversarial bandits

Bayesian/minimax duality for adversarial bandits

Posted onMarch 17, 2019March 7, 20201 Comment

The Bayesian approach to learning starts by choosing a prior probability distribution over the unknown parameters of the world. Then, as the learner makes observation, the prior is updated using Bayes rule to form the posterior, which represents the new Continue Reading

CategoriesAdversarial bandits, Bandits, Bayesian bandits, Game theory

The variance of Exp3

Posted onFebruary 16, 2019March 17, 2019Leave a comment

In an earlier post we analyzed an algorithm called Exp3 for $k$-armed adversarial bandits for which the expected regret is bounded by \begin{align*} R_n = \max_{a \in [k]} \E\left[\sum_{t=1}^n y_{tA_t} – y_{ta}\right] \leq \sqrt{2n k \log(k)}\,. \end{align*} The setting of Continue Reading

CategoriesAdversarial bandits, Bandits, Lower bound

First order bounds for k-armed adversarial bandits

Posted onFebruary 16, 2019October 28, 20214 Comments

To revive the content on this blog a little we have decided to highlight some of the new topics covered in the book that we are excited about and that were not previously covered in the blog. In this post Continue Reading

CategoriesAdversarial bandits, Bandits, Finite-armed bandits

Adversarial linear bandits and the curious case of the unit ball

Posted onNovember 25, 2016March 17, 2019Leave a comment

According to the main result of the previous post, given any finite action set $\cA$ with $K$ actions $a_1,\dots,a_K\in \R^d$, no matter how an adversary selects the loss vectors $y_1,\dots,y_n\in \R^d$, as long as the action losses $\ip{a_k,y_t}$ are in Continue Reading

CategoriesAdversarial bandits, Bandits, Lower bound

Adversarial linear bandits

Posted onNovember 24, 2016March 17, 20191 Comment

In the next few posts we will consider adversarial linear bandits, which, up to a crude first approximation, can be thought of as the adversarial version of stochastic linear bandits. The discussion of the exact nature of the relationship between Continue Reading

CategoriesAdversarial bandits, Bandits

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