Non-trivial two-armed partial-monitoring games are bandits

TL;DR

This paper demonstrates that non-trivial two-action partial-monitoring games can be reduced to bandit problems, leading to a minimax regret rate of a a a(a T).

Contribution

It establishes a reduction from non-trivial two-action partial-monitoring games to bandit problems, clarifying their regret bounds.

Findings

Non-trivial two-action partial-monitoring games are equivalent to bandit problems.

Minimax regret in these games is a(a T).

Reduction simplifies analysis of such games.

Abstract

We consider online learning in partial-monitoring games against an oblivious adversary. We show that when the number of actions available to the learner is two and the game is nontrivial then it is reducible to a bandit-like game and thus the minimax regret is $\Theta(\sqrt{T})$.