We analyze the minimax regret of the adversarial bandit convex optimization problem. Focusing on the one-dimensional case, we prove that the minimax regret is Θ̃( √ T ) and partially resolve a decade-old open problem. Our analysis is non-constructive, as we do not present a concrete algorithm that attains this regret rate. Instead, we use minimax duality to reduce the problem to a Bayesian setti...

Purpose To determine the demographic, clinical, decision-making, and quality-of-life factors that are associated with treatment decision regret among long-term survivors of localized prostate cancer. Patients and Methods We evaluated men who were age ≤ 75 years when diagnosed with localized prostate cancer between October 1994 and October 1995 in one of six SEER tumor registries and who complet...

We analyze the minimax regret of the adversarial bandit convex optimization problem. Focusing on the one-dimensional case, we prove that the minimax regret is Θ̃( √ T ) and partially resolve a decade-old open problem. Our analysis is non-constructive, as we do not present a concrete algorithm that attains this regret rate. Instead, we use minimax duality to reduce the problem to a Bayesian setti...

W characterize the effect of anticipated regret on consumer decisions and on firm profits and policies in an advance selling context where buyers have uncertain valuations. Advance purchases trigger action regret if valuations turn out to be lower than the price paid, whereas delaying purchase may cause inaction regret from missing a discount or facing a stockout. Consumers whom we describe as ...

We present an algorithm that achieves almost optimal pseudo-regret bounds against adversarial and stochastic bandits. Against adversarial bandits the pseudo-regret is O ( K √ n log n ) and against stochastic bandits the pseudo-regret is O ( ∑ i(log n)/∆i). We also show that no algorithm with O (log n) pseudo-regret against stochastic bandits can achieve Õ ( √ n) expected regret against adaptive...

Regret minimization is important in both the Multi-Armed Bandit problem and Monte-Carlo Tree Search (MCTS). Recently, simple regret, i.e., the regret of not recommending the best action, has been proposed as an alternative to cumulative regret in MCTS, i.e., regret accumulated over time. Each type of regret is appropriate in different contexts. Although the majority of MCTS research applies the...