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In bandit with distribution shifts, one aims to automatically adapt to unknown changes in reward distribution, and restart exploration when necessary. While this problem has been studied for many years, a recent breakthrough of Auer et al. (2018, 2019) provides the first adaptive procedure to guarantee an optimal (dynamic) regret $\sqrt{LT}$, for $T$ rounds, and an unknown number $L$ of changes. However, while this rate is tight in the worst case, it remained open whether faster rates are possible, without prior knowledge, if few changes in distribution are actually severe. To resolve this question, we propose a new notion of significant shift, which only counts very severe changes that clearly necessitate a restart: roughly, these are changes involving not only best arm switches, but also involving large aggregate differences in reward overtime. Thus, our resulting procedure adaptively achieves rates always faster (sometimes significantly) than $O(\sqrt{ST})$, where $S\ll L$ only counts best arm switches, while at the same time, always faster than the optimal $O(V^{\frac{1}{3}}T^{\frac{2}{3}})$ when expressed in terms of total variation $V$ (which aggregates differences overtime). Our results are expressed in enough generality to also capture non-stochastic adversarial settings.

Safe deployment of autonomous robots in diverse scenarios requires agents that are capable of efficiently adapting to new environments while satisfying constraints. In this work, we propose a practical and theoretically-justified approach to maintaining safety in the presence of dynamics uncertainty. Our approach leverages Bayesian meta-learning with last-layer adaptation. The expressiveness of neural-network features trained offline, paired with efficient last-layer online adaptation, enables the derivation of tight confidence sets which contract around the true dynamics as the model adapts online. We exploit these confidence sets to plan trajectories that guarantee the safety of the system. Our approach handles problems with high dynamics uncertainty, where reaching the goal safely is potentially initially infeasible, by first \textit{exploring} to gather data and reduce uncertainty, before autonomously \textit{exploiting} the acquired information to safely perform the task. Under reasonable assumptions, we prove that our framework guarantees the high-probability satisfaction of all constraints at all times jointly, i.e. over the total task duration. This theoretical analysis also motivates two regularizers of last-layer meta-learning models that improve online adaptation capabilities as well as performance by reducing the size of the confidence sets. We extensively demonstrate our approach in simulation and on hardware.

We study the problem of $K$-armed dueling bandit for both stochastic and adversarial environments, where the goal of the learner is to aggregate information through relative preferences of pair of decisions points queried in an online sequential manner. We first propose a novel reduction from any (general) dueling bandits to multi-armed bandits and despite the simplicity, it allows us to improve many existing results in dueling bandits. In particular, \emph{we give the first best-of-both world result for the dueling bandits regret minimization problem} -- a unified framework that is guaranteed to perform optimally for both stochastic and adversarial preferences simultaneously. Moreover, our algorithm is also the first to achieve an optimal $O(\sum_{i = 1}^K \frac{\log T}{\Delta_i})$ regret bound against the Condorcet-winner benchmark, which scales optimally both in terms of the arm-size $K$ and the instance-specific suboptimality gaps $\{\Delta_i\}_{i = 1}^K$. This resolves the long-standing problem of designing an instancewise gap-dependent order optimal regret algorithm for dueling bandits (with matching lower bounds up to small constant factors). We further justify the robustness of our proposed algorithm by proving its optimal regret rate under adversarially corrupted preferences -- this outperforms the existing state-of-the-art corrupted dueling results by a large margin. In summary, we believe our reduction idea will find a broader scope in solving a diverse class of dueling bandits setting, which are otherwise studied separately from multi-armed bandits with often more complex solutions and worse guarantees. The efficacy of our proposed algorithms is empirically corroborated against the existing dueling bandit methods.

We consider a special case of bandit problems, named batched bandits, in which an agent observes batches of responses over a certain time period. Unlike previous work, we consider a practically relevant batch-centric scenario of batch learning. That is to say, we provide a policy-agnostic regret analysis and demonstrate upper and lower bounds for the regret of a candidate policy. Our main theoretical results show that the impact of batch learning can be measured proportional to the regret of online behavior. Primarily, we study two settings of the problem: instance-independent and instance-dependent. While the upper bound is the same for both settings, the worst-case lower bound is more comprehensive in the former case and more accurate in the latter one. Also, we provide a more robust result for the 2-armed bandit problem as an important insight. Finally, we demonstrate the consistency of theoretical results by conducting empirical experiments and reflect on the optimal batch size choice.

Deployment efficiency is an important criterion for many real-world applications of reinforcement learning (RL). Despite the community's increasing interest, there lacks a formal theoretical formulation for the problem. In this paper, we propose such a formulation for deployment-efficient RL (DE-RL) from an "optimization with constraints" perspective: we are interested in exploring an MDP and obtaining a near-optimal policy within minimal \emph{deployment complexity}, whereas in each deployment the policy can sample a large batch of data. Using finite-horizon linear MDPs as a concrete structural model, we reveal the fundamental limit in achieving deployment efficiency by establishing information-theoretic lower bounds, and provide algorithms that achieve the optimal deployment efficiency. Moreover, our formulation for DE-RL is flexible and can serve as a building block for other practically relevant settings; we give "Safe DE-RL" and "Sample-Efficient DE-RL" as two examples, which may be worth future investigation.

