arXiv subjects

Branislav Kveton

Publications and source records attributed to Branislav Kveton.

At least 73 records · Page 4Linked to original sources

arXiv2024

Finite-Time Logarithmic Bayes Regret Upper Bounds

We derive the first finite-time logarithmic Bayes regret upper bounds for Bayesian bandits. In a multi-armed bandit, we obtain $O(c_Δ\log n)$ and $O(c_h \log^2 n)$ upper bounds for an upper confidence bound algorithm, where $c_h$ and $c_Δ$ are constants depending on the prior distribution and the gaps of bandit instances sampled from it, respectively. The latter bound asymptotically matches the lower bound of Lai (1987). Our proofs are a major technical departure from prior works, while being simple and general. To show the generality of our techniques, we apply them to linear bandits. Our results provide insights on the value of prior in the Bayesian setting, both in the objective and as a side information given to the learner. They significantly improve upon existing $\tilde{O}(\sqrt{n})$ bounds, which have become standard in the literature despite the logarithmic lower bound of Lai (1987).

cs.LG↗

arXiv2024

Logic-Scaffolding: Personalized Aspect-Instructed Recommendation Explanation Generation using LLMs

The unique capabilities of Large Language Models (LLMs), such as the natural language text generation ability, position them as strong candidates for providing explanation for recommendations. However, despite the size of the LLM, most existing models struggle to produce zero-shot explanations reliably. To address this issue, we propose a framework called Logic-Scaffolding, that combines the ideas of aspect-based explanation and chain-of-thought prompting to generate explanations through intermediate reasoning steps. In this paper, we share our experience in building the framework and present an interactive demonstration for exploring our results.

cs.AI↗

arXiv2024

Pre-trained Recommender Systems: A Causal Debiasing Perspective

Recent studies on pre-trained vision/language models have demonstrated the practical benefit of a new, promising solution-building paradigm in AI where models can be pre-trained on broad data describing a generic task space and then adapted successfully to solve a wide range of downstream tasks, even when training data is severely limited (e.g., in zero- or few-shot learning scenarios). Inspired by such progress, we investigate in this paper the possibilities and challenges of adapting such a paradigm to the context of recommender systems, which is less investigated from the perspective of pre-trained model. In particular, we propose to develop a generic recommender that captures universal interaction patterns by training on generic user-item interaction data extracted from different domains, which can then be fast adapted to improve few-shot learning performance in unseen new domains (with limited data). However, unlike vision/language data which share strong conformity in the semantic space, universal patterns underlying recommendation data collected across different domains (e.g., different countries or different E-commerce platforms) are often occluded by both in-domain and cross-domain biases implicitly imposed by the cultural differences in their user and item bases, as well as their uses of different e-commerce platforms. As shown in our experiments, such heterogeneous biases in the data tend to hinder the effectiveness of the pre-trained model. To address this challenge, we further introduce and formalize a causal debiasing perspective, which is substantiated via a hierarchical Bayesian deep learning model, named PreRec. Our empirical studies on real-world data show that the proposed model could significantly improve the recommendation performance in zero- and few-shot learning settings under both cross-market and cross-platform scenarios.

cs.IR↗

arXiv2023

Pessimistic Off-Policy Multi-Objective Optimization

Multi-objective optimization is a type of decision making problems where multiple conflicting objectives are optimized. We study offline optimization of multi-objective policies from data collected by an existing policy. We propose a pessimistic estimator for the multi-objective policy values that can be easily plugged into existing formulas for hypervolume computation and optimized. The estimator is based on inverse propensity scores (IPS), and improves upon a naive IPS estimator in both theory and experiments. Our analysis is general, and applies beyond our IPS estimators and methods for optimizing them. The pessimistic estimator can be optimized by policy gradients and performs well in all of our experiments.

cs.LG↗

arXiv2023

Only Pay for What Is Uncertain: Variance-Adaptive Thompson Sampling

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

cs.LG↗

arXiv2023

Perturbed-History Exploration in Stochastic Linear Bandits

We propose a new online algorithm for cumulative regret minimization in a stochastic linear bandit. The algorithm pulls the arm with the highest estimated reward in a linear model trained on its perturbed history. Therefore, we call it perturbed-history exploration in a linear bandit (LinPHE). The perturbed history is a mixture of observed rewards and randomly generated i.i.d. pseudo-rewards. We derive a $\tilde{O}(d \sqrt{n})$ gap-free bound on the $n$-round regret of LinPHE, where $d$ is the number of features. The key steps in our analysis are new concentration and anti-concentration bounds on the weighted sum of Bernoulli random variables. To show the generality of our design, we generalize LinPHE to a logistic model. We evaluate our algorithms empirically and show that they are practical.

