Related papers: Low-Rank Generalized Linear Bandit Problems
We study contextual bandits in the presence of a stage-wise constraint when the constraint must be satisfied both with high probability and in expectation. We start with the linear case where both the reward function and the stage-wise…
We study online learning with bandit feedback (i.e. learner has access to only zeroth-order oracle) where cost/reward functions $\f_t$ admit a "pseudo-1d" structure, i.e. $\f_t(\w) = \loss_t(\pred_t(\w))$ where the output of $\pred_t$ is…
On-line linear optimization on combinatorial action sets (d-dimensional actions) with bandit feedback, is known to have complexity in the order of the dimension of the problem. The exponential weighted strategy achieves the best known…
We consider the thresholding bandit problem, whose goal is to find arms of mean rewards above a given threshold $\theta$, with a fixed budget of $T$ trials. We introduce LSA, a new, simple and anytime algorithm that aims to minimize the…
We study the tail behavior of regret in stochastic multi-armed bandits for algorithms that are asymptotically optimal in expectation. While minimizing expected regret is the classical objective, recent work shows that even such algorithms…
It is well-known that for sparse linear bandits, when ignoring the dependency on sparsity which is much smaller than the ambient dimension, the worst-case minimax regret is $\widetilde{\Theta}\left(\sqrt{dT}\right)$ where $d$ is the ambient…
We study linear contextual bandits in the misspecified setting, where the expected reward function can be approximated by a linear function class up to a bounded misspecification level $\zeta>0$. We propose an algorithm based on a novel…
In this study, we explore a collaborative multi-agent stochastic linear bandit setting involving a network of $N$ agents that communicate locally to minimize their collective regret while keeping their expected cost under a specified…
This paper studies batched bandit learning problems for nondegenerate functions. We introduce an algorithm that solves the batched bandit problem for nondegenerate functions near-optimally. More specifically, we introduce an algorithm,…
We propose a linear contextual bandit algorithm with $O(\sqrt{dT\log T})$ regret bound, where $d$ is the dimension of contexts and $T$ isthe time horizon. Our proposed algorithm is equipped with a novel estimator in which exploration is…
We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory…
We consider the problem of online combinatorial optimization under semi-bandit feedback, where a learner has to repeatedly pick actions from a combinatorial decision set in order to minimize the total losses associated with its decisions.…
We consider a partial-feedback variant of the well-studied online PCA problem where a learner attempts to predict a sequence of $d$-dimensional vectors in terms of a quadratic loss, while only having limited feedback about the environment's…
We consider bandit problems involving a large (possibly infinite) collection of arms, in which the expected reward of each arm is a linear function of an $r$-dimensional random vector $\mathbf{Z} \in \mathbb{R}^r$, where $r \geq 2$. The…
We study adaptive regret bounds in terms of the variation of the losses (the so-called path-length bounds) for both multi-armed bandit and more generally linear bandit. We first show that the seemingly suboptimal path-length bound of (Wei…
We tackle a new emerging problem, which is finding an optimal monopartite matching in a weighted graph. The semi-bandit version, where a full matching is sampled at each iteration, has been addressed by \cite{ADMA}, creating an algorithm…
We study the generalized linear bandit (GLB) problem, a contextual multi-armed bandit framework that extends the classical linear model by incorporating a non-linear link function, thereby modeling a broad class of reward distributions such…
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…
Mean rewards of actions are often correlated. The form of these correlations may be complex and unknown a priori, such as the preferences of a user for recommended products and their categories. To maximize statistical efficiency, it is…
We introduce efficient algorithms which achieve nearly optimal regrets for the problem of stochastic online shortest path routing with end-to-end feedback. The setting is a natural application of the combinatorial stochastic bandits…