Interactive decision making, encompassing bandits, contextual bandits, and reinforcement learning, has recently been of interest to theoretical studies of experimentation design and recommender system algorithm research.

Interactive decision making, encompassing bandits, contextual bandits, and reinforcement learning, has recently been of interest to theoretical studies of experimentation design and recommender system algorithm research. One recent finding in this area is that the well-known Graves-Lai constant being zero is a necessary and sufficient condition for achieving bounded (or constant) regret in interactive decision-making. As this condition may be a strong requirement for many applications, the practical usefulness of pursuing bounded regret has been questioned. In this paper, we show that the condition of the Graves-Lai constant being zero is also necessary for a consistent algorithm to achieve delay model robustness when reward delays are unknown (i.e., when feedback is anonymous). Here, model robustness is measured in terms of $\epsilon$-robustness, one of the most widely used and one of the least adversarial robustness concepts in the robust statistics literature. In particular, we show that $\epsilon$-robustness cannot be achieved for a consistent (i.e., uniformly sub-polynomial regret) algorithm, however small the nonzero $\epsilon$ value is, when the Grave-Lai constant is not zero. While this is a strongly negative result, we also provide a positive result for linear rewards models (contextual linear bandits, reinforcement learning with linear MDP) that the Grave-Lai constant being zero is also sufficient for achieving bounded regret without any knowledge of delay models, i.e., the best of both the efficiency world and the delay robustness world.

We study stochastic structured bandits for minimizing regret. The fact that the popular optimistic algorithms do not achieve the asymptotic instance-dependent regret optimality (asymptotic optimality for short) has recently alluded researchers. On the other hand, it is known that one can achieve bounded regret (i.e., does not grow indefinitely with $n$) in certain instances. Unfortunately, existing asymptotically optimal algorithms rely on forced sampling that introduces an $\omega(1)$ term w.r.t. the time horizon $n$ in their regret, failing to adapt to the ``easiness'' of the instance. In this paper, we focus on the finite hypothesis case and ask if one can achieve the asymptotic optimality while enjoying bounded regret whenever possible. We provide a positive answer by introducing a new algorithm called CRush Optimism with Pessimism (CROP) that eliminates optimistic hypotheses by pulling the informative arms indicated by a pessimistic hypothesis. Our finite-time analysis shows that CROP $(i)$ achieves a constant-factor asymptotic optimality and, thanks to the forced-exploration-free design, $(ii)$ adapts to bounded regret, and $(iii)$ its regret bound scales not with $K$ but with an effective number of arms $K_\psi$ that we introduce. We also discuss a problem class where CROP can be exponentially better than existing algorithms in \textit{nonasymptotic} regimes. This problem class also reveals a surprising fact that even a clairvoyant oracle who plays according to the asymptotically optimal arm pull scheme may suffer a linear worst-case regret.

Interactive decision making, encompassing bandits, contextual bandits, and reinforcement learning, has recently been of interest to theoretical studies of experimentation design and recommender system algorithm research.

In this paper, we study stochastic structured bandits for minimizing regret.

We study a new type of K-armed bandit problem where the expected return of one arm may depend on the returns of other arms. We present a new algorithm for this general class of problems and show that under certain circumstances it is possible to achieve finite expected cumulative regret. We also give problemdependent lower bounds on the cumulative regret showing that at least in special cases the new algorithm is nearly optimal.

We study a new type of K-armed bandit problem where the expected return of one arm may depend on the returns of other arms. We present a new algorithm for this general class of problems and show that under certain circumstances it is possible to achieve finite expected cumulative regret. We also give problemdependent lower bounds on the cumulative regret showing that at least in special cases the new algorithm is nearly optimal.

This study addresses the challenge of online learning in contexts where agents accumulate disparate data, face resource constraints, and use different local algorithms. This paper introduces the Switched Online Learning Algorithm (SOLA), designed to solve the heterogeneous online learning problem by amalgamating updates from diverse agents through a dynamic switching mechanism contingent upon their respective performance and available resources. We theoretically analyze the design of the selecting mechanism to ensure that the regret of SOLA is bounded. Our findings show that the number of changes in selection needs to be bounded by a parameter dependent on the performance of the different local algorithms. Additionally, two test cases are presented to emphasize the effectiveness of SOLA, first on an online linear regression problem and then on an online classification problem with the MNIST dataset.

In online exploration systems where users with fixed preferences repeatedly arrive, it has recently been shown that O(1), i.e., bounded regret, can be achieved when the system is modeled as a linear contextual bandit. This result may be of interest for recommender systems, where the popularity of their items is often short-lived, as the exploration itself may be completed quickly before potential long-run non-stationarities come into play. However, in practice, exact knowledge of the linear model is difficult to justify. Furthermore, potential existence of unobservable covariates, uneven user arrival rates, interpretation of the necessary rank condition, and users opting out of private data tracking all need to be addressed for practical recommender system applications. In this work, we conduct a theoretical study to address all these issues while still achieving bounded regret. Aside from proof techniques, the key differentiating assumption we make here is the presence of effective Synthetic Control Methods (SCM), which are shown to be a practical relaxation of the exact linear model knowledge assumption. We verify our theoretical bounded regret result using a minimal simulation experiment.

We consider the bandit-based framework for diversity-preserving recommendations introduced by Celis et al. (2019), who approached it mainly by a reduction to the setting of linear bandits. We design a UCB algorithm using the specific structure of the setting and show that it enjoys a bounded distribution-dependent regret in the natural cases when the optimal mixed actions put some probability mass on all actions (i.e., when diversity is desirable). Simulations illustrate this fact. We also provide regret lower bounds and briefly discuss distribution-free regret bounds.