cs.LG↗

arXiv2023

Randomized Exploration in Generalized Linear Bandits

We study two randomized algorithms for generalized linear bandits. The first, GLM-TSL, samples a generalized linear model (GLM) from the Laplace approximation to the posterior distribution. The second, GLM-FPL, fits a GLM to a randomly perturbed history of past rewards. We analyze both algorithms and derive $\tilde{O}(d \sqrt{n \log K})$ upper bounds on their $n$-round regret, where $d$ is the number of features and $K$ is the number of arms. The former improves on prior work while the latter is the first for Gaussian noise perturbations in non-linear models. We empirically evaluate both GLM-TSL and GLM-FPL in logistic bandits, and apply GLM-FPL to neural network bandits. Our work showcases the role of randomization, beyond posterior sampling, in exploration.

cs.LG↗

arXiv2023

Fixed-Budget Best-Arm Identification in Structured Bandits

Best-arm identification (BAI) in a fixed-budget setting is a bandit problem where the learning agent maximizes the probability of identifying the optimal (best) arm after a fixed number of observations. Most works on this topic study unstructured problems with a small number of arms, which limits their applicability. We propose a general tractable algorithm that incorporates the structure, by successively eliminating suboptimal arms based on their mean reward estimates from a joint generalization model. We analyze our algorithm in linear and generalized linear models (GLMs), and propose a practical implementation based on a G-optimal design. In linear models, our algorithm has competitive error guarantees to prior works and performs at least as well empirically. In GLMs, this is the first practical algorithm with analysis for fixed-budget BAI.

cs.LG↗

arXiv2023

Meta-Learning for Simple Regret Minimization

We develop a meta-learning framework for simple regret minimization in bandits. In this framework, a learning agent interacts with a sequence of bandit tasks, which are sampled i.i.d.\ from an unknown prior distribution, and learns its meta-parameters to perform better on future tasks. We propose the first Bayesian and frequentist meta-learning algorithms for this setting. The Bayesian algorithm has access to a prior distribution over the meta-parameters and its meta simple regret over $m$ bandit tasks with horizon $n$ is mere $\tilde{O}(m / \sqrt{n})$. On the other hand, the meta simple regret of the frequentist algorithm is $\tilde{O}(\sqrt{m} n + m/ \sqrt{n})$. While its regret is worse, the frequentist algorithm is more general because it does not need a prior distribution over the meta-parameters. It can also be analyzed in more settings. We instantiate our algorithms for several classes of bandit problems. Our algorithms are general and we complement our theory by evaluating them empirically in several environments.

cs.LG↗

arXiv2023

Bayesian Fixed-Budget Best-Arm Identification

Fixed-budget best-arm identification (BAI) is a bandit problem where the agent maximizes the probability of identifying the optimal arm within a fixed budget of observations. In this work, we study this problem in the Bayesian setting. We propose a Bayesian elimination algorithm and derive an upper bound on its probability of misidentifying the optimal arm. The bound reflects the quality of the prior and is the first distribution-dependent bound in this setting. We prove it using a frequentist-like argument, where we carry the prior through, and then integrate out the bandit instance at the end. We also provide a lower bound on the probability of misidentification in a $2$-armed Bayesian bandit and show that our upper bound (almost) matches it for any budget. Our experiments show that Bayesian elimination is superior to frequentist methods and competitive with the state-of-the-art Bayesian algorithms that have no guarantees in our setting.

cs.LG↗

arXiv2023

Fixed-Budget Best-Arm Identification with Heterogeneous Reward Variances

We study the problem of best-arm identification (BAI) in the fixed-budget setting with heterogeneous reward variances. We propose two variance-adaptive BAI algorithms for this setting: SHVar for known reward variances and SHAdaVar for unknown reward variances. Our algorithms rely on non-uniform budget allocations among the arms where the arms with higher reward variances are pulled more often than those with lower variances. The main algorithmic novelty is in the design of SHAdaVar, which allocates budget greedily based on overestimating the unknown reward variances. We bound probabilities of misidentifying the best arms in both SHVar and SHAdaVar. Our analyses rely on novel lower bounds on the number of pulls of an arm that do not require closed-form solutions to the budget allocation problem. Since one of our budget allocation problems is analogous to the optimal experiment design with unknown variances, we believe that our results are of a broad interest. Our experiments validate our theory, and show that SHVar and SHAdaVar outperform algorithms from prior works with analytical guarantees.

cs.LG↗

arXiv2023

Mixed-Effect Thompson Sampling

A contextual bandit is a popular framework for online learning to act under uncertainty. In practice, the number of actions is huge and their expected rewards are correlated. In this work, we introduce a general framework for capturing such correlations through a mixed-effect model where actions are related through multiple shared effect parameters. To explore efficiently using this structure, we propose Mixed-Effect Thompson Sampling (meTS) and bound its Bayes regret. The regret bound has two terms, one for learning the action parameters and the other for learning the shared effect parameters. The terms reflect the structure of our model and the quality of priors. Our theoretical findings are validated empirically using both synthetic and real-world problems. We also propose numerous extensions of practical interest. While they do not come with guarantees, they perform well empirically and show the generality of the proposed framework.

