arXiv subjects

Branislav Kveton

Publications and source records attributed to Branislav Kveton.

At least 91 records · Page 5Linked to original sources

arXiv2022

Safe Exploration for Efficient Policy Evaluation and Comparison

High-quality data plays a central role in ensuring the accuracy of policy evaluation. This paper initiates the study of efficient and safe data collection for bandit policy evaluation. We formulate the problem and investigate its several representative variants. For each variant, we analyze its statistical properties, derive the corresponding exploration policy, and design an efficient algorithm for computing it. Both theoretical analysis and experiments support the usefulness of the proposed methods.

cs.LG↗

arXiv2022

Uplifting Bandits

We introduce a multi-armed bandit model where the reward is a sum of multiple random variables, and each action only alters the distributions of some of them. After each action, the agent observes the realizations of all the variables. This model is motivated by marketing campaigns and recommender systems, where the variables represent outcomes on individual customers, such as clicks. We propose UCB-style algorithms that estimate the uplifts of the actions over a baseline. We study multiple variants of the problem, including when the baseline and affected variables are unknown, and prove sublinear regret bounds for all of these. We also provide lower bounds that justify the necessity of our modeling assumptions. Experiments on synthetic and real-world datasets show the benefit of methods that estimate the uplifts over policies that do not use this structure.

stat.ML↗

arXiv2022

Thompson Sampling with a Mixture Prior

We study Thompson sampling (TS) in online decision making, where the uncertain environment is sampled from a mixture distribution. This is relevant in multi-task learning, where a learning agent faces different classes of problems. We incorporate this structure in a natural way by initializing TS with a mixture prior, and call the resulting algorithm MixTS. To analyze MixTS, we develop a novel and general proof technique for analyzing the concentration of mixture distributions. We use it to prove Bayes regret bounds for MixTS in both linear bandits and finite-horizon reinforcement learning. Our bounds capture the structure of the prior, depend on the number of mixture components and their widths. We also demonstrate the empirical effectiveness of MixTS in synthetic and real-world experiments.

cs.LG↗

arXiv2022

Random Effect Bandits

This paper studies regret minimization in a multi-armed bandit. It is well known that side information, such as the prior distribution of arm means in Thompson sampling, can improve the statistical efficiency of the bandit algorithm. While the prior is a blessing when correctly specified, it is a curse when misspecified. To address this issue, we introduce the assumption of a random-effect model to bandits. In this model, the mean arm rewards are drawn independently from an unknown distribution, which we estimate. We derive a random-effect estimator of the arm means, analyze its uncertainty, and design a UCB algorithm ReUCB that uses it. We analyze ReUCB and derive an upper bound on its $n$-round Bayes regret, which improves upon not using the random-effect structure. Our experiments show that ReUCB can outperform Thompson sampling, without knowing the prior distribution of arm means.

cs.LG↗

arXiv2022

Hierarchical Bayesian Bandits

Meta-, multi-task, and federated learning can be all viewed as solving similar tasks, drawn from a distribution that reflects task similarities. We provide a unified view of all these problems, as learning to act in a hierarchical Bayesian bandit. We propose and analyze a natural hierarchical Thompson sampling algorithm (HierTS) for this class of problems. Our regret bounds hold for many variants of the problems, including when the tasks are solved sequentially or in parallel; and show that the regret decreases with a more informative prior. Our proofs rely on a novel total variance decomposition that can be applied beyond our models. Our theory is complemented by experiments, which show that the hierarchy helps with knowledge sharing among the tasks. This confirms that hierarchical Bayesian bandits are a universal and statistically-efficient tool for learning to act with similar bandit tasks.

cs.LG↗

arXiv2022

No Regrets for Learning the Prior in Bandits

We propose ${\tt AdaTS}$, a Thompson sampling algorithm that adapts sequentially to bandit tasks that it interacts with. The key idea in ${\tt AdaTS}$ is to adapt to an unknown task prior distribution by maintaining a distribution over its parameters. When solving a bandit task, that uncertainty is marginalized out and properly accounted for. ${\tt AdaTS}$ is a fully-Bayesian algorithm that can be implemented efficiently in several classes of bandit problems. We derive upper bounds on its Bayes regret that quantify the loss due to not knowing the task prior, and show that it is small. Our theory is supported by experiments, where ${\tt AdaTS}$ outperforms prior algorithms and works well even in challenging real-world problems.

