Stochastic Conservative Contextual Linear Bandits
This work addresses safety-critical decision-making in physical systems with partial information, but it is incremental as it extends existing UCB methods to incorporate safety constraints and context distributions.
The paper tackles the problem of safe real-time decision-making under uncertainty by formulating a conservative stochastic contextual bandit model where only context distributions are known, and proposes a conservative linear UCB algorithm to maximize cumulative reward without violating safety constraints. The result includes a regret bound decomposed into standard linear UCB regret and constant terms for conservatism and unknown contexts, validated through simulations on synthetic and real-world maize data.
Many physical systems have underlying safety considerations that require that the strategy deployed ensures the satisfaction of a set of constraints. Further, often we have only partial information on the state of the system. We study the problem of safe real-time decision making under uncertainty. In this paper, we formulate a conservative stochastic contextual bandit formulation for real-time decision making when an adversary chooses a distribution on the set of possible contexts and the learner is subject to certain safety/performance constraints. The learner observes only the context distribution and the exact context is unknown, and the goal is to develop an algorithm that selects a sequence of optimal actions to maximize the cumulative reward without violating the safety constraints at any time step. By leveraging the UCB algorithm for this setting, we propose a conservative linear UCB algorithm for stochastic bandits with context distribution. We prove an upper bound on the regret of the algorithm and show that it can be decomposed into three terms: (i) an upper bound for the regret of the standard linear UCB algorithm, (ii) a constant term (independent of time horizon) that accounts for the loss of being conservative in order to satisfy the safety constraint, and (ii) a constant term (independent of time horizon) that accounts for the loss for the contexts being unknown and only the distribution being known. To validate the performance of our approach we perform extensive simulations on synthetic data and on real-world maize data collected through the Genomes to Fields (G2F) initiative.