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We consider the adversarial convex bandit problem and we build the first $\mathrm{poly}(T)$-time algorithm with $\mathrm{poly}(n) \sqrt{T}$-regret for this problem. To do so we introduce three new ideas in the derivative-free optimization…

We study the problem of minimising regret in two-armed bandit problems with Gaussian rewards. Our objective is to use this simple setting to illustrate that strategies based on an exploration phase (up to a stopping time) followed by…

Gaussian process upper confidence bound (GP-UCB) is a theoretically established algorithm for Bayesian optimization (BO), where we assume the objective function $f$ follows a GP. One notable drawback of GP-UCB is that the theoretical…

We consider online convex optimization with a zero-order oracle feedback. In particular, the decision maker does not know the explicit representation of the time-varying cost functions, or their gradients. At each time step, she observes…

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 the problem of contextual bandits where actions are subsets of a ground set and mean rewards are modeled by an unknown monotone submodular function that belongs to a class $\mathcal{F}$. We allow time-varying matroid constraints…

As reinforcement learning algorithms are being applied to increasingly complicated and realistic tasks, it is becoming increasingly difficult to solve such problems within a practical time frame. Hence, we focus on a \textit{satisficing}…

We derive near-optimal per-action regret bounds for sleeping bandits, in which both the sets of available arms and their losses in every round are chosen by an adversary. In a setting with $K$ total arms and at most $A$ available arms in…

In this paper, we consider the problem of stochastic optimization under a bandit feedback model. We generalize the GP-UCB algorithm [Srinivas and al., 2012] to arbitrary kernels and search spaces. To do so, we use a notion of localized…

Online reinforcement learning in infinite-horizon Markov decision processes (MDPs) remains less theoretically and algorithmically developed than its episodic counterpart, with many algorithms suffering from high ``burn-in'' costs and…

We prove a regret lower bound for Gaussian-process bandits on a smooth compact Riemannian manifold $\M$ of dimension $d$ with intrinsic Mat\'ern-$\nu$ kernel ($\nu>d/2$) that exposes how the geometry of the arm space enters the constant.…

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…

The dueling bandit is a learning framework wherein the feedback information in the learning process is restricted to a noisy comparison between a pair of actions. In this research, we address a dueling bandit problem based on a cost…

We consider bandit optimization of a smooth reward function, where the goal is cumulative regret minimization. This problem has been studied for $\alpha$-H\"older continuous (including Lipschitz) functions with $0<\alpha\leq 1$. Our main…

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…

In federated multi-armed bandit problems, maximizing global reward while satisfying minimum privacy requirements to protect clients is the main goal. To formulate such problems, we consider a combinatorial contextual bandit setting with…

We analyze the Bayesian regret of the Gaussian process posterior sampling reinforcement learning (GP-PSRL) algorithm. Posterior sampling is an effective heuristic for decision-making under uncertainty that has been used to develop…

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret…

Designing efficient general-purpose contextual bandit algorithms that work with large -- or even continuous -- action spaces would facilitate application to important scenarios such as information retrieval, recommendation systems, and…

Optimising queries in real-world situations under imperfect conditions is still a problem that has not been fully solved. We consider finding the optimal order in which to execute a given set of selection operators under partial ignorance…