cs.LG↗

arXiv2022

Deep Hierarchy in Bandits

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 important to leverage these correlations when learning. We formulate a bandit variant of this problem where the correlations of mean action rewards are represented by a hierarchical Bayesian model with latent variables. Since the hierarchy can have multiple layers, we call it deep. We propose a hierarchical Thompson sampling algorithm (HierTS) for this problem, and show how to implement it efficiently for Gaussian hierarchies. The efficient implementation is possible due to a novel exact hierarchical representation of the posterior, which itself is of independent interest. We use this exact posterior to analyze the Bayes regret of HierTS in Gaussian bandits. Our analysis reflects the structure of the problem, that the regret decreases with the prior width, and also shows that hierarchies reduce the regret by non-constant factors in the number of actions. We confirm these theoretical findings empirically, in both synthetic and real-world experiments.

cs.LG↗

arXiv2022

IMO$^3$: Interactive Multi-Objective Off-Policy Optimization

Most real-world optimization problems have multiple objectives. A system designer needs to find a policy that trades off these objectives to reach a desired operating point. This problem has been studied extensively in the setting of known objective functions. We consider a more practical but challenging setting of unknown objective functions. In industry, this problem is mostly approached with online A/B testing, which is often costly and inefficient. As an alternative, we propose interactive multi-objective off-policy optimization (IMO$^3$). The key idea in our approach is to interact with a system designer using policies evaluated in an off-policy fashion to uncover which policy maximizes her unknown utility function. We theoretically show that IMO$^3$ identifies a near-optimal policy with high probability, depending on the amount of feedback from the designer and training data for off-policy estimation. We demonstrate its effectiveness empirically on multiple multi-objective optimization problems.

cs.LG↗

arXiv2021

Optimal Probing with Statistical Guarantees for Network Monitoring at Scale

Cloud networks are difficult to monitor because they grow rapidly and the budgets for monitoring them are limited. We propose a framework for estimating network metrics, such as latency and packet loss, with guarantees on estimation errors for a fixed monitoring budget. Our proposed algorithms produce a distribution of probes across network paths, which we then monitor; and are based on A- and E-optimal experimental designs in statistics. Unfortunately, these designs are too computationally costly to use at production scale. We propose their scalable and near-optimal approximations based on the Frank-Wolfe algorithm. We validate our approaches in simulation on real network topologies, and also using a production probing system in a real cloud network. We show major gains in reducing the probing budget compared to both production and academic baselines, while maintaining low estimation errors, even with very low probing budgets.

cs.LG↗

arXiv2021

Meta-Thompson Sampling

Efficient exploration in bandits is a fundamental online learning problem. We propose a variant of Thompson sampling that learns to explore better as it interacts with bandit instances drawn from an unknown prior. The algorithm meta-learns the prior and thus we call it MetaTS. We propose several efficient implementations of MetaTS and analyze it in Gaussian bandits. Our analysis shows the benefit of meta-learning and is of a broader interest, because we derive a novel prior-dependent Bayes regret bound for Thompson sampling. Our theory is complemented by empirical evaluation, which shows that MetaTS quickly adapts to the unknown prior.

cs.LG↗

arXiv2021

Non-Stationary Off-Policy Optimization

Off-policy learning is a framework for evaluating and optimizing policies without deploying them, from data collected by another policy. Real-world environments are typically non-stationary and the offline learned policies should adapt to these changes. To address this challenge, we study the novel problem of off-policy optimization in piecewise-stationary contextual bandits. Our proposed solution has two phases. In the offline learning phase, we partition logged data into categorical latent states and learn a near-optimal sub-policy for each state. In the online deployment phase, we adaptively switch between the learned sub-policies based on their performance. This approach is practical and analyzable, and we provide guarantees on both the quality of off-policy optimization and the regret during online deployment. To show the effectiveness of our approach, we compare it to state-of-the-art baselines on both synthetic and real-world datasets. Our approach outperforms methods that act only on observed context.

cs.LG↗

arXiv2021

CORe: Capitalizing On Rewards in Bandit Exploration

We propose a bandit algorithm that explores purely by randomizing its past observations. In particular, the sufficient optimism in the mean reward estimates is achieved by exploiting the variance in the past observed rewards. We name the algorithm Capitalizing On Rewards (CORe). The algorithm is general and can be easily applied to different bandit settings. The main benefit of CORe is that its exploration is fully data-dependent. It does not rely on any external noise and adapts to different problems without parameter tuning. We derive a $\tilde O(d\sqrt{n\log K})$ gap-free bound on the $n$-round regret of CORe in a stochastic linear bandit, where $d$ is the number of features and $K$ is the number of arms. Extensive empirical evaluation on multiple synthetic and real-world problems demonstrates the effectiveness of CORe.

