Meta Learning in Bandits within Shared Affine Subspaces

We study the problem of meta-learning several contextual stochastic bandits tasks by leveraging their concentration around a low-dimensional affine subspace, which we learn via online principal component analysis to reduce the expected regret over the encountered bandits. We propose and theoretically analyze two strategies that solve the problem: One based on the principle of optimism in the face of uncertainty and the other via Thompson sampling. Our framework is generic and includes previously proposed approaches as special cases. Besides, the empirical results show that our methods significantly reduce the regret on several bandit tasks.

Piecewise-Stationary Combinatorial Semi-Bandit with Causally Related Rewards

We study the piecewise stationary combinatorial semi-bandit problem with causally related rewards. In our nonstationary environment, variations in the base arms' distributions, causal relationships between rewards, or both, change the reward generation process. In such an environment, an optimal decision-maker must follow both sources of change and adapt accordingly. The problem becomes aggravated in the combinatorial semi-bandit setting, where the decision-maker only observes the outcome of the selected bundle of arms. The core of our proposed policy is the Upper Confidence Bound (UCB) algorithm. We assume the agent relies on an adaptive approach to overcome the challenge. More specifically, it employs a change-point detector based on the Generalized Likelihood Ratio (GLR) test. Besides, we introduce the notion of group restart as a new alternative restarting strategy in the decision making process in structured environments. Finally, our algorithm integrates a mechanism to trace the variations of the underlying graph structure, which captures the causal relationships between the rewards in the bandit setting. Theoretically, we establish a regret upper bound that reflects the effects of the number of structural- and distribution changes on the performance. The outcome of our numerical experiments in real-world scenarios exhibits applicability and superior performance of our proposal compared to the state-of-the-art benchmarks.

Hypothesis Transfer in Bandits by Weighted Models

We consider the problem of contextual multi-armed bandits in the setting of hypothesis transfer learning. That is, we assume having access to a previously learned model on an unobserved set of contexts, and we leverage it in order to accelerate exploration on a new bandit problem. Our transfer strategy is based on a re-weighting scheme for which we show a reduction in the regret over the classic Linear UCB when transfer is desired, while recovering the classic regret rate when the two tasks are unrelated. We further extend this method to an arbitrary amount of source models, where the algorithm decides which model is preferred at each time step. Additionally we discuss an approach where a dynamic convex combination of source models is given in terms of a biased regularization term in the classic LinUCB algorithm. The algorithms and the theoretical analysis of our proposed methods substantiated by empirical evaluations on simulated and real-world data.