However, they left the adapting to unknown ε as an open question.

We study bandit model selection in stochastic environments. Our approach relies on a master algorithm that selects between candidate base algorithms. We develop a master-base algorithm abstraction that can work with general classes of base algorithms and different type of adversarial master algorithms. Our methods rely on a novel and generic smoothing transformation for bandit algorithms that permits us to obtain optimal $O(\sqrt{T})$ model selection guarantees for stochastic contextual bandit problems as long as the optimal base algorithm satisfies a high probability regret guarantee. We show through a lower bound that even when one of the base algorithms has $O(\log T)$ regret, in general it is impossible to get better than $\Omega(\sqrt{T})$ regret in model selection, even asymptotically.

For years, the discourse around poker AI has been dominated by the concept of solvers and the pursuit of unexploitable, machine-perfect play. This paper challenges that orthodoxy. It presents Patrick, an AI built on the contrary philosophy: that the path to victory lies not in being unexploitable, but in being maximally exploitative. Patrick's architecture is a purpose-built engine for understanding and attacking the flawed, psychological, and often irrational nature of human opponents. Through detailed analysis of its design, its novel prediction-anchored learning method, and its profitable performance in a 64,267-hand trial, this paper makes the case that the solved myth is a distraction from the real, far more interesting challenge: creating AI that can master the art of human imperfection.

In Section D we present the proofs for Section 5.1 In Section H we show the proofs of the lower bounds in Section 6. We outline briefly some other direct applications of our results. CORRAL will achieve regret O ( p | L | dT) . B.1 Original Corral The original Corral algorithm [2] is reproduced below. We reproduce the EXP3.P algorithm (Figure 3.1 in [ 's expected replay regret satisfies: Therefore total regret is bounded by 6 U ( T,) log( T) D.2 Applications of Proposition 5.1 We now show that several algorithms are ( U,, T) bounded: Lemma D.2.

However, they left the adapting to unknown ε as an open question.

These algorithms combine the ideas of finite-horizon approximation [Chen et al., 2022a], special Bernstein-style bonuses of the MVP algorithm [Zhang et al., 2020], adaptive confidence widening [Wei and Luo, 2021], as