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In sparse linear bandits, a learning agent sequentially selects an action and receive reward feedback, and the reward function depends linearly on a few coordinates of the covariates of the actions. This has applications in many real-world…
We consider the problem of stochastic $K$-armed dueling bandit in the contextual setting, where at each round the learner is presented with a context set of $K$ items, each represented by a $d$-dimensional feature vector, and the goal of…
Data that is gathered adaptively --- via bandit algorithms, for example --- exhibits bias. This is true both when gathering simple numeric valued data --- the empirical means kept track of by stochastic bandit algorithms are biased…
In this paper, we analyze the problem of online convex optimization in different settings, including different feedback types (full-information/semi-bandit/bandit/etc) in either stochastic or non-stochastic setting and different notions of…
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…
Causal knowledge can be used to support decision-making problems. This has been recognized in the causal bandits literature, where a causal (multi-armed) bandit is characterized by a causal graphical model and a target variable. The arms…
Combinatorial multi-armed bandits provide a fundamental online decision-making environment where a decision-maker interacts with an environment across $T$ time steps, each time selecting an action and learning the cost of that action. The…
Real-world applications of reinforcement learning for recommendation and experimentation faces a practical challenge: the relative reward of different bandit arms can evolve over the lifetime of the learning agent. To deal with these…
Past research on interactive decision making problems (bandits, reinforcement learning, etc.) mostly focuses on the minimax regret that measures the algorithm's performance on the hardest instance. However, an ideal algorithm should adapt…
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 consider the setting of iterative learning control, or model-based policy learning in the presence of uncertain, time-varying dynamics. In this setting, we propose a new performance metric, planning regret, which replaces the standard…
We study the benefits of sparsity in nonparametric contextual bandit problems, in which the set of candidate features is countably or uncountably infinite. Our contribution is two-fold. First, using a novel reduction to sequences of…
This thesis considers sequential decision problems, where the loss/reward incurred by selecting an action may not be inferred from observed feedback. A major part of this thesis focuses on the unsupervised sequential selection problem,…
The dueling bandit problem, an essential variation of the traditional multi-armed bandit problem, has become significantly prominent recently due to its broad applications in online advertising, recommendation systems, information…
Existing data-dependent and best-of-both-worlds regret bounds for multi-armed bandits problems have limited adaptivity as they are either data-dependent but not best-of-both-worlds (BOBW), BOBW but not data-dependent or have sub-optimal…
This thesis considers sequential decision problems, where the loss/reward incurred by selecting an action may not be inferred from observed feedback. A major part of this thesis focuses on the unsupervised sequential selection problem,…
A stochastic multi-user multi-armed bandit framework is used to develop algorithms for uncoordinated spectrum access. In contrast to prior work, it is assumed that rewards can be non-zero even under collisions, thus allowing for the number…
Bandit algorithms sequentially accumulate data using adaptive sampling policies, offering flexibility for real-world applications. However, excessive sampling can be costly, motivating the devolopment of early stopping methods and reliable…
This paper addresses the problem of learning to sparsify stochastic linear bandits, where a decision-maker sequentially selects actions from a high-dimensional space subject to a sparsity constraint on the number of nonzero elements in the…
In online learning problems, exploiting low variance plays an important role in obtaining tight performance guarantees yet is challenging because variances are often not known a priori. Recently, considerable progress has been made by Zhang…