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We study stochastic logistic bandits with $d$-dimensional action features under the simple-regret objective, where a learner uses $T$ rounds of exploration to output a single final action. The logistic structure is essential here: because…

We consider the multinomial logistic bandit problem in which a learner interacts with an environment by selecting actions to maximize expected rewards based on probabilistic feedback from multiple possible outcomes. In the binary setting,…

Recently, several studies (Zhou et al., 2021a; Zhang et al., 2021b; Kim et al., 2021; Zhou and Gu, 2022) have provided variance-dependent regret bounds for linear contextual bandits, which interpolates the regret for the worst-case regime…

Fast changing states or volatile environments pose a significant challenge to online optimization, which needs to perform rapid adaptation under limited observation. In this paper, we give query and regret optimal bandit algorithms under…

We study the optimal batch-regret tradeoff for batch linear contextual bandits. For any batch number $M$, number of actions $K$, time horizon $T$, and dimension $d$, we provide an algorithm and prove its regret guarantee, which, due to…

We consider the setting of stochastic bandit problems with a continuum of arms. We first point out that the strategies considered so far in the literature only provided theoretical guarantees of the form: given some tuning parameters, the…

In this paper, we study a special bandit setting of online stochastic linear optimization, where only one-bit of information is revealed to the learner at each round. This problem has found many applications including online advertisement…

We consider the maximization of $x^\top \theta$ over $(x,\theta) \in \mathcal{X} \times \Theta$, with $\mathcal{X} \subset \mathbb{R}^d$ convex and $\Theta \subset \mathbb{R}^d$ an ellipsoid. This problem is fundamental in linear bandits,…

We present a new anytime algorithm that achieves near-optimal regret for any instance of finite stochastic partial monitoring. In particular, the new algorithm achieves the minimax regret, within logarithmic factors, for both "easy" and…

We consider minimisation of dynamic regret in non-stationary bandits with a slowly varying property. Namely, we assume that arms' rewards are stochastic and independent over time, but that the absolute difference between the expected…

The Greedy algorithm is the simplest heuristic in sequential decision problem that carelessly takes the locally optimal choice at each round, disregarding any advantages of exploring and/or information gathering. Theoretically, it is known…

We study the contextual continuum bandits problem, where the learner sequentially receives a side information vector and has to choose an action in a convex set, minimizing a function associated with the context. The goal is to minimize all…

Logistic Bandits have recently undergone careful scrutiny by virtue of their combined theoretical and practical relevance. This research effort delivered statistically efficient algorithms, improving the regret of previous strategies by…

Contextual bandits serve as a fundamental model for many sequential decision making tasks. The most popular theoretically justified approaches are based on the optimism principle. While these algorithms can be practical, they are known to…

We propose two linear bandits algorithms with per-step complexity sublinear in the number of arms $K$. The algorithms are designed for applications where the arm set is extremely large and slowly changing. Our key realization is that…

We present improved algorithms with worst-case regret guarantees for the stochastic linear bandit problem. The widely used "optimism in the face of uncertainty" principle reduces a stochastic bandit problem to the construction of a…

We consider the adversarial linear contextual bandit problem, where the loss vectors are selected fully adversarially and the per-round action set (i.e. the context) is drawn from a fixed distribution. Existing methods for this problem…

We study dynamic regret minimization in unconstrained adversarial linear bandit problems. In this setting, a learner must minimize the cumulative loss relative to an arbitrary sequence of comparators…

Stochastic linear bandits are a natural and simple generalisation of finite-armed bandits with numerous practical applications. Current approaches focus on generalising existing techniques for finite-armed bandits, notably the optimism…

In this work we consider the problem of regret minimization for logistic bandits. The main challenge of logistic bandits is reducing the dependence on a potentially large problem dependent constant $\kappa$ that can at worst scale…