cs.LG↗

arXiv2023

Multiplier Bootstrap-based Exploration

Despite the great interest in the bandit problem, designing efficient algorithms for complex models remains challenging, as there is typically no analytical way to quantify uncertainty. In this paper, we propose Multiplier Bootstrap-based Exploration (MBE), a novel exploration strategy that is applicable to any reward model amenable to weighted loss minimization. We prove both instance-dependent and instance-independent rate-optimal regret bounds for MBE in sub-Gaussian multi-armed bandits. With extensive simulation and real data experiments, we show the generality and adaptivity of MBE.

cs.LG↗

arXiv2023

Thompson Sampling with Diffusion Generative Prior

In this work, we initiate the idea of using denoising diffusion models to learn priors for online decision making problems. Our special focus is on the meta-learning for bandit framework, with the goal of learning a strategy that performs well across bandit tasks of a same class. To this end, we train a diffusion model that learns the underlying task distribution and combine Thompson sampling with the learned prior to deal with new tasks at test time. Our posterior sampling algorithm is designed to carefully balance between the learned prior and the noisy observations that come from the learner's interaction with the environment. To capture realistic bandit scenarios, we also propose a novel diffusion model training procedure that trains even from incomplete and/or noisy data, which could be of independent interest. Finally, our extensive experimental evaluations clearly demonstrate the potential of the proposed approach.

cs.LG↗

arXiv2022

Multi-Task Off-Policy Learning from Bandit Feedback

Many practical applications, such as recommender systems and learning to rank, involve solving multiple similar tasks. One example is learning of recommendation policies for users with similar movie preferences, where the users may still rank the individual movies slightly differently. Such tasks can be organized in a hierarchy, where similar tasks are related through a shared structure. In this work, we formulate this problem as a contextual off-policy optimization in a hierarchical graphical model from logged bandit feedback. To solve the problem, we propose a hierarchical off-policy optimization algorithm (HierOPO), which estimates the parameters of the hierarchical model and then acts pessimistically with respect to them. We instantiate HierOPO in linear Gaussian models, for which we also provide an efficient implementation and analysis. We prove per-task bounds on the suboptimality of the learned policies, which show a clear improvement over not using the hierarchical model. We also evaluate the policies empirically. Our theoretical and empirical results show a clear advantage of using the hierarchy over solving each task independently.

cs.LG↗

arXiv2022

Robust Contextual Linear Bandits

Model misspecification is a major consideration in applications of statistical methods and machine learning. However, it is often neglected in contextual bandits. This paper studies a common form of misspecification, an inter-arm heterogeneity that is not captured by context. To address this issue, we assume that the heterogeneity arises due to arm-specific random variables, which can be learned. We call this setting a robust contextual bandit. The arm-specific variables explain the unknown inter-arm heterogeneity, and we incorporate them in the robust contextual estimator of the mean reward and its uncertainty. We develop two efficient bandit algorithms for our setting: a UCB algorithm called RoLinUCB and a posterior-sampling algorithm called RoLinTS. We analyze both algorithms and bound their $n$-round Bayes regret. Our experiments show that RoLinTS is comparably statistically efficient to the classic methods when the misspecification is low, more robust when the misspecification is high, and significantly more computationally efficient than its naive implementation.

cs.LG↗

arXiv2022

From Ranked Lists to Carousels: A Carousel Click Model

Carousel-based recommendation interfaces allow users to explore recommended items in a structured, efficient, and visually-appealing way. This made them a de-facto standard approach to recommending items to end users in many real-life recommenders. In this work, we try to explain the efficiency of carousel recommenders using a \emph{carousel click model}, a generative model of user interaction with carousel-based recommender interfaces. We study this model both analytically and empirically. Our analytical results show that the user can examine more items in the carousel click model than in a single ranked list, due to the structured way of browsing. These results are supported by a series of experiments, where we integrate the carousel click model with a recommender based on matrix factorization. We show that the combined recommender performs well on held-out test data, and leads to higher engagement with recommendations than a traditional single ranked list.

cs.IR↗

arXiv2022

Safe Data Collection for Offline and Online Policy Learning

Motivated by practical needs of experimentation and policy learning in online platforms, we study the problem of safe data collection. Specifically, our goal is to develop a logging policy that efficiently explores different actions to elicit information while achieving competitive reward with a baseline production policy. We first show that a common practice of mixing the production policy with randomized exploration, despite being safe, is sub-optimal in maximizing information gain. Then, we propose a safe optimal logging policy via a novel water-filling technique for the case when no side information about the actions' expected reward is available. We improve upon this design by considering side information and also extend our approaches to the linear contextual model to account for a large number of actions. Along the way, we analyze how our data logging policies impact errors in off(line)-policy learning and empirically validate the benefit of our design by conducting extensive numerical experiments with synthetic and MNIST datasets. To further demonstrate the generality of our approach, we also consider the safe online learning setting. By adaptively applying our techniques, we develop the Safe Phased-Elimination (SafePE) algorithm that can achieve optimal regret bound with only logarithmic number of policy updates.

cs.LG↗