cs.LG↗

arXiv2021

Meta-Learning Bandit Policies by Gradient Ascent

Most bandit policies are designed to either minimize regret in any problem instance, making very few assumptions about the underlying environment, or in a Bayesian sense, assuming a prior distribution over environment parameters. The former are often too conservative in practical settings, while the latter require assumptions that are hard to verify in practice. We study bandit problems that fall between these two extremes, where the learning agent has access to sampled bandit instances from an unknown prior distribution $\mathcal{P}$ and aims to achieve high reward on average over the bandit instances drawn from $\mathcal{P}$. This setting is of a particular importance because it lays foundations for meta-learning of bandit policies and reflects more realistic assumptions in many practical domains. We propose the use of parameterized bandit policies that are differentiable and can be optimized using policy gradients. This provides a broadly applicable framework that is easy to implement. We derive reward gradients that reflect the structure of bandit problems and policies, for both non-contextual and contextual settings, and propose a number of interesting policies that are both differentiable and have low regret. Our algorithmic and theoretical contributions are supported by extensive experiments that show the importance of baseline subtraction, learned biases, and the practicality of our approach on a range problems.

cs.LG↗

arXiv2020

Non-Stationary Latent Bandits

Users of recommender systems often behave in a non-stationary fashion, due to their evolving preferences and tastes over time. In this work, we propose a practical approach for fast personalization to non-stationary users. The key idea is to frame this problem as a latent bandit, where the prototypical models of user behavior are learned offline and the latent state of the user is inferred online from its interactions with the models. We call this problem a non-stationary latent bandit. We propose Thompson sampling algorithms for regret minimization in non-stationary latent bandits, analyze them, and evaluate them on a real-world dataset. The main strength of our approach is that it can be combined with rich offline-learned models, which can be misspecified, and are subsequently fine-tuned online using posterior sampling. In this way, we naturally combine the strengths of offline and online learning.

cs.LG↗

arXiv2020

Influence Diagram Bandits: Variational Thompson Sampling for Structured Bandit Problems

We propose a novel framework for structured bandits, which we call an influence diagram bandit. Our framework captures complex statistical dependencies between actions, latent variables, and observations; and thus unifies and extends many existing models, such as combinatorial semi-bandits, cascading bandits, and low-rank bandits. We develop novel online learning algorithms that learn to act efficiently in our models. The key idea is to track a structured posterior distribution of model parameters, either exactly or approximately. To act, we sample model parameters from their posterior and then use the structure of the influence diagram to find the most optimistic action under the sampled parameters. We empirically evaluate our algorithms in three structured bandit problems, and show that they perform as well as or better than problem-specific state-of-the-art baselines.

cs.LG↗

arXiv2020

Latent Bandits Revisited

A latent bandit problem is one in which the learning agent knows the arm reward distributions conditioned on an unknown discrete latent state. The primary goal of the agent is to identify the latent state, after which it can act optimally. This setting is a natural midpoint between online and offline learning---complex models can be learned offline with the agent identifying latent state online---of practical relevance in, say, recommender systems. In this work, we propose general algorithms for this setting, based on both upper confidence bounds (UCBs) and Thompson sampling. Our methods are contextual and aware of model uncertainty and misspecification. We provide a unified theoretical analysis of our algorithms, which have lower regret than classic bandit policies when the number of latent states is smaller than actions. A comprehensive empirical study showcases the advantages of our approach.

cs.LG↗

arXiv2020

Empirical Bayes Regret Minimization

Most bandit algorithm designs are purely theoretical. Therefore, they have strong regret guarantees, but also are often too conservative in practice. In this work, we pioneer the idea of algorithm design by minimizing the empirical Bayes regret, the average regret over problem instances sampled from a known distribution. We focus on a tractable instance of this problem, the confidence interval and posterior width tuning, and propose an efficient algorithm for solving it. The tuning algorithm is analyzed and evaluated in multi-armed, linear, and generalized linear bandits. We report several-fold reductions in Bayes regret for state-of-the-art bandit algorithms, simply by optimizing over a small sample from a distribution.

cs.LG↗

arXiv2020

Differentiable Bandit Exploration

Exploration policies in Bayesian bandits maximize the average reward over problem instances drawn from some distribution $\mathcal{P}$. In this work, we learn such policies for an unknown distribution $\mathcal{P}$ using samples from $\mathcal{P}$. Our approach is a form of meta-learning and exploits properties of $\mathcal{P}$ without making strong assumptions about its form. To do this, we parameterize our policies in a differentiable way and optimize them by policy gradients, an approach that is general and easy to implement. We derive effective gradient estimators and introduce novel variance reduction techniques. We also analyze and experiment with various bandit policy classes, including neural networks and a novel softmax policy. The latter has regret guarantees and is a natural starting point for our optimization. Our experiments show the versatility of our approach. We also observe that neural network policies can learn implicit biases expressed only through the sampled instances.

cs.LG↗