31 accepted papers
On-policy preference learning algorithms for language model alignment such as online direct policy optimization (DPO) can significantly outperform their offline counterparts. We provide a theoretical explanation for this phenomenon by analyzing how the sampling policy's coverage evolves throughout o…
The best-arm identification (BAI) problem is one of the most fundamental problems in interactive machine learning, which has two flavors: the fixed-budget setting (FB) and the fixed-confidence setting (FC). For $K$-armed bandits with the unique best arm, the optimal sample complexities for both sett…
We study the problem of fixed budget pure exploration in reinforcement learning. The goal is to identify a near-optimal policy, given a fixed budget on the number of interactions with the environment. Unlike the standard PAC setting, we do not require the target error level $\epsilon$ and failure ra…
The best arm identification problem requires identifying the best alternative (i.e., arm) in active experimentation using the smallest number of experiments (i.e., arm pulls), which is crucial for cost-efficient and timely decision-making processes. In the fixed confidence setting, an algorithm must…
We present `GL-LowPopArt`, a novel Catoni-style estimator for generalized low-rank trace regression. Building on `LowPopArt` (Jang et al., 2024), it employs a two-stage approach: nuclear norm regularization followed by matrix Catoni estimation. We establish state-of-the-art estimation error bounds,…
We study the problem of estimating the \emph{value} of the largest mean among $K$ distributions via samples from them (rather than estimating \emph{which} distribution has the largest mean), which arises from various machine learning tasks including Q-learning and Monte Carlo Tree Search (MCTS). Whi…
We propose a novel linear bandit algorithm called LinMED (Linear Minimum Empirical Divergence), which is a linear extension of the MED algorithm that was originally designed for multi-armed bandits. LinMED is a randomized algorithm that admits a closed-form computation of the arm sampling probabilit…
We present a unified likelihood ratio-based confidence sequence (CS) for *any* (self-concordant) generalized linear model (GLM) that is guaranteed to be convex and numerically tight. We show that this is on par or improves upon known CSs for various GLMs, including Gaussian, Bernoulli, and Poisson.…
This paper introduces the confounded pure exploration transductive linear bandit (CPET-LB) problem. As a motivating example, often online services cannot directly assign users to specific control or treatment experiences either for business or practical reasons. In these settings, naively comparin…
We study low-rank matrix trace regression and the related problem of low-rank matrix bandits. Assuming access to the distribution of the covariates, we propose a novel low-rank matrix estimation method called *LowPopArt* and provide its recovery guarantee that depends on a novel quantity denoted by…
Logistic bandit is a ubiquitous framework of modeling users’ choices, e.g., click vs. no click for advertisement recommender system. We observe that the prior works overlook or neglect dependencies in $S \geq \Vert \theta_\star \Vert_2$, where $\theta_\star \in \mathbb{R}^d$ is the unknown parameter…
Adapting to a priori unknown noise level is a very important but challenging problem in sequential decision-making as efficient exploration typically requires knowledge of the noise level, which is often loosely specified. We report significant progress in addressing this issue in linear bandits in…
We study $K$-armed bandit problems where the reward distributions of the arms are all supported on the $[0,1]$ interval. Maillard sampling\cite{maillard13apprentissage}, an attractive alternative to Thompson sampling, has recently been shown to achieve competitive regret guarantees in the sub-Gaussi…
Simple regret is a natural and parameter-free performance criterion for pure exploration in multi-armed bandits yet is less popular than the probability of missing the best arm or an $\epsilon$-good arm, perhaps due to lack of easy ways to characterize it. In this paper, we make a significant progre…
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 that can at worst scale exponentially with the norm of the unknown parameter vector. Previous works ha…
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 et al. (2021) where they obtain a variance-adaptive regre…
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 exponentially large factors. Such algorithms are however striki…
The PhD thesis of Maillard (2013) presents a rather obscure algorithm for the $K$-armed bandit problem. This less-known algorithm, which we call Maillard sampling (MS), computes the probability of choosing each arm in a closed form, which is not true for Thompson sampling, a widely-adopted bandit al…
Linear bandits have a wide variety of applications including recommendation systems yet they make one strong assumption: the algorithms must know an upper bound $S$ on the norm of the unknown parameter $\theta^*$ that governs the reward generation. Such an assumption forces the practitioner to guess…
In sparse linear bandits, a learning agent sequentially selects an action from a fixed action set and receives 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 sequential decision making problems…
We propose improved fixed-design confidence bounds for the linear logistic model. Our bounds significantly improve upon the state-of-the-art bound by Li et al. (2017) via recent developments of the self-concordant analysis of the logistic loss (Faury et al., 2020). Specifically, our confidence bound…
We consider the bilinear bandit problem where the learner chooses a pair of arms, each from two different action spaces of dimension $d_1$ and $d_2$, respectively. The learner then receives a reward whose expectation is a bilinear function of the two chosen arms with an unknown matrix parameter $\Th…
We study stochastic structured bandits for minimizing regret. The fact that the popular optimistic algorithms do not achieve the asymptotic instance-dependent regret optimality (asymptotic optimality for short) has recently alluded researchers. On the other hand, it is known that one can achieve b…
We introduce the bilinear bandit problem with low-rank structure in which an action takes the form of a pair of arms from two different entity types, and the reward is a bilinear function of the known feature vectors of the arms. The unknown in the problem is a $d_1$ by $d_2$ matrix $\mathbf{\Theta}…
In this paper we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a long-standing gap between upper and lower bounds. Moreover,…
We study adversarial attacks that manipulate the reward signals to control the actions chosen by a stochastic multi-armed bandit algorithm. We propose the first attack against two popular bandit algorithms: $\epsilon$-greedy and UCB, \emph{without} knowledge of the mean rewards. The attacker is ab…
This paper describes a new parameter-free online learning algorithm for changing environments. In comparing against algorithms with the same time complexity as ours, we obtain a strongly adaptive regret bound that is a factor of at least $\sqrt\log(T)$ better, where $T$ is the time horizon. Empiri…
Generalized Linear Bandits (GLBs), a natural extension of the stochastic linear bandits, has been popular and successful in recent years. However, existing GLBs scale poorly with the number of rounds and the number of arms, limiting their utility in practice. This paper proposes new, scalable solu…
We introduce anytime Explore-m, a pure exploration problem for multi-armed bandits (MAB) that requires making a prediction of the top-m arms at every time step. Anytime Explore-m is more practical than fixed budget or fixed confidence formulations of the top-m problem, since many applications involv…
We introduce a new multi-armed bandit (MAB) problem in which arms must be sampled in batches, rather than one at a time. This is motivated by applications in social media monitoring and biological experimentation where such batch constraints naturally arise. This paper develops and analyzes algorith…
Imagine a random walk that outputs a state only when visiting it for the first time. The observed output is therefore a repeat-censored version of the underlying walk, and consists of a permutation of the states or a prefix of it. We call this model initial-visit emitting random walk (INVITE). Prior…