We describe two open problems related to first order regret bounds for contextual bandits. The first asks for an algorithm with a regret bound of \\(O^\\tilde(L^*\\sqrt{K\\ln N})\\) where there are \\(K\\) actions, \\(N\\) policies, and \\(L^*\\) is the cumulative loss of the best policy. The second asks for an optimization-oracle-efficient algorithm with regret \\(O^\\tilde({L^*}^{2\/3}poly(K,\\ln(N\/\\delta)))\\). We describe some positive results, such as an inefficient algorithm for the second problem, and some partial negative results.<\/p>\n","protected":false},"excerpt":{"rendered":"
We describe two open problems related to first order regret bounds for contextual bandits. The first asks for an algorithm with a regret bound of where there are actions, policies, and is the cumulative loss of the best policy. The second asks for an optimization-oracle-efficient algorithm with regret . 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