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In online learning, the data is provided in a sequential order, and the goal of the learner is to make online decisions to minimize overall regrets. This note is concerned with continuous-time models and algorithms for several online…
In (online) learning theory the concepts of sparsity, variance and curvature are well-understood and are routinely used to obtain refined regret and generalization bounds. In this paper we further our understanding of these concepts in the…
We consider $K$-armed stochastic bandits and consider cumulative regret bounds up to time $T$. We are interested in strategies achieving simultaneously a distribution-free regret bound of optimal order $\sqrt{KT}$ and a…
We study best-of-both-worlds algorithms for bandits with switching cost, recently addressed by Rouyer, Seldin and Cesa-Bianchi, 2021. We introduce a surprisingly simple and effective algorithm that simultaneously achieves minimax optimal…
We investigate multiarmed bandits with delayed feedback, where the delays need neither be identical nor bounded. We first prove that "delayed" Exp3 achieves the $O(\sqrt{(KT + D)\ln K} )$ regret bound conjectured by Cesa-Bianchi et al.…
We study stochastic multi-armed bandits under simultaneous constraints on space and adaptivity: the learner interacts with the environment in $B$ batches and has only $W$ bits of persistent memory. Prior work shows that each constraint…
We consider the adversarial multi-armed bandit problem under delayed feedback. We analyze variants of the Exp3 algorithm that tune their step-size using only information (about the losses and delays) available at the time of the decisions,…
In this paper, we introduce the notion of replicable policies in the context of stochastic bandits, one of the canonical problems in interactive learning. A policy in the bandit environment is called replicable if it pulls, with high…
We study a stochastic budget-allocation problem over $K$ tasks. At each round $t$, the learner chooses an allocation $X_t \in \Delta_K$. Task $k$ succeeds with probability $F_k(X_{t,k})$, where $F_1,\dots,F_K$ are nondecreasing…
This paper investigates regret minimization, statistical inference, and their interplay in high-dimensional online decision-making based on the sparse linear context bandit model. We integrate the $\varepsilon$-greedy bandit algorithm for…
We revisit lower bounds on the regret in the case of multi-armed bandit problems. We obtain non-asymptotic, distribution-dependent bounds and provide straightforward proofs based only on well-known properties of Kullback-Leibler…
An adversarial bandit problem with memory constraints is studied where only the statistics of a subset of arms can be stored. A hierarchical learning policy that requires only a sublinear order of memory space in terms of the number of arms…
The Colonel Blotto game is a renowned resource allocation problem with a long-standing literature in game theory (almost 100 years). However, its scope of application is still restricted by the lack of studies on the incomplete-information…
Motivated by posted price auctions where buyers are grouped in an unknown number of latent types characterized by their private values for the good on sale, we investigate revenue maximization in stochastic dynamic pricing when the…
We consider a sequential assortment selection problem where the user choice is given by a multinomial logit (MNL) choice model whose parameters are unknown. In each period, the learning agent observes a $d$-dimensional contextual…
We study the non-stationary dueling bandits problem with $K$ arms, where the time horizon $T$ consists of $M$ stationary segments, each of which is associated with its own preference matrix. The learner repeatedly selects a pair of arms and…
We consider the problem of learning in single-player and multiplayer multiarmed bandit models. Bandit problems are classes of online learning problems that capture exploration versus exploitation tradeoffs. In a multiarmed bandit model,…
Multiplayer bandits have recently been extensively studied because of their application to cognitive radio networks. While the literature mostly considers synchronous players, radio networks (e.g. for IoT) tend to have asynchronous devices.…
This paper considers no-regret learning for repeated continuous-kernel games with lossy bandit feedback. Since it is difficult to give the explicit model of the utility functions in dynamic environments, the players' action can only be…
We consider best arm identification in the multi-armed bandit problem. Assuming certain continuity conditions of the prior, we characterize the rate of the Bayesian simple regret. Differing from Bayesian regret minimization (Lai, 1987), the…