We consider the problem of combining and learning over a set of adversarial bandit algorithms with the goal of adaptively tracking the best one on the fly. The CORRAL algorithm of Agarwal et al. (2017) and its variants (Foster et al., 2020a) achieve this goal with a regret overhead of order $\widetilde{O}(\sqrt{MT})$ where $M$ is the number of base algorithms and $T$ is the time horizon. The polynomial dependence on $M$, however, prevents one from applying these algorithms to many applications where $M$ is poly$(T)$ or even larger. Motivated by this issue, we propose a new recipe to corral a larger band of bandit algorithms whose regret overhead has only \emph{logarithmic} dependence on $M$ as long as some conditions are satisfied. As the main example, we apply our recipe to the problem of adversarial linear bandits over a $d$-dimensional $\ell_p$ unit-ball for $p \in (1,2]$. By corralling a large set of $T$ base algorithms, each starting at a different time step, our final algorithm achieves the first optimal switching regret $\widetilde{O}(\sqrt{d S T})$ when competing against a sequence of comparators with $S$ switches (for some known $S$). We further extend our results to linear bandits over a smooth and strongly convex domain as well as unconstrained linear bandits.

We consider the problem of adversarial bandit convex optimization, that is, online learning over a sequence of arbitrary convex loss functions with only one function evaluation for each of them. While all previous works assume known and homogeneous curvature on these loss functions, we study a heterogeneous setting where each function has its own curvature that is only revealed after the learner makes a decision. We develop an efficient algorithm that is able to adapt to the curvature on the fly. Specifically, our algorithm not only recovers or \emph{even improves} existing results for several homogeneous settings, but also leads to surprising results for some heterogeneous settings -- for example, while Hazan and Levy (2014) showed that $\widetilde{O}(d^{3/2}\sqrt{T})$ regret is achievable for a sequence of $T$ smooth and strongly convex $d$-dimensional functions, our algorithm reveals that the same is achievable even if $T^{3/4}$ of them are not strongly convex, and sometimes even if a constant fraction of them are not strongly convex. Our approach is inspired by the framework of Bartlett et al. (2007) who studied a similar heterogeneous setting but with stronger gradient feedback. Extending their framework to the bandit feedback setting requires novel ideas such as lifting the feasible domain and using a logarithmically homogeneous self-concordant barrier regularizer.

We introduce and study the online Bayesian recommendation problem for a platform, who can observe a utility-relevant state of a product, repeatedly interacting with a population of myopic users through an online recommendation mechanism. This paradigm is common in a wide range of scenarios in the current Internet economy. For each user with her own private preference and belief, the platform commits to a recommendation strategy to utilize his information advantage on the product state to persuade the self-interested user to follow the recommendation. The platform does not know user's preferences and beliefs, and has to use an adaptive recommendation strategy to persuade with gradually learning user's preferences and beliefs in the process. We aim to design online learning policies with no Stackelberg regret for the platform, i.e., against the optimum policy in hindsight under the assumption that users will correspondingly adapt their behaviors to the benchmark policy. Our first result is an online policy that achieves double logarithm regret dependence on the number of rounds. We then present a hardness result showing that no adaptive online policy can achieve regret with better dependency on the number of rounds. Finally, by formulating the platform's problem as optimizing a linear program with membership oracle access, we present our second online policy that achieves regret with polynomial dependence on the number of states but logarithm dependence on the number of rounds.

Differential privacy (DP) has been recently introduced to linear contextual bandits to formally address the privacy concerns in its associated personalized services to participating users (e.g., recommendations). Prior work largely focus on two trust models of DP: the central model, where a central server is responsible for protecting users sensitive data, and the (stronger) local model, where information needs to be protected directly on user side. However, there remains a fundamental gap in the utility achieved by learning algorithms under these two privacy models, e.g., $\tilde{O}(\sqrt{T})$ regret in the central model as compared to $\tilde{O}(T^{3/4})$ regret in the local model, if all users are unique within a learning horizon $T$. In this work, we aim to achieve a stronger model of trust than the central model, while suffering a smaller regret than the local model by considering recently popular shuffle model of privacy. We propose a general algorithmic framework for linear contextual bandits under the shuffle trust model, where there exists a trusted shuffler in between users and the central server, that randomly permutes a batch of users data before sending those to the server. We then instantiate this framework with two specific shuffle protocols: one relying on privacy amplification of local mechanisms, and another incorporating a protocol for summing vectors and matrices of bounded norms. We prove that both these instantiations lead to regret guarantees that significantly improve on that of the local model, and can potentially be of the order $\tilde{O}(T^{3/5})$ if all users are unique. We also verify this regret behavior with simulations on synthetic data. Finally, under the practical scenario of non-unique users, we show that the regret of our shuffle private algorithm scale as $\tilde{O}(T^{2/3})$, which matches that the central model could achieve in this case.

Contextual multi-armed bandit (MAB) achieves cutting-edge performance on a variety of problems. When it comes to real-world scenarios such as recommendation system and online advertising, however, it is essential to consider the resource consumption of exploration. In practice, there is typically non-zero cost associated with executing a recommendation (arm) in the environment, and hence, the policy should be learned with a fixed exploration cost constraint. It is challenging to learn a global optimal policy directly, since it is a NP-hard problem and significantly complicates the exploration and exploitation trade-off of bandit algorithms. Existing approaches focus on solving the problems by adopting the greedy policy which estimates the expected rewards and costs and uses a greedy selection based on each arm's expected reward/cost ratio using historical observation until the exploration resource is exhausted. However, existing methods are hard to extend to infinite time horizon, since the learning process will be terminated when there is no more resource. In this paper, we propose a hierarchical adaptive contextual bandit method (HATCH) to conduct the policy learning of contextual bandits with a budget constraint. HATCH adopts an adaptive method to allocate the exploration resource based on the remaining resource/time and the estimation of reward distribution among different user contexts. In addition, we utilize full of contextual feature information to find the best personalized recommendation. Finally, in order to prove the theoretical guarantee, we present a regret bound analysis and prove that HATCH achieves a regret bound as low as $O(\sqrt{T})$. The experimental results demonstrate the effectiveness and efficiency of the proposed method on both synthetic data sets and the real-world applications.