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Algorithms for offline bandits must optimize decisions in uncertainenvironments using only offline data. A compelling and increasingly popularobjective in offline bandits is to learn a policy which achieves low Bayesianregret with high confidence. An appealing approach to this problem, inspired byrecent offline reinforcement learning results, is to maximize a form of lowerconfidence bound (LCB). This paper proposes a new approach that directlyminimizes upper bounds on Bayesian regret using efficient conic optimizationsolvers. Our bounds build on connections among Bayesian regret, Value-at-Risk(VaR), and chance-constrained optimization. Compared to prior work, ouralgorithm attains superior theoretical offline regret bounds and better resultsin numerical simulations. Finally, we provide some evidence that popularLCB-style algorithms may be unsuitable for minimizing Bayesian regret inoffline bandits.

A Convex Relaxation Approach to Bayesian Regret Minimization in Offline Bandits