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Bandit algorithms have various application in safety-critical systems, whereit is important to respect the system constraints that rely on the bandit'sunknown parameters at every round. In this paper, we formulate a linearstochastic multi-armed bandit problem with safety constraints that depend(linearly) on an unknown parameter vector. As such, the learner is unable toidentify all safe actions and must act conservatively in ensuring that heractions satisfy the safety constraint at all rounds (at least with highprobability). For these bandits, we propose a new UCB-based algorithm calledSafe-LUCB, which includes necessary modifications to respect safetyconstraints. The algorithm has two phases. During the pure exploration phasethe learner chooses her actions at random from a restricted set of safe actionswith the goal of learning a good approximation of the entire unknown safe set.Once this goal is achieved, the algorithm begins a safeexploration-exploitation phase where the learner gradually expands theirestimate of the set of safe actions while controlling the growth of regret. Weprovide a general regret bound for the algorithm, as well as a problemdependent bound that is connected to the location of the optimal action withinthe safe set. We then propose a modified heuristic that exploits our problemdependent analysis to improve the regret.

Linear Stochastic Bandits Under Safety Constraints