2019-06-25-lattimore19a.md

abstract	section	title	layout	series	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	publisher	container-title	volume	genre	issued	pdf	extras
We prove a new minimax theorem connecting the worst-case Bayesian regret and minimax regret under finite-action partial monitoring with no assumptions on the space of signals or decisions of the adversary. We then generalise the information-theoretic tools of Russo and Van Roy (2016) for proving Bayesian regret bounds and combine them with the minimax theorem to derive minimax regret bounds for various partial monitoring settings. The highlight is a clean analysis of ‘easy’ and ‘hard’ finite partial monitoring, with new regret bounds that are independent of arbitrarily large game-dependent constants and eliminate the logarithmic dependence on the horizon for easy games that appeared in earlier work. The power of the generalised machinery is further demonstrated by proving that the minimax regret for $k$-armed adversarial bandits is at most $\sqrt{2kn}$, improving on existing results by a factor of 2. Finally, we provide a simple analysis of the cops and robbers game, also improving best known constants.	contributed	An Information-Theoretic Approach to Minimax Regret in Partial Monitoring	inproceedings	Proceedings of Machine Learning Research	lattimore19a	0	An Information-Theoretic Approach to Minimax Regret in Partial Monitoring	2111	2139	2111-2139	2111	false	Lattimore, Tor and Szepesv{\'a}ri, Csaba	given family Tor Lattimore given family Csaba Szepesvári	2019-06-25		PMLR	Proceedings of the Thirty-Second Conference on Learning Theory	99	inproceedings	date-parts 2019 6 25	http://proceedings.mlr.press/v99/lattimore19a/lattimore19a.pdf